diff options
| author | Karl Berry <karl@freefriends.org> | 2006-01-09 00:45:48 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2006-01-09 00:45:48 +0000 |
| commit | 5dc602d16c5be2fd035b254ca23484a90aebd6dc (patch) | |
| tree | 72efb15fba318cc2096a8cc6999ed3fa0bff317d /Master/texmf-dist/doc/xmltex | |
| parent | b4fc5f639874db951177ec539299d20908adb654 (diff) | |
doc 5
git-svn-id: svn://tug.org/texlive/trunk@81 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/xmltex')
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/base/englishutf16.xml | bin | 0 -> 194 bytes | |||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/base/russianutf8.xml | 7 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/ChangeLog | 24 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01 | 150 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/README.passivetex | 33 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/index.html | 2771 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/latextei-fo.xml | 647 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/latextei.tex | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/latextei.xml | 972 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml | 388 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/properties.xml | 592 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/test.xml | 280 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/xmltex/passivetex/xsa.xml | 14 |
13 files changed, 5882 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/xmltex/base/englishutf16.xml b/Master/texmf-dist/doc/xmltex/base/englishutf16.xml Binary files differnew file mode 100644 index 00000000000..c51d565faf7 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/base/englishutf16.xml diff --git a/Master/texmf-dist/doc/xmltex/base/russianutf8.xml b/Master/texmf-dist/doc/xmltex/base/russianutf8.xml new file mode 100644 index 00000000000..735c9151641 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/base/russianutf8.xml @@ -0,0 +1,7 @@ +<документ атт="русский" > + <раздел> + <голова>Тест</голова> + Здравствуй Мир! + </раздел> +</документ> + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog b/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog new file mode 100644 index 00000000000..c95d5048a58 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog @@ -0,0 +1,24 @@ +2001-06-19 Sebastian Rahtz <sebastian.rahtz@computing-services.oxford.ac.uk> + + * passivetex.xml: releasing current version with broken tables + +2000-09-24 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk> + + * fotex.xmt: preserve value of "extent" attribute on + page-master-name basis, and use in \@outputpage + +2000-07-27 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk> + + * added break-after to FOEndBlock + * added FOlabel to fo:inline and fo:list-item + +2000-03-21 Sebastian Rahtz <sebastian.rahtz@computing-services.oxford.ac.uk> + + * unicode.sty: changed mmasym to "if loaded", instead of "if exists" + +2000-01-13 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk> + + * mlnames.sty (subsection{Languages}): add + \languageshorthands{none} to all \selectlanguage lines + + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01 b/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01 new file mode 100644 index 00000000000..a6491765fbe --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01 @@ -0,0 +1,150 @@ +1. Facilitating <fo:block span="all"> +FOTEX.XMT +in \XMLelement{fo:block}: detect the span="all" attribute and if so, end +multicol layout before (if present), and resume multicol layout (if there +was one) after. +FOTEX.STY +new user-interface macros for loading nomulticols.sty if present, otherwise +resorting to multicols, if present, otherwise defining a fake multicols +environment. If nomulticols could not be loaded, care is taken that fo:block +span="all" is disabled, otherwise the TeX run will fail. +In \@outputpage, call refreshmulticols, which will possibly refresh the +multicol layout. +NOMULTICOL.STY +new file, same functionality as MULTICOL.STY, but does not use an +environment. With some extra macros to interrupt a multicolumnlayout. It is +now possible to say + +begin multicol layout + start group + *1* + start group + end multicol layout *2* + start group + do something interesting + end group + begin multicol layout *4* + end group + *3* + end group +end multicol layout + +CAVEAT 1: a lot of assignments of nomulticol have been made global, may be +too much. For example, if something is set at point *1*, it should be +restored at point *3*, but if this thing is also set by nomulticol, it will +undergo a global change at point *2* and/or *4*, and hence will not be +restored by TeX's grouping mechanism anymore. +So may be it is needed to carefully discriminate between counts, dimens, +boxes, and macros that are particular to multicol (the should be treated +wholly globally), and the (La)TeX-quantities that are dependent on them, and +they might be set locally. + +CAVEAT 2: care must be taken that nomulticol interacts well with an other +change by me: every time a page is output, a fresh page setup will be +computed, if necessary. After this page setup, the multicol environment must +be refreshed (if it was in force). But refreshing should not occur twice in +a row for the same page. Although it seems that I have succeeded in +preventing this double refreshment, I still wonder why it can occur at the +first place. +2. Facilitating multiple special pages +XSL-FO facilitates the specification of a sequence of special pages before +an unbounded, repeating page sequence starts. +PassiveTeX only allowed one special page, labelled First. I allow for the +definition of a sequence of such pages, labelled Lead<counter>. In \@output +page a counter keeps track of which Lead page should be set up. A page setup +will be done if necessary. +This change interacts with multicol, see previous item. +Note also, that blank pages, caused by explicit page-breaks of number +continuating properties, will be detected as blank pages, and hence react to +the blank-or-not-blank attribute. +3. Implementation of xsl-footnote-separator +A rather crude implementation, by storing the static content of +xsl-footnote-separator in the macro \footnoterule, and adjusting the +\skip\footins too match the height+ depth of the new \footnoterule. +4. Enabling footnotes in tables +Footnotes in tables work. This is done by saving footnotes insides tables +into a tokenlist \BoxedFootnotes, doing the corresponding \insert-s at the +end of the table. + +CAVEAT: this is not reallly a nice implementation: if the table breaks +across pages, the footnotetexts will not appear on the same page as the +footnotemarks. +5. Vertical align in tables +If I work with an explicit line-height, the vertical space allocation for +the first and last row of a table comes out wrong. Also, when there is a +line-break inside a cell, the cell-height comes out too small. Something +gets discarded. I have made some changes to the interlineskip (following the +TeXBook definition of \offinterlineskip), in order to fix this, but I have +not succeeded completely. +6. Inheriting table-cell properties from table-column +According to XSL-FO table-cells my inherit properties from corresponding +table-columns by using +att-x="from-column(att-x)" +PassiveTeX only implements inheritance of column-width and column-number, +without the need to use from-column("column-width"). +I have made only an adhoc improvement: text-align will be inherited from the +column, and it happens automatically, without using from-column(text-align). +I have done this with the Array implementation, used for column-width and +column-number. More properties can added easily. It should not be too +difficult to implement from-column(att-x) for a fixed set of attributes, but +implementing this for all possible attributes is more difficult. +7. vskip vs kern +In the code for typesetting blocks, I have changed some vskips in kern, +because I trust the kern better than te vskip (kerns will not be discarded, +vskips might be, and I am not completely sure about the conditions). +8. Bug in FOBoxedBlock +There is some weird code at the start of \FOBoxedBlock (see comments in +fotex.sty at that point). +I have also added some \relax calls after assignments to be sure that the +text after \fi etc is not gobbled up by the preceding assignment. +9. Percenttests +I have increased the use of percented attribute values. Also, \percenttest +was not always able to see the % character, because it was still unexpanded +when fed to it. I have changed that, so that any percent in the +attributetext is surely expanded to a % with catcode 12 before being fed to +percenttest. +(Mostly % appears as an active char, and by means of a limitied-scope +definition of % to be % with catcode 12, this case will be brought to meet +the assumption). +10. Overline +I have added the overline formatting for inlines, but not nearly as nice as +the underline of ulem.sty. I just needed it in simple cases, so I took the +easy option. +11. Pagenumber filtering +The algorithm to filter page number sequences generated by indexes (a very +nice feature of passivetex, by the way), had a few obvious mistakes. I have +corrected them. +12. Horizontal alignment +There were still some problems with alignment, I made some corrections to +\FOOutputblock in fotex.sty. +See also mlnames.sty, definition of \Q@end +13 Page breaks +In \FONormalBlcok I found that a \penalty -\@M did not generate a page +break, so I changed it to \newpage (a few times). (see also changes in +\FOEndBlockTwo +14 Sub- Superscript +PassiveTeX adjusted the fontsize of sub/superscripts, but this should be +governed by the fo-tree. +So I adjusted \textsub/superscript in fotex.sty +15 Dimensions of the page +Page dimensions now work additive, more according to the XSL-FO spec. +16 attribute="inherit" +Now the inherit mechanism can also be triggered by the explicit value of +"inherit". This was achieved by redefining a macro of xmltex: \XML@attrib@x +(in fotex.xmt) +17. fo:external-graphic +scale-to-fit behaviour modified: scaled to the local container instead of +the page (hsize, vsize instead of linewidth, textheight) +18. fo:leader implemetation improved +The code for fo:leader in xmt has been improved +19. fo-retrieve-marker +Some trivial improvements in the code of fo:retrieve-marker +20. More unicode characters +Added definitions for unicode   and   (em and n squares) in +ucharacters.sty +A. Nested fo:block in fo:table-cell +Something goes wrong with <fo:table-cell><fo:block><fo:block>. +The count \FOinTable records whether we are inside a table. But I think that +it should also record wheter we are immediately below a <fo:table-cell> or +deeper. But I have not found out what to do in the latter case ... + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex b/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex new file mode 100644 index 00000000000..23061d7e5c1 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex @@ -0,0 +1,33 @@ +PassiveTeX + +Sebastian Rahtz, February 10th 2000 + +The files in this directory provide an implementation of XSL +formatting objects. If an XSLT processor is used to write out XSL +objects in serialized XML format, the result can be formatted using +xmltex. In addition, an extended xmltex control file for TEI +documents is provided. + +This package consists of the following files: + +The core xmltex `style' files for XSL FO XML: + + fotex.xmt + fotex.sty + +A test file, containing TEI + MathML markup: + + latextei.xml (original) + latextei-fo.xml (transformed to XSL FO) + +Support for direct formatting of TEI XML with xmltex + + tei.xmt + latextei.tex (wrapper for xmltex of sample file) + +Some support files, shared with Jadetex: + + unicode.sty + ucharacters.sty + mlnames.sty + dummyels.sty diff --git a/Master/texmf-dist/doc/xmltex/passivetex/index.html b/Master/texmf-dist/doc/xmltex/passivetex/index.html new file mode 100644 index 00000000000..367a991547d --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/index.html @@ -0,0 +1,2771 @@ + +<!DOCTYPE html + PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> +<html> + <!--THIS FILE IS GENERATED FROM AN XML MASTER. + DO NOT EDIT--> + <head> + <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> + + <title>PassiveTeX</title> + <link rel="stylesheet" type="text/css" href="http://www.oucs.ox.ac.uk/stylesheets/tei-oucs.css"> + </head> + <body><a name="TOP"></a><table class="header" width="100%"> + <tr> + <td rowspan="3"><a target="_top" href="http://www.ox.ac.uk/"><img border="0" width="78" height="94" src="http://www.oucs.ox.ac.uk/icons/ncrest.gif" alt="Oxford University"></a></td> + <td align="left"> + <h2 class="institution">Oxford University Computing Services</h2> + </td> + </tr> + <tr> + <td align="left"> + <h1 class="maintitle">PassiveTeX</h1> + </td> + </tr> + </table> + <hr> + + + + + + + <h2>Contents</h2> + <ul class="toc"> + <li class="toc">1. <a class="toc" href="#index-div-c16ab3b3b1">Summary</a></li> + <li class="toc">2. <a class="toc" href="#index-div-c16ab3b3b3">How does it work?</a></li> + <li class="toc">3. <a class="toc" href="#index-div-c16ab3b3b5">Installation</a></li> + <ul class="toc"> + <li class="toc">3.1. <a class="toc" href="#index-div-c16ab3b3b5c11">LaTeX package dependencies</a></li> + </ul> + <li class="toc">4. <a class="toc" href="#index-div-c16ab3b3b7">Extensions</a></li> + <li class="toc">5. <a class="toc" href="#index-div-c16ab3b3b9">Notes on conformance to the XSL draft specification of November 2000</a></li> + <ul class="toc"> + <li class="toc">5.1. <a class="toc" href="#index-div-c16ab3b3b9b9">Properties needed for basic conformance</a></li> + <li class="toc">5.2. <a class="toc" href="#index-div-c16ab3b3b9c11">Properties needed for full conformance</a></li> + <li class="toc">5.3. <a class="toc" href="#index-div-c16ab3b3b9c13">Properties needed for extended conformance</a></li> + </ul> + <li class="toc">6. <a class="toc" href="#index-div-c16ab3b3c11">Sample files</a></li> + <li class="toc">7. <a class="toc" href="#index-div-c16ab3b3c13">Concerns and problems</a></li> + <li class="toc">8. <a class="toc" href="#index-div-c16ab3b3c15">Things for LaTeX users to remember</a></li> + <li class="toc">9. <a class="toc" href="#index-div-c16ab3b3c17">Future directions</a></li> + </ul> + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3b1"></a>1. Summary + </h2> + + + <ul> + <li><a name="c16ab3b3b1b3b1"></a> + PassiveTeX is a library of TeX macros which can be used to process an XML + document which results from an XSL transformation to formatting objects. + + </li> + <li><a name="c16ab3b3b1b3b3"></a> + PassiveTeX provides a rapid development environment for experimenting + with XSL FO, using a reliable pre-existing formatter + + </li> + <li><a name="c16ab3b3b1b3b5"></a> + Running PassiveTeX with the pdfTeX variant of TeX generates high-quality + PDF files in a single operation. + + </li> + <li><a name="c16ab3b3b1b3b7"></a> + PassiveTeX shows how TeX can remain the formatter of choice for XML, while + hiding the details of its operation from the user. + + </li> + </ul> + + <p><a name="c16ab3b3b1b5"></a> + Available from <tt><a href="http://users.ox.ac.uk/~rahtz/passivetex/" target="_top">http://users.ox.ac.uk/~rahtz/passivetex/</a></tt>. + The current version is 1.4, 2000/12/11. + + </p> + + </div> + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3b3"></a>2. How does it work? + </h2> + + <p><a name="c16ab3b3b3b2"></a> + PassiveTeX relies heavily on work by David Carlisle + (his namespace-aware XML parser written in + TeX, <tt>xmltex</tt>), and was developed from my + <a href="http://www.tug.org/applications/jadetex/" target="_top">JadeTeX</a> + macros for processing DSSSL via Jade. + + </p> + + <p><a name="c16ab3b3b3b4"></a> + Taking the XML version of the TEI Lite guidelines + (<a href="test/teiu5.xml" target="_top">teiu5.xml</a>, with DTD + <a href="test/teixlite.dtd" target="_top">teixlite.dtd</a>), we apply an XSL stylesheet + (see my page of <a href="http://users.ox.ac.uk/~rahtz/tei" target="_top">TEI style sheets</a>), + and run it through James Clark's XT XSL processor: + <pre> + java com.jclark.xsl.sax.Driver teiu5.xml tei.xsl teiu5.fo +</pre> + (assuming you have <tt>xt.jar</tt>, <tt>xp.jar</tt> and <tt>sax.jar</tt> + on your CLASSPATH ). This creates the new XML file + <a href="test/teiu5.fo" target="_top">teiu5.fo</a>. We now run XMLTeX on this + <pre> + pdfxmltex teiu5.fo +</pre> + which creates <a href="test/teiu5.pdf" target="_top">teiu5.pdf</a>. Voila! + Actually, we need to do + <pre> + pdfxmltex teiu5.fo +</pre> + again, to resolve page-number references in the table of contents. For a comparison + with an HTML rendering of the same document (using XSL again), + see <a href="http://users.ox.ac.uk/~rahtz/tei/teiu5.html" target="_top">teiu5.html</a> + on my TEI page. + </p> + + </div> + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3b5"></a>3. Installation + </h2> + + + <p><a name="c16ab3b3b5b3"></a> + The PassiveTeX macros should be downloaded (as a ZIP file, + <tt><a href="passivetex.zip" target="_top">passivetex.zip</a></tt>), unpacked, and installed in a TeX system (eg in + <tt>texmf/tex/latex/passivetex</tt>) in the normal place where you put + macros. Consult your local documentation or local expert if you do not know + how to install a new package; on a web2c-based system, don't forget to + run <tt>mktexlsr</tt> when you have the files in place, + to update the file lookup table. + + </p> + + <p><a name="c16ab3b3b5b5"></a> + What about that <tt>pdfxmltex</tt> command we saw in the last section? + You don't have it on your system? You need to download + <a href="ftp://ftp.tex.ac.uk/tex-archive/macros/xmltex/base.zip" target="_top">xmltex</a> + (that link gives you a ZIP archive of the system) and install it in the your TeX system. + It too is just a set of TeX macro packages. + Then you can use it on a file called (eg) <tt>teiu5.fo</tt> in one of two ways: + + <ol> + <li><a name="c16ab3b3b5b5b7b1"></a>Build an <tt>xmltex</tt> format file for pdfTeX with + <pre> +pdftex -ini "&pdflatex" pdfxmltex.ini +</pre> + and process your file with + <pre> +pdflatex "&pdfxmltex" teiu5.fo +</pre> + Or, + </li> + <li><a name="c16ab3b3b5b5b7b3"></a> + Make a wrapper file called (eg) <tt>teiu5.tex</tt> looking like this: + <pre> +\def\xmlfile{teiu5.fo} +\input xmltex +</pre> + and run pdfTeX on it as normal with + <pre> +pdflatex teiu5.tex +</pre> + </li> + </ol> + Do not worry, <tt>xmltex</tt> knows how to find the PassiveTeX macros as + it needs them. You will likely need to increase TeX memory + values (in the file <tt>texmf.cnf</tt> if you use a Web2c-based TeX); + I use: + <pre> +main_memory = 2500000 +param_size = 1500 +stack_size = 1500 +hash_extra = 50000 +string_vacancies = 45000 +pool_free = 47500 +nest_size = 500 +save_size = 10000 +pool_size = 500000 +max_strings = 55000 +</pre> + </p> + + <p><a name="c16ab3b3b5b7"></a> + For reference, the PassiveTeX package consists of the following files: + + <ul> + <li><a name="c16ab3b3b5b7b1b1"></a>The core xmltex `style' files for XSL FO XML: + <pre> + fotex.xmt + fotex.sty +</pre> + </li> + <li><a name="c16ab3b3b5b7b1b3"></a> + Support for direct formatting of TEI XML with xmltex + <pre> + tei.xmt + teixml.sty +</pre> + </li> + <li><a name="c16ab3b3b5b7b1b5"></a> + Some support files, shared with JadeTeX: + <pre> + unicode.sty + ucharacters.sty + mlnames.sty + dummyels.sty +</pre> + </li> + </ul> + + </p> + + <p><a name="c16ab3b3b5b9"></a> + NOTE: TeX has a limit + on the length of line it can read, + and some .fo files you generate may cause + TeX to die with an message about increasing buf_size. + If you get that, edit your + <tt>texmf.cnf</tt> file, increase the size of <tt>buf_size</tt> (mine is + 200000), and remake any format files. + + </p> + + <div class="teidiv"> + <h3><a name="index-div-c16ab3b3b5c11"></a>3.1. LaTeX package dependencies + </h3> + + <p><a name="c16ab3b3b5c11b2"></a>This setup assumes you have a decent modern TeX setup. The TeX Live 5 CD-ROM + is what I use, and it is up to date + (see <tt><a href="http://www.tug.org/texlive/" target="_top">http://www.tug.org/texlive/</a></tt>). + + </p> + + <p><a name="c16ab3b3b5c11b4"></a> Here is a + list of the packages loaded in a typical run of + PassiveTeX, with their version numbers where known: + + <div align="center"> + <table rules="all" border="1"> + + <tr> + <td> amsbsy.sty </td> + <td> 1999/11/29 v1.2d</td> + </tr> + + <tr> + <td>amsfonts.sty </td> + <td> 1997/09/17 v2.2e</td> + </tr> + + <tr> + <td> amsgen.sty </td> + <td> 1999/11/30 v2.0</td> + </tr> + + <tr> + <td> amsmath.sty </td> + <td> 2000/03/29 v2.08 AMS math features</td> + </tr> + + <tr> + <td> amsopn.sty </td> + <td> 1999/12/14 v2.01 operator names</td> + </tr> + + <tr> + <td> amssymb.sty </td> + <td> 1996/11/03 v2.2b</td> + </tr> + + <tr> + <td> amstext.sty </td> + <td> 1999/11/15 v2.0</td> + </tr> + + <tr> + <td> array.sty </td> + <td> 1998/05/13 v2.3m Tabular extension package (FMi)</td> + </tr> + + <tr> + <td> article.cls </td> + <td> 1999/09/10 v1.4a Standard LaTeX document class</td> + </tr> + + <tr> + <td> bm.sty </td> + <td> 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi)</td> + </tr> + + <tr> + <td> color.sty </td> + <td> 1999/02/16 v1.0i Standard LaTeX Color (DPC)</td> + </tr> + + <tr> + <td> fontenc.sty </td> + <td> (version not available)</td> + </tr> + + <tr> + <td>graphics.sty </td> + <td> 1999/02/16 v1.0l Standard LaTeX Graphics (DPC,SPQR)</td> + </tr> + + <tr> + <td>graphicx.sty </td> + <td> 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)</td> + </tr> + + <tr> + <td> hpdftex.def </td> + <td> 2000/05/08 v6.70f Hyperref driver for pdfTeX</td> + </tr> + + <tr> + <td>hyperref.sty </td> + <td> 2000/05/08 v6.70f Hypertext links for LaTeX</td> + </tr> + + <tr> + <td> ifthen.sty </td> + <td> 1999/09/10 v1.1b Standard LaTeX ifthen package (DPC)</td> + </tr> + + <tr> + <td> keyval.sty </td> + <td> 1999/03/16 v1.13 key=value parser (DPC)</td> + </tr> + + <tr> + <td>longtable.sty </td> + <td> 1998/05/13 v4.09 Multi-page Table package (DPC)</td> + </tr> + + <tr> + <td>multicol.sty </td> + <td> 1999/10/21 v1.5w multicolumn formatting (FMi)</td> + </tr> + + <tr> + <td> nameref.sty </td> + <td> 2000/05/08 v2.18 Cross-referencing by name of section</td> + </tr> + + <tr> + <td> ot1phv.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 scalable font definitions for OT1/phv.</td> + </tr> + + <tr> + <td> pd1enc.def </td> + <td> 2000/05/08 v6.70f Hyperref: PDFDocEncoding definition (HO)</td> + </tr> + + <tr> + <td> pifont.sty </td> + <td> 2000/01/12 PSNFSS-v8.1 Pi font support (SPQR) </td> + </tr> + + <tr> + <td>rotating.sty </td> + <td> 1997/09/26, v2.13 Rotation package</td> + </tr> + + <tr> + <td> size10.clo </td> + <td> 1999/09/10 v1.4a Standard LaTeX file (size option)</td> + </tr> + + <tr> + <td>stmaryrd.sty </td> + <td> 1994/03/03 St Mary's Road symbol package</td> + </tr> + + <tr> + <td> t1enc.def </td> + <td> 1999/12/08 v1.9x Standard LaTeX file</td> + </tr> + + <tr> + <td> t1phv.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 scalable font definitions for T1/phv.</td> + </tr> + + <tr> + <td> t1ptm.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 font definitions for T1/ptm.</td> + </tr> + + <tr> + <td> t2acmr.fd </td> + <td> 1999/01/07 v1.0 Computer Modern Cyrillic font definitions</td> + </tr> + + <tr> + <td> t2aenc.def </td> + <td> 1999/11/29 v1.0c Cyrillic encoding definition file</td> + </tr> + + <tr> + <td> t3enc.def </td> + <td> (version not available)</td> + </tr> + + <tr> + <td>textcomp.sty </td> + <td> 1999/12/08 v1.9x Standard LaTeX package</td> + </tr> + + <tr> + <td> times.sty </td> + <td> 2000/01/12 PSNFSS-v8.1 Times font as default roman (SPQR) </td> + </tr> + + <tr> + <td> tipa.sty </td> + <td> 1996/06/10 TIPA version 1.0</td> + </tr> + + <tr> + <td> trig.sty </td> + <td> 1999/03/16 v1.09 sin cos tan (DPC)</td> + </tr> + + <tr> + <td> ts1cmr.fd </td> + <td> 1999/05/25 v2.5h Standard LaTeX font definitions</td> + </tr> + + <tr> + <td> ts1enc.def </td> + <td> 1998/06/12 v3.0d (jk/car/fm) Standard LaTeX file</td> + </tr> + + <tr> + <td> ts1ptm.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 font definitions for TS1/ptm.</td> + </tr> + + <tr> + <td> ulem.sty </td> + <td> 1997/04/21</td> + </tr> + + <tr> + <td> umsa.fd </td> + <td> 1995/01/05 v2.2e AMS font definitions</td> + </tr> + + <tr> + <td> umsb.fd </td> + <td> 1995/01/05 v2.2e AMS font definitions</td> + </tr> + + <tr> + <td> upsy.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 font definitions for U/psy.</td> + </tr> + + <tr> + <td> upzd.fd </td> + <td> 2000/01/12 PSNFSS-v8.1 font definitions for U/pzd.</td> + </tr> + + <tr> + <td> url.sty </td> + <td> 1999/03/28 ver 1.5x Verb mode for urls, etc.</td> + </tr> + + <tr> + <td> Ustmry.fd </td> + <td> (version not available)</td> + </tr> + + <tr> + <td> uwasy.fd </td> + <td> 1999/05/13 v1.0iWasy-2 symbol font definitions</td> + </tr> + + <tr> + <td> wasysym.sty </td> + <td> 1999/05/13 v1.0i Wasy-2 symbol support package</td> + </tr> + + </table> + </div> + + </p> + + </div> + + </div> + + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3b7"></a>4. Extensions + </h2> + + + <p><a name="c16ab3b3b7b3"></a> + PassiveTeX interprets MathML natively (elements must use the MathML namespace). + I also support a <tt>bookmark</tt> element in the + <tt>fotex</tt> namespace, used to make PDF bookmarks. Usage is like this: + <pre> +<xsl:template match="div2"> + <xsl:apply-templates select="head"/> + <fotex:bookmark + xmlns:fotex="http://www.tug.org/fotex" + fotex-bookmark-level="2" + fotex-bookmark-label="{@id}"> + <xsl:value-of select="head"/> + </fotex:bookmark> + </fo:block> +</xsl:template> +</pre> + </p> + + </div> + + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3b9"></a>5. Notes on conformance to the XSL draft specification of November 2000 + </h2> + + + + <p><a name="c16ab3b3b9b5"></a> + The following general limitations apply to most of the PassiveTeX + implementation of XSL FO: + + <ol> + <li><a name="c16ab3b3b9b5b1b1"></a>The `px' unit is not recognised + </li> + <li><a name="c16ab3b3b9b5b1b3"></a>Absolute dimensions always work, but proportional ones + are often not recognized + </li> + <li><a name="c16ab3b3b9b5b1b5"></a>The functions allowed in attribute values are usually not + recognized + </li> + <li><a name="c16ab3b3b9b5b1b7"></a>There is no error checking at all, and all properies are + recognized; do not assume that they do anything... + </li> + </ol> + + </p> + + <p><a name="c16ab3b3b9b7"></a> + Most of the formatting objects are implemented more or less; the + following are not implemented at all: + + <ol> + <li><a name="c16ab3b3b9b7b1b1"></a><tt>fo:bidi-override</tt></li> + <li><a name="c16ab3b3b9b7b1b3"></a><tt>fo:color-profile</tt></li> + <li><a name="c16ab3b3b9b7b1b5"></a><tt>fo:declarations</tt></li> + <li><a name="c16ab3b3b9b7b1b7"></a><tt>fo:initial-property-set</tt></li> + <li><a name="c16ab3b3b9b7b1b9"></a><tt>fo:instream-foreign-object</tt></li> + <li><a name="c16ab3b3b9b7b1c11"></a><tt>fo:multi-case</tt></li> + <li><a name="c16ab3b3b9b7b1c13"></a><tt>fo:multi-properties</tt></li> + <li><a name="c16ab3b3b9b7b1c15"></a><tt>fo:multi-property-set</tt></li> + <li><a name="c16ab3b3b9b7b1c17"></a><tt>fo:multi-switch</tt></li> + <li><a name="c16ab3b3b9b7b1c19"></a><tt>fo:multi-toggle</tt></li> + <li><a name="c16ab3b3b9b7b1c21"></a><tt>fo:region-end</tt></li> + <li><a name="c16ab3b3b9b7b1c23"></a><tt>fo:region-start</tt></li> + <li><a name="c16ab3b3b9b7b1c25"></a><tt>fo:table-footer</tt></li> + </ol> + + </p> + + <div class="teidiv"> + <h3><a name="index-div-c16ab3b3b9b9"></a>5.1. Properties needed for basic conformance + </h3> + + <p><a name="c16ab3b3b9b9b2"></a> + + <div align="center"> + <table rules="all" border="1"> + + <tr> + <td>alignment-adjust</td> + <td>auto | percentage | length | inherit</td> + <td>Basic</td> + + <td>2. should be possible </td> + </tr> + + + <tr> + <td>azimuth</td> + <td>angle | [[ left-side | far-left | left | center-left | center | center-right | right | far-right | right-side + ] || behind ] | leftwards | rightwards | inherit + </td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>background-color</td> + <td>color | transparent | inherit</td> + <td>Basic</td> + <td>3. does not really map in TeX </td> + </tr> + + + <tr> + <td>baseline-identifier</td> + <td>baseline | before-edge | text-before-edge | middle | after-edge + | text-after-edge | ideographic | alphabetic | hanging | mathematical + | inherit + </td> + <td>Basic</td> + + <td>3. not at all sure where to start </td> + </tr> + + + <tr> + <td>baseline-shift</td> + <td>baseline | sub | super | percentage | length | inherit</td> + <td>Basic</td> + + <td>1. basically works </td> + </tr> + + + <tr> + <td>block-progression-dimension</td> + <td>auto | length | percentage | length-range | inherit</td> + <td>Basic</td> + + <td>3. do not really understand it </td> + </tr> + + + <tr> + <td>border-after-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-after-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-after-width</td> + <td>border-width | length-conditional | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-before-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-before-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-before-width</td> + <td>border-width | length-conditional | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-bottom-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-bottom-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>1. used in places </td> + </tr> + + + <tr> + <td>border-bottom-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-end-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-end-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-end-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-left-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-left-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-left-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-right-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-right-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-right-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-start-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-start-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-start-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-top-color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>border-top-style</td> + <td>border-style | inherit</td> + <td>Basic</td> + <td>1. used in places </td> + </tr> + + + <tr> + <td>border-top-width</td> + <td>border-width | inherit</td> + <td>Basic</td> + <td>2. works for blocks (non-breaking) </td> + </tr> + + + <tr> + <td>break-after</td> + <td>auto | column | page | even-page | odd-page | inherit</td> + <td>Basic</td> + <td>0. should be working </td> + </tr> + + + <tr> + <td>break-before</td> + <td>auto | column | page | even-page | odd-page | inherit</td> + <td>Basic</td> + <td>0. should be working </td> + </tr> + + + <tr> + <td>character</td> + <td>character</td> + <td>Basic</td> + <td>0. should be working </td> + </tr> + + + <tr> + <td>clip</td> + <td>shape | auto | inherit</td> + <td>Basic</td> + <td>2. theoretically possible </td> + </tr> + + + <tr> + <td>color</td> + <td>color | inherit</td> + <td>Basic</td> + <td>1. more or less complete </td> + </tr> + + + <tr> + <td>column-number</td> + <td>number</td> + <td>Basic</td> + <td>0. OK </td> + </tr> + + + <tr> + <td>column-width</td> + <td>length</td> + <td>Basic</td> + <td>0. OK </td> + </tr> + + + <tr> + <td>content-type</td> + <td>string | auto</td> + <td>Basic</td> + <td>4. N/A, I think </td> + </tr> + + + <tr> + <td>cue-after</td> + <td>uri | none | inherit </td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>cue-before</td> + <td>uri | none | inherit </td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>direction</td> + <td>ltr | rtl | inherit</td> + <td>Basic</td> + <td>3. waiting for extended TeX </td> + </tr> + + + <tr> + <td>display-align</td> + <td>auto | before | center | after | inherit</td> + <td>Basic</td> + + <td>0. working </td> + </tr> + + + <tr> + <td>dominant-baseline</td> + <td>auto | autosense-script | no-change | reset-size | ideographic | alphabetic | hanging | mathematical + | inherit + </td> + <td>Basic</td> + + <td>3. dont know where to begin </td> + </tr> + + + <tr> + <td>elevation</td> + <td>angle | below | level | above | higher | lower | inherit</td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>end-indent</td> + <td>length | inherit</td> + <td>Basic</td> + <td>0. working </td> + </tr> + + + <tr> + <td>flow-name</td> + <td>name</td> + <td>Basic</td> + <td>0. working </td> + </tr> + + + <tr> + <td>font-family</td> + <td>[[ family-name | generic-family ],]* [family-name | generic-family] | inherit</td> + <td>Basic</td> + + <td>1. more or less OK </td> + </tr> + + + <tr> + <td>font-size</td> + <td>absolute-size | relative-size | length | percentage | inherit</td> + <td>Basic</td> + + <td>1. more or less all implemented </td> + </tr> + + + <tr> + <td>font-style</td> + <td>normal | italic | oblique | backslant | inherit</td> + <td>Basic</td> + <td>1. no oblique or backslant </td> + </tr> + + + <tr> + <td>font-variant</td> + <td>normal | small-caps | inherit</td> + <td>Basic</td> + <td>0. done </td> + </tr> + + + <tr> + <td>font-weight</td> + <td>normal | bold | bolder | lighter | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | inherit</td> + <td>Basic</td> + + <td>1. normal and bold only at present, others to follow</td> + </tr> + + + <tr> + <td>format</td> + <td>string</td> + <td>Basic</td> + <td>3. dont want to think about it </td> + </tr> + + + <tr> + <td>grouping-separator</td> + <td>character</td> + <td>Basic</td> + <td>3. dont want to think about it </td> + </tr> + + + <tr> + <td>grouping-size</td> + <td>number</td> + <td>Basic</td> + <td>3. dont want to think about it </td> + </tr> + + + <tr> + <td>height</td> + <td>length | percentage | auto | inherit</td> + <td>Basic</td> + <td>2. should be OK, waiting for a need </td> + </tr> + + + <tr> + <td>id</td> + <td> id</td> + <td>Basic</td> + <td>0. used </td> + </tr> + + + <tr> + <td>initial-page-number</td> + <td>auto | auto-odd | auto-even | number | inherit</td> + <td>Basic</td> + <td>0. done </td> + </tr> + + + <tr> + <td>inline-progression-dimension</td> + <td>auto | length | percentage | length-range | inherit</td> + <td>Basic</td> + + <td>3. have not considered at all </td> + </tr> + + + <tr> + <td>keep-with-next</td> + <td>keep | inherit</td> + <td>Basic</td> + <td>1. done in theory, not working 100%</td> + </tr> + + + <tr> + <td>keep-with-previous</td> + <td>keep | inherit</td> + <td>Basic</td> + <td>1. done in theory, not working 100% </td> + </tr> + + + <tr> + <td>leader-length</td> + <td>length-range | inherit</td> + <td>Basic</td> + <td>2. waiting to do soon </td> + </tr> + + + <tr> + <td>leader-pattern</td> + <td>space | rule | dots | use-content | inherit</td> + <td>Basic</td> + <td>2. waiting to do soon </td> + </tr> + + + <tr> + <td>letter-value</td> + <td>auto | alphabetic | traditional</td> + <td>Basic</td> + <td>3. dont want to think about it </td> + </tr> + + + <tr> + <td>line-height</td> + <td>normal | length | number | percentage | space | inherit</td> + <td>Basic</td> + + <td>1. largely done </td> + </tr> + + + <tr> + <td>line-stacking-strategy</td> + <td>line-height | font-height | max-height | inherit</td> + <td>Basic</td> + <td>3. untouched </td> + </tr> + + + <tr> + <td>margin-bottom</td> + <td>margin-width | inherit</td> + <td>Basic</td> + <td>1. done in places </td> + </tr> + + + <tr> + <td>margin-left</td> + <td>margin-width | inherit</td> + <td>Basic</td> + <td>1. done in places </td> + </tr> + + + <tr> + <td>margin-right</td> + <td>margin-width | inherit</td> + <td>Basic</td> + <td>1. done in places </td> + </tr> + + + <tr> + <td>margin-top</td> + <td>margin-width | inherit</td> + <td>Basic</td> + <td>1. done in places </td> + </tr> + + + <tr> + <td>master-name</td> + <td>name</td> + <td>Basic</td> + <td>0. ok </td> + </tr> + + + <tr> + <td>max-height</td> + <td>length | percentage | none | inherit </td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>max-width</td> + <td>length | percentage | none | inherit</td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>min-height</td> + <td>length | percentage | inherit </td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>min-width</td> + <td>length | percentage | inherit</td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>number-columns-repeated</td> + <td>number</td> + <td>Basic</td> + + <td>2. doable in theory </td> + </tr> + + + <tr> + <td>number-columns-spanned</td> + <td>number</td> + <td>Basic</td> + <td>2. doable in theory </td> + </tr> + + + <tr> + <td>number-rows-spanned</td> + <td>number</td> + <td>Basic</td> + <td>2. doable in theory </td> + </tr> + + + <tr> + <td>orphans</td> + <td>integer | inherit</td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>overflow</td> + <td>visible | hidden | scroll | auto | inherit</td> + <td>Basic</td> + <td>2. theoretically </td> + </tr> + + + <tr> + <td>padding-after</td> + <td>padding-width | length-conditional | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-before</td> + <td>padding-width | length-conditional | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-bottom</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-end</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-left</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-right</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-start</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>padding-top</td> + <td>padding-width | inherit</td> + <td>Basic</td> + <td>1. implemented crudely </td> + </tr> + + + <tr> + <td>page-break-after</td> + <td>auto | always | avoid | left | right | inherit</td> + <td>Basic</td> + <td>1. Mostly implemented </td> + </tr> + + + <tr> + <td>page-break-before</td> + <td>auto | always | avoid | left | right | inherit</td> + <td>Basic</td> + <td>1. Mostly implemented </td> + </tr> + + + <tr> + <td>page-height</td> + <td>auto | indefinite | length | inherit</td> + <td>Basic</td> + <td>1. not all possibilities</td> + </tr> + + + <tr> + <td>page-width</td> + <td>auto | indefinite | length | inherit</td> + <td>Basic</td> + <td>1. not all possibilities</td> + </tr> + + + <tr> + <td>pause-after</td> + <td>time | percentage | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>pause-before</td> + <td>time | percentage | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>pitch</td> + <td>frequency | x-low | low | medium | high | x-high | inherit</td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>pitch-range</td> + <td>number | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>play-during</td> + <td>uri mix? repeat? | auto | none | inherit </td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>precedence</td> + <td>true | false | inherit</td> + <td>Basic</td> + <td>3. do not know where to start </td> + </tr> + + + <tr> + <td>provisional-distance-between-starts</td> + <td>length | inherit</td> + <td>Basic</td> + <td>1. does something, probably wrong </td> + </tr> + + + <tr> + <td>provisional-label-separation</td> + <td>length | inherit</td> + <td>Basic</td> + <td>1. does something, probably wrong </td> + </tr> + + + <tr> + <td>ref-id</td> + <td>idref | inherit</td> + <td>Basic</td> + <td>0. used in pagenumber </td> + </tr> + + + <tr> + <td>reference-orientation</td> + <td> 0 | 90 | 180 | 270 | -90 | -180 | -270 | inherit</td> + <td>Basic</td> + <td>2. doable for most objects </td> + </tr> + + + <tr> + <td>region-name</td> + <td>xsl-region-body | xsl-region-start | xsl-region-end | xsl-region-before | xsl-region-after | xsl-before-float-separator + | xsl-footnote-separator | name + </td> + <td>Basic</td> + + <td>0. done </td> + </tr> + + + <tr> + <td>relative-align</td> + <td>before | baseline | inherit</td> + <td>Basic</td> + + <td>3. have not got to grips with this </td> + </tr> + + + <tr> + <td>richness</td> + <td>number | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>role</td> + <td>string | none | inherit</td> + <td>Basic</td> + <td>4. N/A what should I do with it?</td> + </tr> + + + <tr> + <td>rule-style</td> + <td>none | dotted | dashed | solid | double | groove | ridge | inherit</td> + <td>Basic</td> + + <td>1. done as far as possible </td> + </tr> + + + <tr> + <td>rule-thickness</td> + <td>length</td> + <td>Basic</td> + <td>0. done </td> + </tr> + + + <tr> + <td>source-document</td> + <td>uri+ | none | inherit</td> + <td>Basic</td> + <td>4. N/A not sure what to do with it</td> + </tr> + + + <tr> + <td>space-after</td> + <td>space | inherit</td> + <td>Basic</td> + <td>1. working more or less </td> + </tr> + + + <tr> + <td>space-before</td> + <td>space | inherit</td> + <td>Basic</td> + <td>1. working more or less </td> + </tr> + + + <tr> + <td>space-end</td> + <td>space | inherit</td> + <td>Basic</td> + <td>1. working more or less </td> + </tr> + + + <tr> + <td>space-start</td> + <td>space | inherit</td> + <td>Basic</td> + <td>1. working more or less </td> + </tr> + + + <tr> + <td>speak</td> + <td>normal | none | spell-out | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>speak-header</td> + <td>once | always | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>speak-numeral</td> + <td>digits | continuous | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>speak-punctuation</td> + <td>code | none | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>speech-rate</td> + <td>number | x-slow | slow | medium | fast | x-fast | faster | slower | inherit</td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>src</td> + <td> uri | inherit</td> + <td>Basic</td> + <td>0. implemented </td> + </tr> + + + <tr> + <td>start-indent</td> + <td>length | inherit</td> + <td>Basic</td> + <td>0. done </td> + </tr> + + + <tr> + <td>stress</td> + <td>number | inherit</td> + <td>Basic</td> + <td>4. N/A </td> + </tr> + + + <tr> + <td>text-align</td> + <td>start | center | end | justify | inside | outside | left | right | string | inherit</td> + <td>Basic</td> + + <td>0. done </td> + </tr> + + + <tr> + <td>text-indent</td> + <td>length | percentage | inherit</td> + <td>Basic</td> + <td>0. done </td> + </tr> + + + <tr> + <td>visibility</td> + <td>visible | hidden | collapse | inherit</td> + <td>Basic</td> + <td>2. I think can do this </td> + </tr> + + + <tr> + <td>voice-family</td> + <td>[[specific-voice | generic-voice ],]* [specific-voice | generic-voice ] | inherit</td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>volume</td> + <td>number | percentage | silent | x-soft | soft | medium | loud | x-loud | inherit</td> + <td>Basic</td> + + <td>4. N/A </td> + </tr> + + + <tr> + <td>widows</td> + <td>integer | inherit</td> + <td>Basic</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>width</td> + <td>length | percentage | auto | inherit</td> + <td>Basic</td> + <td>2. should be OK, waiting for a need </td> + </tr> + + + <tr> + <td>wrap-option</td> + <td>no-wrap | wrap | inherit</td> + <td>Basic</td> + <td>0. should be working </td> + </tr> + + + <tr> + <td>writing-mode</td> + <td>lr-tb | rl-tb | tb-rl | lr | rl | tb | inherit</td> + <td>Basic</td> + <td>3. will need an extended TeX </td> + </tr> + + + <tr> + <td>z-index</td> + <td>auto | integer | inherit</td> + <td>Basic</td> + <td>3. dont know where to start </td> + </tr> + + </table> + </div> + + </p> + + </div> + + + + <div class="teidiv"> + <h3><a name="index-div-c16ab3b3b9c11"></a>5.2. Properties needed for full conformance + </h3> + + <p><a name="c16ab3b3b9c11b2"></a> + + <div align="center"> + <table rules="all" border="1"> + + <tr> + <td>absolute-position</td> + <td>auto | absolute | fixed | inherit</td> + <td>Complete</td> + <td>2. should be doable </td> + </tr> + + + <tr> + <td>background</td> + <td>[background-color || background-image + || background-repeat || background-attachment || background-position + | ]]inherit + </td> + <td>Complete</td> + + <td>1. implemented but very fragile </td> + </tr> + + + <tr> + <td>background-position</td> + <td>[ [percentage | length ]{1,2} | [ [top | center | bottom] || [left | center | right] ] ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border</td> + <td>[ border-width || border-style || color ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border-bottom</td> + <td>[ border-top-width || border-style || color ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border-color</td> + <td>color{1,4} | transparent | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>border-left</td> + <td>[ border-top-width || border-style || color ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border-right</td> + <td>[ border-top-width || border-style || color ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border-spacing</td> + <td>length length? | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>border-style</td> + <td>border-style{1,4} | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>border-top</td> + <td>[ border-top-width || border-style || color ] | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>border-width</td> + <td>border-width{1,4} | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>caption-side</td> + <td>before | after | start | end | top | bottom | left | right | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>cue</td> + <td>cue-before || cue-after | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>font</td> + <td>[ [ font-style || font-variant || font-weight ]? font-size [ / line-height]? font-family + ] | caption | icon | menu | message-box | small-caption | status-bar + | inherit + </td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>margin</td> + <td>margin-width{1,4} | inherit </td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>padding</td> + <td>padding-width{1,4} | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>page-break-inside</td> + <td>avoid | auto | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>pause</td> + <td>[time | percentage]{1,2} | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>position</td> + <td>static | relative | absolute | fixed | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>size</td> + <td>length{1,2} | auto | landscape | portrait | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>vertical-align</td> + <td>baseline | middle | sub | super | text-top | text-bottom | percentage | length | top | bottom | inherit</td> + <td>Complete</td> + + <td> </td> + </tr> + + + <tr> + <td>white-space</td> + <td>normal | pre | nowrap | inherit</td> + <td>Complete</td> + <td> </td> + </tr> + + + <tr> + <td>xml:lang</td> + <td>country-language | inherit</td> + <td>Complete</td> + <td>2. not done yet, but will be </td> + </tr> + + </table> + </div> + + </p> + + </div> + + + <div class="teidiv"> + <h3><a name="index-div-c16ab3b3b9c13"></a>5.3. Properties needed for extended conformance + </h3> + + <p><a name="c16ab3b3b9c13b2"></a> + + <div align="center"> + <table rules="all" border="1"> + + <tr> + <td>table-layout</td> + <td>auto | fixed | inherit</td> + <td>Extended.Fallback: fixed</td> + <td> </td> + </tr> + + + <tr> + <td>background-attachment</td> + <td>scroll | fixed | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. I can see where I might start </td> + </tr> + + + <tr> + <td>background-image</td> + <td>uri | none | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. I can see where I might start </td> + </tr> + + + <tr> + <td>background-position-horizontal</td> + <td>percentage | length | left | center | right | inherit</td> + <td>Extended.Fallback: Initial value</td> + + <td>2. I can see where I might start </td> + </tr> + + + <tr> + <td>background-position-vertical</td> + <td>percentage | length | top | center | bottom | inherit</td> + <td>Extended.Fallback: Initial value</td> + + <td>2. I can see where I might start </td> + </tr> + + + <tr> + <td>border-collapse</td> + <td>collapse | separate | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>border-separation</td> + <td>length-bp-ip-direction | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>column-count</td> + <td>number | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. implemented </td> + </tr> + + + <tr> + <td>content-height</td> + <td>auto | length | percentage | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>1. done for graphics </td> + </tr> + + + <tr> + <td>content-width</td> + <td>auto | length | percentage | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>1. done for graphics </td> + </tr> + + + <tr> + <td>country</td> + <td>none | country | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. waiting to find a use for it </td> + </tr> + + + <tr> + <td>empty-cells</td> + <td>show | hide | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>ends-row</td> + <td>yes | no</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>font-height-override-after</td> + <td>use-font-metrics | length | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. need extended TeX </td> + </tr> + + + <tr> + <td>font-height-override-before</td> + <td>use-font-metrics | length | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. need extended TeX </td> + </tr> + + + <tr> + <td>font-size-adjust</td> + <td>number | none | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. doable, I think </td> + </tr> + + + <tr> + <td>font-stretch</td> + <td>normal | wider | narrower | ultra-condensed | extra-condensed | condensed | semi-condensed | semi-expanded | + expanded | extra-expanded | ultra-expanded |inherit + </td> + <td>Extended.Fallback: Initial value</td> + + <td>0. should be OK </td> + </tr> + + + <tr> + <td>glyph-orientation-horizontal</td> + <td>angle | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. need extended TeX </td> + </tr> + + + <tr> + <td>glyph-orientation-vertical</td> + <td>auto | angle | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. need extended TeX </td> + </tr> + + + <tr> + <td>hyphenate</td> + <td>false | true | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. done </td> + </tr> + + + <tr> + <td>keep-together</td> + <td>keep | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>language</td> + <td>none | language | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. done, if underlying TeX system OK </td> + </tr> + + + <tr> + <td>last-line-end-indent</td> + <td>length | percentage | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>leader-alignment</td> + <td>none | reference-area | page | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>leader-pattern-width</td> + <td>use-font-metrics | length | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>letter-spacing</td> + <td>normal | length | space | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. doable in limited circumstances </td> + </tr> + + + <tr> + <td>line-height-shift-adjustment</td> + <td>consider-shifts | disregard-shifts | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>linefeed-treatment</td> + <td>ignore | preserve | treat-as-space | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>2. doable, if tiresome </td> + </tr> + + + <tr> + <td>relative-position</td> + <td>auto | static | relative | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>scaling</td> + <td>uniform | non-uniform | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. ok </td> + </tr> + + + <tr> + <td>scaling-method</td> + <td>auto | integer-pixels | resample-any-method | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>4. N/A, I think </td> + </tr> + + + <tr> + <td>score-spaces</td> + <td>true | false | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. dont think I can do this </td> + </tr> + + + <tr> + <td>space-treatment</td> + <td>ignore | preserve | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. seems to work </td> + </tr> + + + <tr> + <td>span</td> + <td>none | all | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>3. proving hard </td> + </tr> + + + <tr> + <td>starts-row</td> + <td>yes | + no + </td> + <td>Extended.Fallback: Initial value</td> + + <td>0. works</td> + </tr> + + + <tr> + <td>suppress-at-line-break</td> + <td>auto | suppress | retain | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>table-omit-footer-at-break</td> + <td>yes | no</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>table-omit-header-at-break</td> + <td>yes | no</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>text-align-last</td> + <td>relative | start | center | end | justify | inside | outside | left | right | string | inherit</td> + <td>Extended.Fallback: Initial value</td> + + <td>1. works, usually </td> + </tr> + + + <tr> + <td>text-decoration</td> + <td>none | [ [ underline | no-underline] || [ overline | no-overline ] || [ line-through | no-line-through ] || [ blink | no-blink + ] ] + + | inherit + </td> + <td>Extended.Fallback: Initial value</td> + + <td>1. done for some possibilities, not all </td> + </tr> + + + <tr> + <td>text-shadow</td> + <td>none | [color || length length length? ,]* [color || length length length?] | inherit</td> + <td>Extended.Fallback: Initial value</td> + + <td> </td> + </tr> + + + <tr> + <td>text-transform</td> + <td>capitalize | uppercase | lowercase | none | </td> + <td>Extended.Fallback: Initial value</td> + <td>2. doable </td> + </tr> + + + <tr> + <td>treat-as-word-space</td> + <td>auto | yes | no | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>white-space-collapse</td> + <td>false | true | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td>0. Done </td> + </tr> + + + <tr> + <td>word-spacing</td> + <td>normal | length | space | inherit</td> + <td>Extended.Fallback: Initial value</td> + <td> </td> + </tr> + + + <tr> + <td>bottom</td> + <td>length | percentage | auto | inherit</td> + <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td> + <td>2. doable, I think </td> + </tr> + + + <tr> + <td>left</td> + <td>length | percentage | auto | inherit</td> + <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td> + <td>2. doable, I think </td> + </tr> + + + <tr> + <td>right</td> + <td>length | percentage | auto | inherit</td> + <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td> + <td>2. doable, I think </td> + </tr> + + + <tr> + <td>top</td> + <td>length | percentage | auto | inherit</td> + <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td> + <td>2. doable, I think </td> + </tr> + + + <tr> + <td>column-gap</td> + <td>length | percentage | inherit</td> + <td>Extended.Fallback: N/A due to fallback for column-count</td> + <td>1. implemented (not for all value types) </td> + </tr> + + + <tr> + <td>hyphenation-character</td> + <td>character | inherit</td> + <td>Extended.Fallback: N/A due to fallback for hyphenate</td> + <td>3. need to think about how to do this </td> + </tr> + + + <tr> + <td>hyphenation-keep</td> + <td>auto | column | page | inherit</td> + <td>Extended.Fallback: N/A due to fallback for hyphenate</td> + <td>3. not sure how to do this </td> + </tr> + + + <tr> + <td>hyphenation-ladder-count</td> + <td>no-limit | number | inherit</td> + <td>Extended.Fallback: N/A due to fallback for hyphenate</td> + <td>3. I dont see how to do this </td> + </tr> + + + <tr> + <td>hyphenation-push-character-count</td> + <td>number | inherit</td> + <td>Extended.Fallback: N/A due to fallback for hyphenate</td> + <td>2. I think this maps in TeX </td> + </tr> + + + <tr> + <td>hyphenation-remain-character-count</td> + <td>number | inherit</td> + <td>Extended.Fallback: N/A due to fallback for hyphenate</td> + <td>2. I think this maps in TeX </td> + </tr> + + + <tr> + <td>color-profile-name</td> + <td>name | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:color-profile</td> + <td>3. would need a lot of thought </td> + </tr> + + + <tr> + <td>rendering-intent</td> + <td>auto | perceptual | relative-colorimetric | saturation | absolute-colorimetric | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:color-profile</td> + <td>3. not sure how to do this </td> + </tr> + + + <tr> + <td>clear</td> + <td>start | end | left | right | both | none | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:float</td> + <td> </td> + </tr> + + + <tr> + <td>float</td> + <td>before | start | end | left | right | none | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:float</td> + <td> </td> + </tr> + + + <tr> + <td>marker-class-name</td> + <td>name</td> + <td>Extended.Fallback: N/A use fallback for fo:marker</td> + <td> </td> + </tr> + + + <tr> + <td>active-state</td> + <td>link | visited | active | hover | focus</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-properties</td> + <td> </td> + </tr> + + + <tr> + <td>auto-restore</td> + <td>yes | no</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td> + <td> </td> + </tr> + + + <tr> + <td>case-name</td> + <td>name</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td> + <td> </td> + </tr> + + + <tr> + <td>case-title</td> + <td>string</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td> + <td> </td> + </tr> + + + <tr> + <td>starting-state</td> + <td>show | hide</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td> + <td> </td> + </tr> + + + <tr> + <td>switch-to</td> + <td>xsl-preceding | xsl-following | xsl-any | name[ name]*</td> + <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td> + <td> </td> + </tr> + + + <tr> + <td>extent</td> + <td>length | percentage | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:region-before, fo:region-after, fo:region-start, and fo:region-end</td> + <td> </td> + </tr> + + + <tr> + <td>blank-or-not-blank</td> + <td>blank | not-blank | any | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td> + <td>3. dont want to think about it </td> + </tr> + + + <tr> + <td>odd-or-even</td> + <td>odd | even | any | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td> + <td> </td> + </tr> + + + <tr> + <td>page-position</td> + <td>first | last | rest | any | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td> + <td> </td> + </tr> + + + <tr> + <td>maximum-repeats</td> + <td>number | no-limit | inherit</td> + <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-reference and fo:repeatable-page-master-alternatives</td> + <td> </td> + </tr> + + + <tr> + <td>retrieve-boundary</td> + <td>page | page-sequence | document</td> + <td>Extended.Fallback: N/A use fallback for fo:retrieve-marker</td> + <td> </td> + </tr> + + + <tr> + <td>retrieve-class-name</td> + <td>name</td> + <td>Extended.Fallback: + N/A use fallback for fo:retrieve-marker + </td> + <td>1. works usually </td> + </tr> + + + <tr> + <td>retrieve-position</td> + <td>first-starting-within-page | first-including-carryover | last-starting-within-page | last-ending-within-page</td> + <td>Extended.Fallback: N/A use fallback for fo:retrieve-marker</td> + + <td> </td> + </tr> + + + <tr> + <td>destination-placement-offset</td> + <td>length</td> + <td>Extended.Fallback: N/A use fallback for fo:simple-link</td> + <td> </td> + </tr> + + + <tr> + <td>external-destination</td> + <td>uri-reference</td> + <td>Extended.Fallback: + N/A use fallback for fo:simple-link + </td> + <td>0. works ok </td> + </tr> + + + <tr> + <td>indicate-destination</td> + <td>yes | + no + </td> + <td>Extended.Fallback: N/A use fallback for + fo:simple-link + </td> + <td>1. should work </td> + </tr> + + + <tr> + <td>internal-destination</td> + <td>null string | + idref + </td> + <td>Extended.Fallback: N/A use fallback for + fo:simple-link + </td> + <td>0. works </td> + </tr> + + + <tr> + <td>show-destination</td> + <td>replace | new</td> + <td>Extended.Fallback: N/A use fallback for fo:simple-link</td> + <td> </td> + </tr> + + + <tr> + <td>force-page-count</td> + <td>auto | even | odd | end-on-even | end-on-odd | no-force | inherit</td> + <td>Extended.Fallback: no-force</td> + + <td> </td> + </tr> + + + <tr> + <td>background-repeat</td> + <td>repeat | repeat-x | repeat-y | no-repeat | inherit</td> + <td>Extended.Fallback: no-repeat</td> + <td> </td> + </tr> + + + <tr> + <td>script</td> + <td>none | auto | script | inherit</td> + <td>Extended.Fallback: none</td> + <td>4. dont know what to do with it </td> + </tr> + + + <tr> + <td>unicode-bidi</td> + <td>normal | embed | bidi-override | inherit</td> + <td>Extended.Fallback: See prose</td> + <td> </td> + + </tr> + + </table> + </div> + + </p> + + </div> + + + </div> + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3c11"></a>6. Sample files + </h2> + + + <p><a name="c16ab3b3c11b3"></a> + + <ul> + <li><a name="c16ab3b3c11b3b1b1"></a> The TEI Lite description (<a href="test/teiu5.xml" target="_top">teiu5.xml</a>) converted PDF as <a href="test/teiu5.pdf" target="_top">teiu5.pdf</a></li> + <li><a name="c16ab3b3c11b3b1b3"></a> A TEI test file (<a href="test/exercise.xml" target="_top">exercise.xml</a>) + converted to PDF as <a href="test/exercise.pdf" target="_top">exercise.pdf</a></li> + <li><a name="c16ab3b3c11b3b1b5"></a> A physics paper (<a href="test/latextei.xml" target="_top">latextei.xml</a>) containing a fair + amount of MathML markup, originally + translated from LaTeX into XML. + It is used extensively as an example in the + <a href="http://cseng.awl.com/bookpage.taf?ISBN=0-201-43311-7&ptype=0&catid=&navmin=&ctype=author&catpage=&seriesid=" target="_top">LaTeX Web Companion</a>. + Here we see it + converted to <a href="test/latextei.pdf" target="_top">latextei.pdf</a> using + <a href="test/latextei.xsl" target="_top">test/latextei.xsl</a></li> + <li><a name="c16ab3b3c11b3b1b7"></a> James Tauber prepared a simple XSL spec (<a href="test/darkness.xsl" target="_top">darkness.xsl</a>) for Joseph Conrad's + <a href="test/darkness.xml" target="_top"><em>Heart of + Darkness</em></a>, which I ran to PDF as <a href="test/darkness.pdf" target="_top">darkness.pdf</a></li> + </ul> + + </p> + + </div> + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3c13"></a>7. Concerns and problems + </h2> + + + <p><a name="c16ab3b3c13b3"></a> + Some points to bear in mind + + <ol> + <li><a name="c16ab3b3c13b3b1b1"></a> Obviously, the XSL FO spec is still a draft. + And this system is not conforming + precisely to the current draft. + </li> + <li><a name="c16ab3b3c13b3b1b3"></a> This is an experiment system to check whether the + idea works. Expect something more polished eventually. + </li> + <li><a name="c16ab3b3c13b3b1b5"></a> You need a modern TeX setup (like + <a href="http://www.tug.org/teTeX/" target="_top">teTeX</a> or + <a href="http://www.tug.org/texlive/" target="_top">TeX Live</a>) + to get to grips with it. + </li> + <li><a name="c16ab3b3c13b3b1b7"></a> Quite a few flow objects and characteristics are not dealt with yet. + I will add support for more things as needed or requested. + </li> + <li><a name="c16ab3b3c13b3b1b9"></a> I do not have any objective check that what I think XSL FOs are + supposed to do is actually right :-} + </li> + <li><a name="c16ab3b3c13b3b1c11"></a> I have only worked so far with the TEI Lite (XML version) and + Docbook DTDs, and probably misinterpreted half of what they say. + </li> + </ol> + + </p> + + </div> + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3c15"></a>8. Things for LaTeX users to remember + </h2> + + + <p><a name="c16ab3b3c15b3"></a> + + <ul> + <li><a name="c16ab3b3c15b3b1b1"></a> No use is made of LaTeX high-level constructs. No sections, + no lists, no cross-refs, no bibliographies; on the other hand, + some extensions in the <tt>fotex:</tt> namespace are supported + (eg to get Acrobat bookmarks) + + </li> + <li><a name="c16ab3b3c15b3b1b3"></a> XSL FO's underlying character set is Unicode; by default, + entities are mapped to their Unicode position; + + </li> + <li><a name="c16ab3b3c15b3b1b5"></a> All vertical and horizontal space is explicit in the + specification + + </li> + <li><a name="c16ab3b3c15b3b1b7"></a> Page and line breaking is left to TeX: the rest is up to you. + + </li> + </ul> + + </p> + + </div> + + + <div class="teidiv"> + <h2><a name="index-div-c16ab3b3c17"></a>9. Future directions + </h2> + + + <p><a name="c16ab3b3c17b3"></a> + + <ul> + <li><a name="c16ab3b3c17b3b1b1"></a>Complete the MathML handling + </li> + <li><a name="c16ab3b3c17b3b1b3"></a>Handle more variety in property values (eg colors, fonts) + </li> + <li><a name="c16ab3b3c17b3b1b5"></a>Deal with more complex tables + </li> + <li><a name="c16ab3b3c17b3b1b7"></a>Support SVG. How? + + <ul> + <li><a name="c16ab3b3c17b3b1b7b1b1"></a>By direct intepretation and mapping to raw PDF + </li> + <li><a name="c16ab3b3c17b3b1b7b1b3"></a>By translation to MetaPost, and spawning a MetaPost process + </li> + <li><a name="c16ab3b3c17b3b1b7b1b5"></a>By pre-processing to existing TeX graphics languages + </li> + </ul> + In any case, SVG fragments need to be recognized directly to perform in-line + graphical functions (setting text at an angle?) + + </li> + <li><a name="c16ab3b3c17b3b1b9"></a>Use Unicode-based TeX variant (Omega) to handle non-Latin material + more naturally + </li> + </ul> + + </p> + + <p><a name="c16ab3b3c17b5"></a> + I will be very glad to discuss details with anyone. Contact me (Sebastian Rahtz) as + <a href="mailto:sebastian.rahtz@oucs.ox.ac.uk" target="_top">sebastian.rahtz@oucs.ox.ac.uk</a> + + </p> + + </div> + + <hr> + <div class="footer"><a target="_top" class="plain" href="http://www.ox.ac.uk/">Oxford University</a> + | <a target="_top" class="plain" href="http://www.oucs.ox.ac.uk/">OUCS</a> + | <a target="_top" class="plain" href="http://wwwsearch.ox.ac.uk/cgi-bin/oxunit?oucs">Search</a> + | <a target="_top" class="plain" href="mailto:feedback@oucs.ox.ac.uk">Feedback</a></div> + <hr> + <address>Date: November 2000 + (revised 2000/12/11) + Author: . + <br><a href="/documentation/copyright.html">©</a> Oxford + University Computing Services. + <!--Generated + using an XSLT version 1 stylesheet + based on http://www.oucs.ox.ac.uk/stylesheets/teihtml.xsl + processed using: + `SAXON 5.5.1 from Michael Kay of ICL' + +--> + </address> + </body> +</html>
\ No newline at end of file diff --git a/Master/texmf-dist/doc/xmltex/passivetex/latextei-fo.xml b/Master/texmf-dist/doc/xmltex/passivetex/latextei-fo.xml new file mode 100644 index 00000000000..bfc33c1f6bb --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/latextei-fo.xml @@ -0,0 +1,647 @@ +<?xml version="1.0" encoding="utf-8"?> +<fo:root xmlns:fo="http://www.w3.org/XSL/Format/1.0" xmlns:fop="http://www.jtauber.com/fop" xmlns:fotex="http://www.tug.org/fotex"><fo:layout-master-set><fo:simple-page-master page-master-name="left" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master><fo:simple-page-master page-master-name="right" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master><fo:simple-page-master page-master-name="first" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master></fo:layout-master-set><fo:page-sequence><fo:static-content flow-name="xsl-after"/><fo:static-content flow-name="xsl-before"/><fo:sequence-specification><fo:sequence-specifier-single page-master="right"/></fo:sequence-specification><fo:flow> + <fo:block font-size="18pt" space-after="8pt" text-align-last="centered"> + Simulation of Energy Loss Straggling + </fo:block> + <fo:block space-after="6pt" font-size="14pt" text-align-last="centered"><fo:inline-sequence font-style="italic">Maria Physicist</fo:inline-sequence></fo:block> + <fo:block space-after="6pt" font-size="16pt" text-align-last="centered">January 17, 1999</fo:block> + </fo:flow></fo:page-sequence><fo:page-sequence initial-page-number="1"><fo:sequence-specification><fo:sequence-specifier-alternating page-master-first="first" page-master-odd="right" page-master-even="left"/></fo:sequence-specification><fo:static-content flow-name="xsl-after" fop:master="right"><fo:block font-size="10pt"><fo:inline-rule rule-thickness="0pt"/><fo:page-number/></fo:block></fo:static-content><fo:static-content flow-name="xsl-after" fop:master="left"><fo:block font-size="10pt"><fo:page-number/><fo:inline-rule rule-thickness="0pt"/></fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="right"><fo:block text-align-last="centered" font-size="10pt"><!--Running Head: title-->Simulation of Energy Loss Straggling</fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="left"><fo:block text-align-last="centered" font-size="10pt"><!--Running Head: author-->Maria Physicist</fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="first"/><fo:static-content flow-name="xsl-after" fop:master="first"><fo:block font-size="10pt"><fo:inline-rule rule-thickness="0pt"/><fo:page-number/><fo:inline-rule rule-thickness="0pt"/></fo:block></fo:static-content><fo:flow font-family="Times Roman" font-size="10pt"> <fo:block keep-with-next="true" id="intro" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">1. Introduction<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="intro">1. Introduction</fotex:bookmark></fo:block> <fo:block font-size="10pt" text-align="justified">Due to +the statistical nature of ionisation energy loss, large fluctuations +can occur in the amount of energy deposited by a particle traversing +an absorber element. Continuous processes such as multiple scattering +and energy loss play a relevant role in the longitudinal and lateral +development of electromagnetic and hadronic showers, and in the case +of sampling calorimeters the measured resolution can be significantly +affected by such fluctuations in their active layers. The description +of ionisation fluctuations is characterised by the significance +parameter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>, which is +proportional to the ratio of mean energy loss to the maximum allowed +energy transfer in a single collision with an atomic electron + <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> <mi>κ</mi><mo>=</mo> +<mfrac> + <mrow><mi>ξ</mi></mrow> + <mrow> + <msub><mi>E</mi><mi>max</mi></msub> + </mrow> +</mfrac> +</mrow> +</fotex:displaymath> +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath> is the +maximum transferable energy in a single collision with an atomic electron. +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> + <msub><mi>E</mi><mi>max</mi></msub><mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>γ</mi><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub><mo>+</mo><msup><mfenced open="(" close=")"><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub> </mfenced><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo> +</mrow></fotex:displaymath> where +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath>, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi></fotex:inlinemath> is energy and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath> the mass of the +incident particle, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mrow><mn>2</mn></mrow></msup></fotex:inlinemath> +and <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>e</mi></mrow></msub></fotex:inlinemath> is the +electron mass. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi></fotex:inlinemath> +comes from the Rutherford scattering crosss section and is defined as: + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>π</mi><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow><mn>4</mn></mrow></msup><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub><mi>Z</mi><mi>ρ</mi><mi>δ</mi><mi>x</mi></mrow><mrow><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>A</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">3</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Z</mi></mrow><mrow><mi>A</mi></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">ρ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi><mspace width="12pt" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">keV </mi><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +where +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N610"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">z</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>charge of the incident particle </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>Avogadro's number </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic number of the material</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">A</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic weight of the material </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ρ</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>density </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>thickness of the material </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence> </fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container> +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> +measures the contribution of the collisions with energy transfer close to +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath>. For a given absorber, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> tends towards large +values if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> is large +and/or if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">β</mi></fotex:inlinemath> is small. +Likewise, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> tends +towards zero if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> is +small and/or if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">β</mi></fotex:inlinemath> +approaches 1. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The value of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> +distinguishes two regimes which occur in the description of ionisation fluctuations +: +</fo:block><fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> +<fo:block font-size="10pt" text-align="justified">A +large +number +of +collisions +involving +the +loss +of +all +or +most +of +the +incident +particle +energy +during +the +traversal +of +an +absorber. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">As +the +total +energy +transfer +is +composed +of +a +multitude +of +small +energy +losses, +we +can +apply +the +central +limit +theorem +and +describe +the +fluctuations +by +a +Gaussian +distribution. +This +case +is +applicable +to +non-relativistic +particles +and +is +described +by +the +inequality +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">></mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> +(i.e. +when +the +mean +energy +loss +in +the +absorber +is +greater +than +the +maximum +energy +transfer +in +a +single +collision). +</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> +<fo:block font-size="10pt" text-align="justified">Particles +traversing +thin +counters +and +incident +electrons +under +any +conditions. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The +relevant +inequalities +and +distributions +are +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML"><</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML"><</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>, +Vavilov +distribution, +and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML"><</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>, +Landau +distribution.</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">An additional regime is defined by the contribution of the collisions +with low energy transfer which can be estimated with the relation +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath>, +where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath> +is the mean ionisation potential of the atom. Landau theory assumes that +the number of these collisions is high, and consequently, it has a restriction +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≫</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>. In <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> (see +URL <fo:inline-sequence font-family="Computer-Modern-Typewriter" color="green"><fo:simple-link external-destination="http://wwwinfo.cern.ch/asdoc/geant/geantall.html">http://wwwinfo.cern.ch/asdoc/geant/geantall.html</fo:simple-link></fo:inline-sequence>), the limit of Landau theory has +been set at <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>. +Below this limit special models taking into account the atomic structure of the material are +used. This is important in thin layers and gaseous materials. Figure <fo:inline-sequence color="green"><fo:simple-link internal-destination="fg:phys332-1">1</fo:simple-link></fo:inline-sequence> shows the behaviour +of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath> as +a function of the layer thickness for an electron of 100 keV and 1 GeV of kinetic +energy in Argon, Silicon and Uranium. +</fo:block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:float id="fg:phys332-1"><fo:block text-align-last="centered"><fo:display-graphic href="phys332-1"/></fo:block><fo:block text-align-last="centered">Figure 1. The variable <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath> +can be used to measure the validity range of the Landau +theory. It depends on the type and energy of the particle, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi></fotex:inlinemath>, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">A</mi></fotex:inlinemath> +and the ionisation potential of the material and the layer thickness. </fo:block></fo:float></fo:block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">In the following sections, the different theories and models for the energy loss +fluctuation are described. First, the Landau theory and its limitations are discussed, +and then, the Vavilov and Gaussian straggling functions and the methods in the thin +layers and gaseous materials are presented. +</fo:block> + +<fo:block keep-with-next="true" id="sec:phys332-1" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">2. Landau theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="sec:phys332-1">2. Landau theory</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">For a particle of mass <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath> traversing +a thickness of material <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath>, +the Landau probability distribution may be written in terms of the universal Landau +function <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></fotex:inlinemath> +as<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-LAND"> [1]</fo:simple-link></fo:inline-sequence>: + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>x</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +where + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo> + <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>ln</mo><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi></mfenced><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi><mspace width="2cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover></mrow><mrow><mi>ξ</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">′</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">′</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">8</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mtext xmlns="http://www.w3.org/1998/Math/MathML">(Eulers constant)</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>ε</mi><mrow/></munderover> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML">average energy loss</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ε</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML">actual energy loss</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +</fo:block> +<fo:block keep-with-next="true" id="N1783" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">2.1. Restrictions<fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N1783">2.1. Restrictions</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">The Landau formalism makes two restrictive assumptions : +</fo:block><fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> +<fo:block font-size="10pt" text-align="justified">The +typical +energy +loss +is +small +compared +to +the +maximum +energy +loss +in +a +single +collision. +This +restriction +is +removed +in +the +Vavilov +theory +(see +section +<fo:inline-sequence color="green"><fo:simple-link internal-destination="vavref">3 (Vavilov theory)</fo:simple-link></fo:inline-sequence>). +</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> +<fo:block font-size="10pt" text-align="justified">The +typical +energy +loss +in +the +absorber +should +be +large +compared +to +the +binding +energy +of +the +most +tightly +bound +electron. +For +gaseous +detectors, +typical +energy +losses +are +a +few +keV +which +is +comparable +to +the +binding +energies +of +the +inner +electrons. +In +such +cases +a +more +sophisticated +approach +which +accounts +for +atomic +energy +levels<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-TALM"> [4]</fo:simple-link></fo:inline-sequence> +is +necessary +to +accurately +simulate +data +distributions. +In +<fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence>, +a +parameterised +model +by +L. +Urbán +is +used +(see +section +<fo:inline-sequence color="green"><fo:simple-link internal-destination="urban">5 (Urbán model)</fo:simple-link></fo:inline-sequence>).</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">In addition, the average value of the Landau distribution is infinite. +Summing the Landau fluctuation obtained to the average energy from the +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> +tables, we obtain a value which is larger than the one coming from the table. The +probability to sample a large value is small, so it takes a large number of steps +(extractions) for the average fluctuation to be significantly larger than zero. This +introduces a dependence of the energy loss on the step size which can affect +calculations. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">A solution to this has been to introduce a limit on the value of the +variable sampled by the Landau distribution in order to keep the average +fluctuation to 0. The value obtained from the <fo:inline-sequence font-family="Computer-Modern-Typewriter">GLANDO</fo:inline-sequence> routine is: +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>δ</mi><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo>=</mo><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover><mo>=</mo><mi>ξ</mi><mrow><mo>(</mo><mi>λ</mi><mo>-</mo><mi>γ</mi><mi>′</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> <mo>)</mo></mrow> +</mrow></fotex:displaymath> +In order for this to have average 0, we must impose that: +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> + <munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>=</mo><mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> +</mrow></fotex:displaymath> +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">This is realised introducing a <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>)</mo></mrow></fotex:inlinemath> +such that if only values of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></fotex:inlinemath> +are accepted, the average value of the distribution is +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>λ</mi><mrow/></munderover></fotex:inlinemath>. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">A parametric fit to the universal Landau distribution has been performed, with following result: +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> + <msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>0</mn><mn>7</mn><mn>1</mn><mn>5</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>1</mn><mn>9</mn><mn>3</mn><mn>4</mn><munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>+</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>7</mn><mn>7</mn><mn>9</mn><mn>4</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>5</mn><mn>2</mn><mn>3</mn><mn>8</mn><mn>2</mn><munderover accent="true"><mi>λ</mi><mrow/><mo>̄</mo></munderover><mo>)</mo></mrow><mo>exp</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>9</mn><mn>4</mn><mn>7</mn><mn>5</mn><mn>3</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mn>4</mn><mn>4</mn><mn>4</mn><mn>2</mn><munderover accent="true"><mi>λ</mi><mrow/><mo>̄</mo></munderover><mo>)</mo></mrow> +</mrow></fotex:displaymath> only values +smaller than <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></fotex:inlinemath> +are accepted, otherwise the distribution is resampled. +</fo:block> + + +<fo:block keep-with-next="true" id="vavref" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">3. Vavilov theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="vavref">3. Vavilov theory</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">Vavilov<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-VAVI"> [5]</fo:simple-link></fo:inline-sequence> derived a more accurate straggling distribution by introducing the kinematic +limit on the maximum transferable energy in a single collision, rather than using +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">∞</mi></fotex:inlinemath>. Now +we can write<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-SCH1"> [2]</fo:simple-link></fo:inline-sequence>: + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi></mrow></mfrac><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +where + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo> + <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mi>λ</mi><mi>s</mi></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">s</mi><mspace width="2cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>γ</mi><mo>)</mo></mrow></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ψ</mi> <mfenced open="(" close=")"><mi>s</mi></mfenced></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ψ</mi> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mi xmlns="http://www.w3.org/1998/Math/MathML">s</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>s</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>κ</mi><mo>)</mo></mrow><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mo>ln</mo><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>E</mi><mrow> +<mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mi>s</mi><mo>/</mo><mi>κ</mi></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +and + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>z</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"> <mo>∫</mo> + <mrow><mi>∞</mi></mrow><mrow><mi>z</mi></mrow></msubsup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mi>t</mi></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">t</mi><mspace width="1cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mtext xmlns="http://www.w3.org/1998/Math/MathML">(the exponential integral)</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover></mrow><mrow><mi>ξ</mi></mrow></mfrac> <mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The Vavilov parameters are simply related to the Landau parameter by +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>. It can be shown that +as <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">→</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>, the distribution of +the variable <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath> approaches +that of Landau. For <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath> +the two distributions are already practically identical. Contrary to what many textbooks +report, the Vavilov distribution <fo:inline-sequence font-style="italic">does not</fo:inline-sequence> approximate the Landau distribution for small +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>, but rather the +distribution of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath> +defined above tends to the distribution of the true +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi></fotex:inlinemath> from +the Landau density function. Thus the routine <fo:inline-sequence font-family="Computer-Modern-Typewriter">GVAVIV</fo:inline-sequence> samples the variable +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath> rather +than <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub></fotex:inlinemath>. +For <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> +the Vavilov distribution tends to a Gaussian distribution (see next section). +</fo:block> + +<fo:block keep-with-next="true" id="N3325" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">4. Gaussian Theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="N3325">4. Gaussian Theory</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">Various conflicting forms have been proposed for Gaussian straggling functions, but most +of these appear to have little theoretical or experimental basis. However, it has been shown<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-SELT"> [3]</fo:simple-link></fo:inline-sequence> +that for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> +the Vavilov distribution can be replaced by a Gaussian of the form: + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">≈</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi><msqrt><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mi>κ</mi></mrow></mfrac> <mfenced open="(" close=")"><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn></mfenced></msqrt></mrow></mfrac><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mrow><mo>(</mo><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac> <mfrac><mrow><mi>κ</mi></mrow><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></mfrac></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +thus implying + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">mean</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>ε</mi><mrow/></munderover> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>κ</mi></mrow></mfrac> <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi> +max</mi></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> +</fotex:subeqn></fotex:eqnarray> +</fo:block> + +<fo:block keep-with-next="true" id="urban" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">5. Urbán model<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="urban">5. Urbán model</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">The method for computing restricted energy losses with +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi></fotex:inlinemath>-ray +production above given threshold energy in <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> is a Monte Carlo method that +can be used for thin layers. It is fast and it can be used for any thickness of a +medium. Approaching the limit of the validity of Landau's theory, the loss +distribution approaches smoothly the Landau form as shown in Figure <fo:inline-sequence color="green"><fo:simple-link internal-destination="fg:phys332-2">2</fo:simple-link></fo:inline-sequence>. +</fo:block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:float id="fg:phys332-2"><fo:block text-align-last="centered"><fo:display-graphic href="phys332-2"/></fo:block><fo:block text-align-last="centered">Figure 2. Energy loss distribution for a 3 GeV electron in Argon as given by +standard GEANT. The width of the layers is given in centimeters.</fo:block></fo:float></fo:block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">It is assumed that the atoms have only two energy levels with binding energy +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>. +The particle--atom interaction will then be an excitation with energy loss +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> or +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>, or +an ionisation with an energy loss distributed according to a function +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">∼</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msup></fotex:inlinemath>: +<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> +<mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> +</fotex:equation></fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The +macroscopic cross-section for excitations (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">i</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn></fotex:inlinemath>) +is <fotex:equation id="eq:sigex" xmlns:m="http://www.w3.org/1998/Math/MathML"> + <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>I</mi><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><mi>r</mi><mo>)</mo></mrow> </fotex:equation>and +the macroscopic cross-section for ionisation is +<fotex:equation id="eq:sigion" xmlns:m="http://www.w3.org/1998/Math/MathML"> + <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><mi>I</mi><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>ln</mo><mrow><mo>(</mo><mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow><mrow><mi>I</mi></mrow></mfrac> <mo>)</mo></mrow></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi> </fotex:equation> +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath> +is the <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> cut for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi></fotex:inlinemath>-production, +or the maximum energy transfer minus mean ionisation energy, if it is smaller than +this cut-off value. The following notation is used: +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N4332"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>parameters of the model</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic energy levels </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>mean ionisation energy </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>oscillator strengths </fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container> +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The model has the parameters <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>, +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath> and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>1</mn><mo>)</mo></mrow></fotex:inlinemath>. The oscillator +strengths <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath> and the +atomic level energies <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath> +should satisfy the constraints + <fotex:eqnarray><fotex:subeqn id="eq:fisum" xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn id="eq:flnsum" xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi> +</fotex:subeqn></fotex:eqnarray> +The parameter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath> +can be defined with the help of the mean energy loss +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> in the following way: The +numbers of collisions (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>, +i = 1,2 for the excitation and 3 for the ionisation) follow the Poisson distribution with a mean +number <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow></fotex:inlinemath>. In a step +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> the mean number +of collisions is <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi> +</fotex:displaymath>The +mean energy loss <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> +in a step is the sum of the excitation and ionisation contributions +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mi>E</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Σ</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><msubsup><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi></mfenced><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi> +</fotex:displaymath>From +this, using the equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:sigex">2</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:sigion">3</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:fisum">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:flnsum">1</fo:simple-link></fo:inline-sequence>), one can define the parameter +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath> +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mi>E</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> +</fotex:displaymath> +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The following values have been chosen in <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> for the other parameters: +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> + <mtable equalrows="false" equalcolumns="false"><mtr><mtd><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfenced open="{"><mtable equalrows="false" equalcolumns="false"><mtr><mtd><mn>0</mn> </mtd><mtd><mi>if</mi><mi>Z</mi><mo>≤</mo><mn>2</mn></mtd> +</mtr><mtr><mtd><mn>2</mn><mo>/</mo><mi>Z</mi></mtd><mtd><mi>if</mi><mi>Z</mi><mo>></mo><mn>2</mn></mtd> +</mtr><mtr><mtd> </mtd></mtr></mtable> </mfenced></mtd><mtd><mo>⇒</mo></mtd><mtd><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn><mo>-</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> </mtd> + </mtr><mtr><mtd><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn><msup><mi>Z</mi><mrow><mn>2</mn></mrow></msup><mi>eV </mi> </mtd><mtd><mo>⇒</mo></mtd><mtd><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><msup><mfenced open="(" close=")"> <mfrac><mrow><mi>I</mi></mrow><mrow><msubsup><mi>E</mi><mrow><mn>2</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></mfrac> </mfenced><mrow> <mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac> </mrow></msup></mtd> + </mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn> </mtd><mtd> </mtd><mtd> </mtd> + </mtr><mtr><mtd> </mtd></mtr></mtable> +</mrow></fotex:displaymath> With these values +the atomic level <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath> +corresponds approximately the K-shell energy of the atoms and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath> the number of +K-shell electrons. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi></fotex:inlinemath> +is the only variable which can be tuned freely. It determines the relative contribution +of ionisation and excitation to the energy loss. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The energy loss is computed with the assumption that the step length (or the relative +energy loss) is small, and---in consequence---the cross-section can be considered +constant along the path length. The energy loss due to the excitation is +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>1</mn></mrow></msub><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>2</mn></mrow></msub><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub> +</fotex:displaymath>where +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath> +are sampled from Poisson distribution as discussed above. The +loss due to the ionisation can be generated from the distribution +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow></fotex:inlinemath> by +the inverse transformation method: + <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"> <mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>E</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>u</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><mi>u</mi> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> +</fotex:subeqn></fotex:eqnarray> +where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi></fotex:inlinemath> is a uniform random +number between <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>. The contribution from the +ionisations will be <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo> + <mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></mrow></msubsup> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>j</mi></mrow></msub> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> +</fotex:displaymath>where +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath> is the +number of ionisation (sampled from Poisson distribution). The energy loss in a step will +then be <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>. +</fo:block> +<fo:block keep-with-next="true" id="N5956" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">5.1. Fast simulation for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">6</mn></fotex:inlinemath><fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N5956">5.1. Fast simulation for n3≥16</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">If the number of ionisation <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath> +is bigger than 16, a faster sampling method can be used. The possible energy loss +interval is divided in two parts: one in which the number of collisions is large and the +sampling can be done from a Gaussian distribution and the other in which +the energy loss is sampled for each collision. Let us call the former interval +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>I</mi><mo>,</mo><mi>α</mi><mi>I</mi><mo>]</mo></mrow></fotex:inlinemath> the interval A, +and the latter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>α</mi><mi>I</mi><mo>,</mo><msub><mi>E</mi><mi>max</mi></msub><mo>]</mo></mrow></fotex:inlinemath> the +interval B. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi></fotex:inlinemath> lies +between 1 and <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi></fotex:inlinemath>. +A collision with a loss in the interval A happens with the probability +<fotex:displaymath id="eq:phys332-5" xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mi>α</mi></mrow></mfrac> +</fotex:displaymath>The +mean energy loss and the standard deviation for this type of collision are +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>>;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mi>α</mi><mo>ln</mo><mi>α</mi></mrow><mrow><mi>α</mi><mo>-</mo><mn>1</mn></mrow></mfrac> +</fotex:displaymath>and <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>2</mn></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo> <mfrac><mrow><mi>α</mi><msup><mo>ln</mo><mrow><mn>2</mn></mrow></msup><mi>α</mi></mrow><mrow><msup><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mfenced> +</fotex:displaymath>If the +collision number is high, we assume that the number of the type A collisions can be +calculated from a Gaussian distribution with the following mean value and standard +deviation: + <fotex:eqnarray><fotex:subeqn id="eq:phys332-1" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn id="eq:phys332-2" xmlns:m="http://www.w3.org/1998/Math/MathML"><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>)</mo></mrow> +</fotex:subeqn></fotex:eqnarray> +It is further assumed that the energy loss in these collisions has a Gaussian +distribution with + <fotex:eqnarray><fotex:subeqn id="eq:phys332-3" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>>;</mo></mrow> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn id="eq:phys332-4" xmlns:m="http://www.w3.org/1998/Math/MathML"><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi></mrow></msub><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow> +</fotex:subeqn></fotex:eqnarray> +The energy loss of these collision can then be sampled from the Gaussian +distribution. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The collisions where the energy loss is in the interval B are sampled directly from +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>B</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo> + <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub></mrow></msubsup> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>α</mi><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>i</mi></mrow></msub> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>-</mo><mi>α</mi><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> +</fotex:displaymath>The +total energy loss is the sum of these two types of collisions: +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"> + <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>B</mi></mrow></msub> +</fotex:displaymath></fo:block> +<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The approximation of equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-1">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-2">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-3">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-4">1</fo:simple-link></fo:inline-sequence>) can be used under the following +conditions: + <fotex:eqnarray><fotex:subeqn id="eq:phys332-6" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn id="eq:phys332-7" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub> + </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"> + </fotex:subeqn><fotex:subeqn id="eq:phys332-8" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> +</fotex:subeqn></fotex:eqnarray> +where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn></fotex:inlinemath>. From +the equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-5">6</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-1">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-3">1</fo:simple-link></fo:inline-sequence>) and from the conditions (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-6">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-7">1</fo:simple-link></fo:inline-sequence>) the following limits can be +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mrow><mi>min</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>I</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mrow><mtext>max</mtext></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><mrow><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>I</mi></mrow></mfrac> +</fotex:displaymath>This +conditions gives a lower limit to number of the ionisations +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath> for which the fast +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mrow><mn>2</mn></mrow></msup> </fotex:displaymath>As +in the conditions (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-6">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-7">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-8">1</fo:simple-link></fo:inline-sequence>) the value of +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi></fotex:inlinemath> is as minimum +4, one gets <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">6</mn></fotex:inlinemath>. +In order to speed the simulation, the maximum value is used for +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi></fotex:inlinemath>. +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The number of collisions with energy loss in the interval B (the number of interactions +which has to be simulated directly) increases slowly with the total number of collisions +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath>. +The maximum number of these collisions can be estimated as +<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≈</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub><mo>)</mo></mrow> +</fotex:equation>From the previous +expressions for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow></fotex:inlinemath> and +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub></fotex:inlinemath> one can derive the +<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> +</fotex:equation>The following +values are obtained with <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn></fotex:inlinemath>: +</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N7981"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>16 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>16 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 200</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 29.63</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>20 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>17.78 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 500</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 31.01</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>50 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>24.24 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 1000</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 31.50</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>100 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>27.59 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">∞</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 32.00</fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container> +</fo:block> + +<fo:block keep-with-next="true" id="N8234" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">5.2. Special sampling for lower part of the spectrum<fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N8234">5.2. Special sampling for lower part of the spectrum</fotex:bookmark></fo:block> + +<fo:block font-size="10pt" text-align="justified">If the step length is very small (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn></fotex:inlinemath> +mm in gases, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo></fotex:inlinemath> +2-3 <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">μ</mi></fotex:inlinemath>m in solids) +the model gives 0 energy loss for some events. To avoid this, the probability of 0 energy loss is +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>Δ</mi><mi>E</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mrow><mo>(</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>></mo></mrow><mo>)</mo></mrow></mrow></msup> +</fotex:displaymath>If the +probability is bigger than 0.01 a special sampling is done, taking into account the fact that in +these cases the projectile interacts only with the outer electrons of the atom. An energy level +<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> eV is chosen +to correspond to the outer electrons. The mean number of collisions can be calculated from +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mi>n</mi><mo>></mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac> +</fotex:displaymath>The number +of collisions <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">n</mi></fotex:inlinemath> +is sampled from Poisson distribution. In the case of the thin layers, all the +collisions are considered as ionisations and the energy loss is computed as +<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo> + <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup> +<mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>-</mo> +<mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow> +<mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac> +<msub><mi>u</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> +</fotex:displaymath> +</fo:block> <fo:block keep-with-next="true" id="N8570" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">6. References<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="N8570">6. References</fotex:bookmark></fo:block> <fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label id="bib-LAND"><fo:block margin-right="2.5pt" text-align="end"> [1]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">L.Landau. On the Energy Loss of Fast Particles by +Ionisation. Originally published in <fo:inline-sequence font-style="italic">J. Phys.</fo:inline-sequence>, 8:201, +1944. Reprinted in D.ter Haar, Editor, <fo:inline-sequence font-style="italic">L.D.Landau, Collected +papers</fo:inline-sequence>, page 417. Pergamon Press, Oxford, 1965. +</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-SCH1"><fo:block margin-right="2.5pt" text-align="end"> [2]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">B.Schorr. Programs for +the Landau and the Vavilov distributions and the corresponding random +numbers. <fo:inline-sequence font-style="italic">Comp. Phys. Comm.</fo:inline-sequence>, 7:216, 1974. +</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-SELT"><fo:block margin-right="2.5pt" text-align="end"> [3]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">S.M.Seltzer and +M.J.Berger. Energy loss straggling of protons and mesons. In +<fo:inline-sequence font-style="italic">Studies in Penetration of Charged Particles in Matter</fo:inline-sequence>, +Nuclear Science Series 39, Nat. Academy of Sciences, Washington DC, +1964. </fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-TALM"><fo:block margin-right="2.5pt" text-align="end"> [4]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">R.Talman. On the +statistics of particle identification using ionization. <fo:inline-sequence font-style="italic">Nucl. +Inst. Meth.</fo:inline-sequence>, 159:189, 1979. </fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-VAVI"><fo:block margin-right="2.5pt" text-align="end"> [5]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">P.V.Vavilov. Ionisation losses of high energy +heavy particles. <fo:inline-sequence font-style="italic">Soviet Physics JETP</fo:inline-sequence>, 5:749, +1957.</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block> + </fo:flow></fo:page-sequence></fo:root>
\ No newline at end of file diff --git a/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex b/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex new file mode 100644 index 00000000000..40e379d8aa4 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex @@ -0,0 +1,4 @@ +\def\xmlfile{latextei.xml} +\input xmltex + + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml b/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml new file mode 100644 index 00000000000..af9fbb686c4 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml @@ -0,0 +1,972 @@ +<?xml version="1.0"?> +<!DOCTYPE TEI.2 SYSTEM "http://www.oucs.ox.ac.uk/dtds/tei-oucs.dtd" [ +<!ENTITY aacute "á"> +<!ENTITY ap "≈"> +<!ENTITY alpha "α"> +<!ENTITY barwed "⊼"> +<!ENTITY beta "β"> +<!ENTITY commaspace " "> +<!ENTITY gamma "γ"> +<!ENTITY delta "δ"> +<!ENTITY Delta "Δ"> +<!ENTITY dots "…"> +<!ENTITY epsi "ε"> +<!ENTITY gg "⋙"> +<!ENTITY Gt "≫"> +<!ENTITY geq "≥"> +<!ENTITY infin "∞"> +<!ENTITY infty "∞"> +<!ENTITY int "∫"> +<!ENTITY kappa "κ"> +<!ENTITY lambda "λ"> +<!ENTITY langle "〈"> +<!ENTITY leq "≤"> +<!ENTITY mu "μ"> +<!ENTITY nbsp " "> +<!ENTITY phi "φ"> +<!ENTITY pi "π"> +<!ENTITY psi "ψ"> +<!ENTITY rangle "〉"> +<!ENTITY rho "ρ"> +<!ENTITY sigma "σ"> +<!ENTITY Sigma "Σ"> +<!ENTITY sim "∼"> +<!ENTITY thinspace " "> +<!ENTITY thickspace " "> +<!ENTITY xi "ξ"> +<!ENTITY prime "′"> +<!ENTITY isinv "∈"> +<!ENTITY macr "̄"> +<!ENTITY Emax "<msub><mi>E</mi><mi>max</mi></msub>"> +<!ENTITY exp "E<mtext>exp</mtext>"> +<!ENTITY ln "E<mtext>ln</mtext>"> +<!ENTITY Rarr "⇒"> +<!ENTITY rarr "→"> +<!ENTITY GEANT "GEANT"> +<!ENTITY sum "∑"> +]> +<TEI.2> + <teiHeader> + <fileDesc> + <titleStmt> + <title>A sample article</title> + </titleStmt> + <publicationStmt> + <availability><p>Converted from LaTeX by Sebastian Rahtz</p> </availability> + </publicationStmt> + <sourceDesc> + <p></p> + </sourceDesc> + </fileDesc> + <revisionDesc> + <list> + <item> + <date>23 Oct 1999</date> SR converted from LaTeX</item> + </list> + </revisionDesc> + </teiHeader> + <text> + <front> + <docTitle> + <titlePart type="main">Simulation of Energy Loss Straggling</titlePart> + </docTitle> + <docAuthor>Maria Physicist</docAuthor> + <docDate>January 17, 1999</docDate> + </front> + <body> <div id="intro"> <head>Introduction</head> <p>Due to +the statistical nature of ionisation energy loss, large fluctuations +can occur in the amount of energy deposited by a particle traversing +an absorber element. Continuous processes such as multiple scattering +and energy loss play a relevant role in the longitudinal and lateral +development of electromagnetic and hadronic showers, and in the case +of sampling calorimeters the measured resolution can be significantly +affected by such fluctuations in their active layers. The description +of ionisation fluctuations is characterised by the significance +parameter <formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math></formula>, which is +proportional to the ratio of mean energy loss to the maximum allowed +energy transfer in a single collision with an atomic electron + <formula +type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow> <mi>κ</mi><mo>=</mo> +<mfrac> + <mrow><mi>ξ</mi></mrow> + <mrow> + &Emax; + </mrow> +</mfrac> +</mrow> +</math></formula> +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +>&Emax;</math></formula> is the +maximum transferable energy in a single collision with an atomic electron. +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow> + &Emax;<mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup></mrow><!--____________ +--><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>γ</mi><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub><mo>+</mo><msup><mfenced +open='(' close=')'><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub> </mfenced><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo> +</mrow></math></formula> where +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>γ</mi><mo>=</mo><mi>E</mi><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula>, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>E</mi></math></formula> is energy and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula> the mass of the +incident particle, <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>-</mo><mn>1</mn><mo>/</mo><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup></math></formula> +and <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub></math></formula> is the +electron mass. <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi></math></formula> +comes from the Rutherford scattering crosss section and is defined as: + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ξ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow><mn>4</mn></mrow></msup><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub><mi>Z</mi><mi>ρ</mi><mi>δ</mi><mi>x</mi></mrow><!-- + --><mrow><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>A</mi></mrow></mfrac> <mo>=</mo><mn>1</mn><mn>5</mn><mn>3</mn><mo>.</mo><mn>4</mn> <mfrac><mrow><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup></mrow><!-- +--><mrow><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mfrac><mrow><mi>Z</mi></mrow><!-- +--><mrow><mi>A</mi></mrow></mfrac><mi>ρ</mi><mi>δ</mi><mi>x</mi><mspace width='12pt'/><mi>keV </mi><mo>,</mo> <mtext></mtext> +</math></formula></cell></row></table> +where +</p><p><table rend="inline"><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>z</mi></math></formula></cell><cell +>charge of the incident particle </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub></math></formula></cell><cell +>Avogadro's number </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>Z</mi></math></formula></cell><cell +>atomic number of the material</cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>A</mi></math></formula></cell><cell +>atomic weight of the material </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ρ</mi></math></formula></cell><cell +>density </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi><mi>x</mi></math></formula></cell><cell +>thickness of the material </cell> +</row><row><cell +> </cell> +</row></table> +</p><p><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi></math></formula> +measures the contribution of the collisions with energy transfer close to +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +>&Emax;</math></formula>. For a given absorber, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi></math></formula> tends towards large +values if <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi><mi>x</mi></math></formula> is large +and/or if <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>β</mi></math></formula> is small. +Likewise, <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi></math></formula> tends +towards zero if <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi><mi>x</mi></math></formula> is +small and/or if <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>β</mi></math></formula> +approaches 1. +</p><p>The value of <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi></math></formula> +distinguishes two regimes which occur in the description of ionisation fluctuations +: +</p><list type="enumerate"> +<item> +<p>A +large +number +of +collisions +involving +the +loss +of +all +or +most +of +the +incident +particle +energy +during +the +traversal +of +an +absorber. +</p><p>As +the +total +energy +transfer +is +composed +of +a +multitude +of +small +energy +losses, +we +can +apply +the +central +limit +theorem +and +describe +the +fluctuations +by +a +Gaussian +distribution. +This +case +is +applicable +to +non-relativistic +particles +and +is +described +by +the +inequality +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo>></mo><mn>1</mn><mn>0</mn></math></formula> +(i.e. +when +the +mean +energy +loss +in +the +absorber +is +greater +than +the +maximum +energy +transfer +in +a +single +collision). +</p></item> +<item> +<p>Particles +traversing +thin +counters +and +incident +electrons +under +any +conditions. +</p><p>The +relevant +inequalities +and +distributions +are +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn><mo><</mo><mi>κ</mi><mo><</mo><mn>1</mn><mn>0</mn></math></formula>, +Vavilov +distribution, +and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo><</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn></math></formula>, +Landau +distribution.</p></item></list> +<p>An additional regime is defined by the contribution of the collisions +with low energy transfer which can be estimated with the relation +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula>, +where <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula> +is the mean ionisation potential of the atom. Landau theory assumes that +the number of these collisions is high, and consequently, it has a restriction +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo>≫</mo><mn>1</mn></math></formula>. In <code>GEANT</code> (see +URL <xptr url="http://wwwinfo.cern.ch/asdoc/geant/geantall.html"/>), the limit of Landau theory has +been set at <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>5</mn><mn>0</mn></math></formula>. +Below this limit special models taking into account the atomic structure of the material are +used. This is important in thin layers and gaseous materials. Figure <ptr target="fg:phys332-1"/> shows the behaviour +of <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula> as +a function of the layer thickness for an electron of 100 keV and 1 GeV of kinetic +energy in Argon, Silicon and Uranium. +</p> +<p><figure file="phys332-1" id="fg:phys332-1"> +<head>The variable <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>ξ</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula> +can be used to measure the validity range of the Landau +theory. It depends on the type and energy of the particle, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>Z</mi></math></formula>, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>A</mi></math></formula> +and the ionisation potential of the material and the layer thickness. </head> +</figure></p> +<p>In the following sections, the different theories and models for the energy loss +fluctuation are described. First, the Landau theory and its limitations are discussed, +and then, the Vavilov and Gaussian straggling functions and the methods in the thin +layers and gaseous materials are presented. +</p> +</div> +<div id="sec:phys332-1"> +<head>Landau theory</head> +<p>For a particle of mass <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula> traversing +a thickness of material <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi><mi>x</mi></math></formula>, +the Landau probability distribution may be written in terms of the universal Landau +function <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>φ</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></math></formula> +as<ptr target="bib-LAND"/>: + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>x</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!-- +--><mrow><mi>ξ</mi></mrow></mfrac><mi>φ</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mtext></mtext> +</math></formula></cell></row></table> +where + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--_ +--><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup><mo>∫</mo> + <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mo>exp</mo><mfenced +open='(' close=')'><mi>u</mi><mo>ln</mo><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi></mfenced><mi>d</mi><mi>u</mi><mspace width='2cm'/><mi>c</mi><mo>≥</mo><mn>0</mn> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi> <mo>=</mo> <mfrac><mrow><mi>ε</mi><mo>-</mo><munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover></mrow><!-- + --><mrow><mi>ξ</mi></mrow></mfrac> <mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><!-- ___ +--><mrow>&Emax;</mrow></mfrac> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mi>′</mi> <mo>=</mo> <mn>0</mn><mo>.</mo><mn>4</mn><mn>2</mn><mn>2</mn><mn>7</mn><mn>8</mn><mn>4</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>=</mo><mn>1</mn><mo>-</mo><mi>γ</mi> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi> <mo>=</mo> <mn>0</mn><mo>.</mo><mn>5</mn><mn>7</mn><mn>7</mn><mn>2</mn><mn>1</mn><mn>5</mn><mo>.</mo><mo>.</mo><mo>.</mo><mtext>(Eulers constant)</mtext> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover> <mo>=</mo> <mtext>average energy loss</mtext> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi> <mo>=</mo> <mtext>actual energy loss</mtext> <mtext></mtext> +</math></formula></cell></row></table> +</p> +<div > +<head>Restrictions</head> +<p>The Landau formalism makes two restrictive assumptions : +</p><list type="enumerate"> +<item> +<p>The +typical +energy +loss +is +small +compared +to +the +maximum +energy +loss +in +a +single +collision. +This +restriction +is +removed +in +the +Vavilov +theory +(see +section +<ptr target="vavref"/>). +</p></item> +<item> +<p>The +typical +energy +loss +in +the +absorber +should +be +large +compared +to +the +binding +energy +of +the +most +tightly +bound +electron. +For +gaseous +detectors, +typical +energy +losses +are +a +few +keV +which +is +comparable +to +the +binding +energies +of +the +inner +electrons. +In +such +cases +a +more +sophisticated +approach +which +accounts +for +atomic +energy +levels<ptr target="bib-TALM"/> +is +necessary +to +accurately +simulate +data +distributions. +In +<code>GEANT</code>, +a +parameterised +model +by +L. +Urbán +is +used +(see +section +<ptr target="urban"/>).</p></item></list> +<p>In addition, the average value of the Landau distribution is infinite. +Summing the Landau fluctuation obtained to the average energy from the +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula> +tables, we obtain a value which is larger than the one coming from the table. The +probability to sample a large value is small, so it takes a large number of steps +(extractions) for the average fluctuation to be significantly larger than zero. This +introduces a dependence of the energy loss on the step size which can affect +calculations. +</p><p>A solution to this has been to introduce a limit on the value of the +variable sampled by the Landau distribution in order to keep the average +fluctuation to 0. The value obtained from the <code>GLANDO</code> routine is: +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow> + <mi>δ</mi><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo>=</mo><mi>ε</mi><mo>-</mo><munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover><mo>=</mo><mi>ξ</mi><mrow><mo>(</mo><mi>λ</mi><mo>-</mo><mi>γ</mi><mi>′</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><!-- ___ +--><mrow>&Emax;</mrow></mfrac> <mo>)</mo></mrow> +</mrow></math></formula> +In order for this to have average 0, we must impose that: +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow> + <munderover accent='true'><mo>¯</mo><mi>λ</mi><mrow></mrow></munderover><mo>=</mo><mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><!-- ___ +--><mrow>&Emax;</mrow></mfrac> +</mrow></math></formula> +</p><p>This is realised introducing a <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mrow><mo>(</mo><munderover accent='true'><mo>¯</mo><mi>λ</mi><mrow></mrow></munderover><mo>)</mo></mrow></math></formula> +such that if only values of <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>λ</mi><mo>≤</mo><msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></math></formula> +are accepted, the average value of the distribution is +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><munderover accent='true'><mo>¯</mo><mi>λ</mi><mrow></mrow></munderover></math></formula>. +</p><p>A parametric fit to the universal Landau distribution has been performed, with following result: +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow> + <msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>0</mn><mn>7</mn><mn>1</mn><mn>5</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>1</mn><mn>9</mn><mn>3</mn><mn>4</mn><munderover accent='true'><mo>¯</mo><mi>λ</mi><mrow></mrow></munderover><mo>+</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>7</mn><mn>7</mn><mn>9</mn><mn>4</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>5</mn><mn>2</mn><mn>3</mn><mn>8</mn><mn>2</mn><munderover accent='true'><mi>λ</mi><mrow></mrow><mo>¯</mo></munderover><mo>)</mo></mrow><mo>exp</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>9</mn><mn>4</mn><mn>7</mn><mn>5</mn><mn>3</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mn>4</mn><mn>4</mn><mn>4</mn><mn>2</mn><munderover accent='true'><mi>λ</mi><mrow></mrow><mo>¯</mo></munderover><mo>)</mo></mrow> +</mrow></math></formula> only values +smaller than <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></math></formula> +are accepted, otherwise the distribution is resampled. +</p> +</div> +</div> +<div id="vavref"> +<head>Vavilov theory</head> +<p>Vavilov<ptr target="bib-VAVI"/> derived a more accurate straggling distribution by introducing the kinematic +limit on the maximum transferable energy in a single collision, rather than using +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +>&Emax;<mo>=</mo><mi>∞</mi></math></formula>. Now +we can write<ptr target="bib-SCH1"/>: + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi> <mfenced +open='(' close=')'><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi></mfenced> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!-- +--><mrow><mi>ξ</mi></mrow></mfrac><msub><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced +open='(' close=')'><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext></mtext> +</math></formula></cell></row></table> +where + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced +open='(' close=')'><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--_ +--><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup><mo>∫</mo> + <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mi>φ</mi><mfenced +open='(' close=')'><mi>s</mi></mfenced><msup><mi>e</mi><mrow><mi>λ</mi><mi>s</mi></mrow></msup><mi>d</mi><mi>s</mi><mspace width='2cm'/><mi>c</mi><mo>≥</mo><mn>0</mn> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mfenced +open='(' close=')'><mi>s</mi></mfenced> <mo>=</mo> <mo>exp</mo><mfenced +open='[' close=']'><mi>κ</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>γ</mi><mo>)</mo></mrow></mfenced><mo>exp</mo><mfenced +open='[' close=']'><mi>ψ</mi> <mfenced +open='(' close=')'><mi>s</mi></mfenced></mfenced><mo>,</mo> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ψ</mi> <mfenced +open='(' close=')'><mi>s</mi></mfenced> <mo>=</mo> <mi>s</mi><mo>ln</mo><mi>κ</mi><mo>+</mo><mrow><mo>(</mo><mi>s</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>κ</mi><mo>)</mo></mrow><mfenced +open='[' close=']'><mo>ln</mo><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>E</mi><mrow> +<mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow></mfenced><mo>-</mo><mi>κ</mi><msup><mi>e</mi><mrow><mo>-</mo><mi>s</mi><mo>/</mo><mi>κ</mi></mrow></msup><mo>,</mo> <mtext></mtext> +</math></formula></cell></row></table> +and + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow> <mo>=</mo><msubsup> <mo>∫</mo> + <mrow><mi>∞</mi></mrow><mrow><mi>z</mi></mrow></msubsup><msup><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi></mrow></msup><mi>d</mi><mi>t</mi><mspace width='1cm'/><mtext>(the exponential integral)</mtext> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub> <mo>=</mo> <mi>κ</mi><mfenced +open='[' close=']'><mfrac><mrow><mi>ε</mi><mo>-</mo><munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover></mrow><!-- + --><mrow><mi>ξ</mi></mrow></mfrac> <mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext></mtext> +</math></formula></cell></row></table> +</p><p>The Vavilov parameters are simply related to the Landau parameter by +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mi>L</mi></mrow></msub><mo>=</mo><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>/</mo><mi>κ</mi><mo>-</mo><mo>ln</mo><mi>κ</mi></math></formula>. It can be shown that +as <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo>→</mo><mn>0</mn></math></formula>, the distribution of +the variable <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mi>L</mi></mrow></msub></math></formula> approaches +that of Landau. For <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn></math></formula> +the two distributions are already practically identical. Contrary to what many textbooks +report, the Vavilov distribution <emph>does not</emph> approximate the Landau distribution for small +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi></math></formula>, but rather the +distribution of <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mi>L</mi></mrow></msub></math></formula> +defined above tends to the distribution of the true +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>λ</mi></math></formula> from +the Landau density function. Thus the routine <code>GVAVIV</code> samples the variable +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mi>L</mi></mrow></msub></math></formula> rather +than <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub></math></formula>. +For <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo>≥</mo><mn>1</mn><mn>0</mn></math></formula> +the Vavilov distribution tends to a Gaussian distribution (see next section). +</p> +</div> +<div > +<head>Gaussian Theory</head> +<p>Various conflicting forms have been proposed for Gaussian straggling functions, but most +of these appear to have little theoretical or experimental basis. However, it has been shown<ptr target="bib-SELT"/> +that for <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>κ</mi><mo>≥</mo><mn>1</mn><mn>0</mn></math></formula> +the Vavilov distribution can be replaced by a Gaussian of the form: + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi><mo>)</mo></mrow><mo>≈</mo> <mfrac><mrow><mn>1</mn></mrow><!--________ +--><mrow><mi>ξ</mi><msqrt><!--<mi>&radical;</mi> + ______________--><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><!-- + --><mrow><mi>κ</mi></mrow></mfrac> <mfenced +open='(' close=')'><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn></mfenced></msqrt></mrow></mfrac><mo>exp</mo><mfenced +open='[' close=']'><mfrac><mrow><msup><mrow><mo>(</mo><mi>ε</mi><mo>-</mo><munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><!-- + --><mrow><mn>2</mn></mrow></mfrac> <mfrac><mrow><mi>κ</mi></mrow><!-- _______ +--><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></mfrac></mfenced> <mtext></mtext> +</math></formula></cell></row></table> +thus implying + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mean</mi> <mo>=</mo> <munderover accent='true'><mo>¯</mo><mi>ε</mi><mrow></mrow></munderover> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mrow><mn>2</mn></mrow></msup> <mo>=</mo> <mfrac><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup></mrow><!-- + --><mrow><mi>κ</mi></mrow></mfrac> <mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mi>ξ</mi><msub><mi>E</mi><mrow><mi> +max</mi></mrow></msub><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow> <mtext></mtext> +</math></formula></cell></row></table> +</p> +</div> +<div id="urban"> +<head>Urbán model</head> +<p>The method for computing restricted energy losses with +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi></math></formula>-ray +production above given threshold energy in <code>GEANT</code> is a Monte Carlo method that +can be used for thin layers. It is fast and it can be used for any thickness of a +medium. Approaching the limit of the validity of Landau's theory, the loss +distribution approaches smoothly the Landau form as shown in Figure <ptr target="fg:phys332-2"/>. +</p> +<p><figure file="phys332-2" id="fg:phys332-2"> +<head>Energy loss distribution for a 3 GeV electron in Argon as given by +standard GEANT. The width of the layers is given in centimeters.</head> +</figure></p> +<p>It is assumed that the atoms have only two energy levels with binding energy +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub></math></formula> and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula>. +The particle--atom interaction will then be an excitation with energy loss +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub></math></formula> or +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula>, or +an ionisation with an energy loss distributed according to a function +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo>∼</mo><mn>1</mn><mo>/</mo><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></math></formula>: +<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mi>I</mi></mrow><!-- + --><mrow>&Emax;</mrow></mfrac> +<mfrac><mrow><mn>1</mn></mrow><!-- _ +--><mrow><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> +</math></formula></p><p>The +macroscopic cross-section for excitations (<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></formula>) +is <formula id="eq:sigex" type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <msub><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>C</mi> <mfrac><mrow><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></mrow><!-- +--><mrow><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> <mfrac><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow><!-- + --><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>I</mi><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>r</mi><mo>)</mo></mrow> </math></formula>and +the macroscopic cross-section for ionisation is +<formula id="eq:sigion" type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <msub><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><mo>=</mo><mi>C</mi> <mfrac><mrow>&Emax;</mrow><!-- ________________ +--><mrow><mi>I</mi><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>ln</mo><mrow><mo>(</mo><mfrac><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow><!-- + --><mrow><mi>I</mi></mrow></mfrac> <mo>)</mo></mrow></mrow></mfrac><mi>r</mi> </math></formula> +<formula><math xmlns="http://www.w3.org/1998/Math/MathML">&Emax;</math></formula> +is the <code>GEANT</code> cut for <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>δ</mi></math></formula>-production, +or the maximum energy transfer minus mean ionisation energy, if it is smaller than +this cut-off value. The following notation is used: +</p><p><table rend="inline"><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>r</mi><mo>,</mo><mi>C</mi></math></formula></cell><cell +>parameters of the model</cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula></cell><cell +>atomic energy levels </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>I</mi></math></formula></cell><cell +>mean ionisation energy </cell> +</row><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula></cell><cell +>oscillator strengths </cell> +</row></table> +</p><p>The model has the parameters <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula>, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula>, +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>C</mi></math></formula> and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>1</mn><mo>)</mo></mrow></math></formula>. The oscillator +strengths <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula> and the +atomic level energies <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula> +should satisfy the constraints + <table rend="inline"><row><cell><formula type="subeqn" id="eq:fisum"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> <mo>=</mo> <mn>1</mn> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:flnsum"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>ln</mo><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>ln</mo><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub> <mo>=</mo> <mo>ln</mo><mi>I</mi> +</math></formula></cell></row></table> +The parameter <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>C</mi></math></formula> +can be defined with the help of the mean energy loss +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula> in the following way: The +numbers of collisions (<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub></math></formula>, +i = 1,2 for the excitation and 3 for the ionisation) follow the Poisson distribution with a mean +number <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow></math></formula>. In a step +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>Δ</mi><mi>x</mi></math></formula> the mean number +of collisions is <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mrow><mo><</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow><mo>=</mo><msub><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mi>Δ</mi><mi>x</mi> +</math></formula>The +mean energy loss <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula> +in a step is the sum of the excitation and ionisation contributions +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mfrac><mrow><mi>d</mi><mi>E</mi></mrow><!-- +--><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> <mi>Δ</mi><mi>x</mi><mo>=</mo><mfenced +open='[' close=']'><msub><mi>Σ</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><msubsup><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi></mfenced><mi>Δ</mi><mi>x</mi> +</math></formula>From +this, using the equations (<ptr target="eq:sigex"/>), (<ptr target="eq:sigion"/>), (<ptr target="eq:fisum"/>) and (<ptr target="eq:flnsum"/>), one can define the parameter +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>C</mi></math></formula> +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>C</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>E</mi></mrow><!-- +--><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> +</math></formula> +</p><p>The following values have been chosen in <code>GEANT</code> for the other parameters: +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow> + <mtable equalrows='false' equalcolumns='false'><mtr><mtd><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfenced +open='{' ><mtable equalrows='false' equalcolumns='false'><mtr><mtd><mn>0</mn> </mtd><mtd><mi>if</mi><mi>Z</mi><mo>≤</mo><mn>2</mn></mtd> +</mtr><mtr><mtd><mn>2</mn><mo>/</mo><mi>Z</mi></mtd><mtd><mi>if</mi><mi>Z</mi><mo>></mo><mn>2</mn></mtd> +</mtr><mtr><mtd> </mtd></mtr></mtable> </mfenced></mtd><mtd><mo>↠</mo></mtd><mtd><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn><mo>-</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> </mtd> + </mtr><mtr><mtd><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn><msup><mi>Z</mi><mrow><mn>2</mn></mrow></msup><mi>eV </mi> </mtd><mtd><mo>↠</mo></mtd><mtd><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><msup><mfenced +open='(' close=')'> <mfrac><mrow><mi>I</mi></mrow><!--___ +--><mrow><msubsup><mi>E</mi><mrow><mn>2</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></mfrac> </mfenced><mrow> <mfrac><mrow><mn>1</mn></mrow><!-- _ +--><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac> </mrow></msup></mtd> + </mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn> </mtd><mtd> </mtd><mtd> </mtd> + </mtr><mtr><mtd> </mtd></mtr></mtable> +</mrow></math></formula> With these values +the atomic level <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula> +corresponds approximately the K-shell energy of the atoms and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>Z</mi><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></math></formula> the number of +K-shell electrons. <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>r</mi></math></formula> +is the only variable which can be tuned freely. It determines the relative contribution +of ionisation and excitation to the energy loss. +</p><p>The energy loss is computed with the assumption that the step length (or the relative +energy loss) is small, and---in consequence---the cross-section can be considered +constant along the path length. The energy loss due to the excitation is +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>Δ</mi><msub><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo>=</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub> +</math></formula>where +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub></math></formula> and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub></math></formula> +are sampled from Poisson distribution as discussed above. The +loss due to the ionisation can be generated from the distribution +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></math></formula> by +the inverse transformation method: + <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow> <mo>=</mo><msubsup> <mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>E</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>x</mi> <mtext></mtext> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><msup><mi>F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mi>I</mi></mrow><!--____ +--><mrow><mn>1</mn><mo>-</mo><mi>u</mi> <mfrac><mrow>&Emax;</mrow><!-- ___ +--><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> +</math></formula></cell></row></table> +where <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>u</mi></math></formula> is a uniform random +number between <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>F</mi><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></math></formula> and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>F</mi><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></math></formula>. The contribution from the +ionisations will be <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>Δ</mi><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>=</mo><msubsup><mo>∑</mo> + <mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></mrow></msubsup> <mfrac><mrow><mi>I</mi></mrow><!--________ +--><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>j</mi></mrow></msub> <mfrac><mrow>&Emax;</mrow><!-- ___ +--><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> +</math></formula>where +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula> is the +number of ionisation (sampled from Poisson distribution). The energy loss in a step will +then be <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>Δ</mi><mi>E</mi><mo>=</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo>+</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula>. +</p> +<div > +<head>Fast simulation for <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>≥</mo><mn>1</mn><mn>6</mn></math></formula></head> +<p>If the number of ionisation <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula> +is bigger than 16, a faster sampling method can be used. The possible energy loss +interval is divided in two parts: one in which the number of collisions is large and the +sampling can be done from a Gaussian distribution and the other in which +the energy loss is sampled for each collision. Let us call the former interval +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow><mo>[</mo><mi>I</mi><mo>,</mo><mi>α</mi><mi>I</mi><mo>]</mo></mrow></math></formula> the interval A, +and the latter <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow><mo>[</mo><mi>α</mi><mi>I</mi><mo>,</mo>&Emax;<mo>]</mo></mrow></math></formula> the +interval B. <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>α</mi></math></formula> lies +between 1 and <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +>&Emax;<mo>/</mo><mi>I</mi></math></formula>. +A collision with a loss in the interval A happens with the probability +<formula type="display" id="eq:phys332-5"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><mfrac><mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><!-- + --><mrow>&Emax;<mi>α</mi></mrow></mfrac> +</math></formula>The +mean energy loss and the standard deviation for this type of collision are +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mrow><mo><</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>>;</mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--___ +--><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><mfrac><mrow><mi>I</mi><mi>α</mi><mo>ln</mo><mi>α</mi></mrow><!-- + --><mrow><mi>α</mi><mo>-</mo><mn>1</mn></mrow></mfrac> +</math></formula>and <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--___ +--><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup><mo>∫</mo> + <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><msup><mi>I</mi><mrow><mn>2</mn></mrow></msup><mi>α</mi><mfenced +open='(' close=')'><mn>1</mn><mo>-</mo> <mfrac><mrow><mi>α</mi><msup><mo>ln</mo><mrow><mn>2</mn></mrow></msup><mi>α</mi></mrow><!--_ +--><mrow><msup><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mfenced> +</math></formula>If the +collision number is high, we assume that the number of the type A collisions can be +calculated from a Gaussian distribution with the following mean value and standard +deviation: + <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo>=</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-2"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>σ</mi><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo>=</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>)</mo></mrow> +</math></formula></cell></row></table> +It is further assumed that the energy loss in these collisions has a Gaussian +distribution with + <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo>=</mo> <msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mrow><mo><</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>>;</mo></mrow> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-4"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo>=</mo> <msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><msup><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow> +</math></formula></cell></row></table> +The energy loss of these collision can then be sampled from the Gaussian +distribution. +</p><p>The collisions where the energy loss is in the interval B are sampled directly from +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>Δ</mi><msub><mi>E</mi><mrow><mi>B</mi></mrow></msub><mo>=</mo><msubsup><mo>∑</mo> + <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub></mrow></msubsup> <mfrac><mrow><mi>α</mi><mi>I</mi></mrow><!--_________ +--><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>i</mi></mrow></msub> <mfrac><mrow>&Emax;<mo>+</mo><mi>I</mi><mo>-</mo><mi>α</mi><mi>I</mi></mrow><!-- + --><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac> +</math></formula>The +total energy loss is the sum of these two types of collisions: +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"> + <mi>Δ</mi><mi>E</mi><mo>=</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>+</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>B</mi></mrow></msub> +</math></formula></p> +<p>The approximation of equations (<ptr target="eq:phys332-1"/>), (<ptr target="eq:phys332-2"/>), (<ptr target="eq:phys332-3"/>) and (<ptr target="eq:phys332-4"/>) can be used under the following +conditions: + <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-6"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><mi>c</mi><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo>≥</mo> <mn>0</mn> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-7"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>+</mo><mi>c</mi><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo>≤</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub> + </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"> + </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-8"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><mi>c</mi><msub><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow></msub> <mo>≥</mo> <mn>0</mn> +</math></formula></cell></row></table> +where <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>c</mi><mo>≥</mo><mn>4</mn></math></formula>. From +the equations (<ptr target="eq:phys332-5"/>), (<ptr target="eq:phys332-1"/>) and (<ptr target="eq:phys332-3"/>) and from the conditions (<ptr target="eq:phys332-6"/>) and (<ptr target="eq:phys332-7"/>) the following limits can be +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mrow><mi>min</mi></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><!-- +--><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>I</mi></mrow></mfrac> <mo>≤</mo><mi>α</mi><mo>≤</mo><msub><mi>α</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><!-- +--><mrow><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>I</mi></mrow></mfrac> +</math></formula>This +conditions gives a lower limit to number of the ionisations +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula> for which the fast +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>≥</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup> </math></formula>As +in the conditions (<ptr target="eq:phys332-6"/>), (<ptr target="eq:phys332-7"/>) and (<ptr target="eq:phys332-8"/>) the value of +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>c</mi></math></formula> is as minimum +4, one gets <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>≥</mo><mn>1</mn><mn>6</mn></math></formula>. +In order to speed the simulation, the maximum value is used for +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>α</mi></math></formula>. +</p><p>The number of collisions with energy loss in the interval B (the number of interactions +which has to be simulated directly) increases slowly with the total number of collisions +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula>. +The maximum number of these collisions can be estimated as +<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>≈</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub><mo>)</mo></mrow> +</math></formula>From the previous +expressions for <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mrow><mo><</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow></math></formula> and +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub></math></formula> one can derive the +<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mi>B</mi></mrow></msub><mo>≤</mo><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow><!--_ +--><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> +</math></formula>The following +values are obtained with <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>c</mi><mo>=</mo><mn>4</mn></math></formula>: +</p><p><table rend="inline"><row><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula></cell><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></formula></cell><cell +></cell><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula></cell><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></formula></cell> +</row><row><cell +>16 </cell><cell +>16 </cell><cell +></cell><cell +> 200</cell><cell +> 29.63</cell> +</row><row><cell +>20 </cell><cell +>17.78 </cell><cell +></cell><cell +> 500</cell><cell +> 31.01</cell> +</row><row><cell +>50 </cell><cell +>24.24 </cell><cell +></cell><cell +> 1000</cell><cell +> 31.50</cell> +</row><row><cell +>100 </cell><cell +>27.59 </cell><cell +></cell><cell +><formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>∞</mi></math></formula></cell><cell +> 32.00</cell> +</row></table> +</p> +</div> +<div > +<head>Special sampling for lower part of the spectrum</head> +<p>If the step length is very small (<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mo>≤</mo><mn>5</mn></math></formula> +mm in gases, <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mo>≤</mo></math></formula> +2-3 <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>μ</mi></math></formula>m in solids) +the model gives 0 energy loss for some events. To avoid this, the probability of 0 energy loss is +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mrow><mo>(</mo><mi>Δ</mi><mi>E</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mrow><mo>(</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo><</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>></mo></mrow><mo>)</mo></mrow></mrow></msup> +</math></formula>If the +probability is bigger than 0.01 a special sampling is done, taking into account the fact that in +these cases the projectile interacts only with the outer electrons of the atom. An energy level +<formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn></math></formula> eV is chosen +to correspond to the outer electrons. The mean number of collisions can be calculated from +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><mi>n</mi><mo>></mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac> +</math></formula>The number +of collisions <formula><math xmlns="http://www.w3.org/1998/Math/MathML" +><mi>n</mi></math></formula> +is sampled from Poisson distribution. In the case of the thin layers, all the +collisions are considered as ionisations and the energy loss is computed as +<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>E</mi><mo>=</mo><msubsup><mo>∑</mo> + <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup> +<mfrac><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>-</mo> +<mfrac><mrow>&Emax;</mrow> +<mrow>&Emax;<mo>+</mo><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac> +<msub><mi>u</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> +</math></formula> +</p> </div> </div> <div +type="star"> <head>References</head> <list type="bibliography"> <item +id="bib-LAND"> <p>L.Landau. On the Energy Loss of Fast Particles by +Ionisation. Originally published in <emph>J. Phys.</emph>, 8:201, +1944. Reprinted in D.ter Haar, Editor, <emph>L.D.Landau, Collected +papers</emph>, page 417. Pergamon Press, Oxford, 1965. +</p></item> <item id="bib-SCH1"> <p>B.Schorr. Programs for +the Landau and the Vavilov distributions and the corresponding random +numbers. <emph>Comp. Phys. Comm.</emph>, 7:216, 1974. +</p></item> <item id="bib-SELT"> <p>S.M.Seltzer and +M.J.Berger. Energy loss straggling of protons and mesons. In +<emph>Studies in Penetration of Charged Particles in Matter</emph>, +Nuclear Science Series 39, Nat. Academy of Sciences, Washington DC, +1964. </p></item> <item id="bib-TALM"> <p>R.Talman. On the +statistics of particle identification using ionization. <emph>Nucl. +Inst. Meth.</emph>, 159:189, 1979. </p></item> <item +id="bib-VAVI"> <p>P.V.Vavilov. Ionisation losses of high energy +heavy particles. <emph>Soviet Physics JETP</emph>, 5:749, +1957.</p></item></list> </div> + </body> </text> </TEI.2> + + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml b/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml new file mode 100644 index 00000000000..87ddc55816f --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml @@ -0,0 +1,388 @@ +<?xml version="1.0"?> +<!DOCTYPE TEI.2 SYSTEM "http://www.oucs.ox.ac.uk/dtds/tei-oucs.dtd" [ + <!ENTITY properties SYSTEM "properties.xml"> +]> +<TEI.2> + <teiHeader> + <fileDesc> + <titleStmt> + <title>PassiveTeX</title> + </titleStmt> + <publicationStmt> + <p> </p> + </publicationStmt> + <sourceDesc> + <p></p> + </sourceDesc> + </fileDesc> + <revisionDesc> + <list> + <item><date>2000/12/11</date>version 1.4 </item> + <item><date>2000/11/23</date>version 1.3 </item> + <item><date>2000/10/04</date>version 1.1 </item> + <item><date>2000/09/13</date>A couple of changes to property list</item> + <item><date>2000/09/12</date>Notes on memory sizes</item> + <item><date>2000/06/24</date>Checking links</item> + <item><date>2000/05/30</date>Added conformance and dependency notes</item> + <item><date>2000/02/07</date>Second version</item> + <item><date>1999/08/08</date>First version, authored in TEI XML</item> + </list> + </revisionDesc> + </teiHeader> + <text> +<front> +<titlePage> +<docTitle> + <titlePart type="main">PassiveTeX</titlePart> +</docTitle> +<docAuthor>Sebastian Rahtz</docAuthor> +<docDate>November 2000</docDate> +</titlePage> +</front> +<body> +<div> +<head>Summary</head> +<list type="unordered"> +<item> +PassiveTeX is a library of TeX macros which can be used to process an XML +document which results from an XSL transformation to formatting objects. +</item> +<item> +PassiveTeX provides a rapid development environment for experimenting +with XSL FO, using a reliable pre-existing formatter +</item> +<item> +Running PassiveTeX with the pdfTeX variant of TeX generates high-quality +PDF files in a single operation. +</item> +<item> +PassiveTeX shows how TeX can remain the formatter of choice for XML, while +hiding the details of its operation from the user. +</item> +</list> +<p> +Available from <xptr + url="http://users.ox.ac.uk/~rahtz/passivetex/"/>. + The current version is 1.4, 2000/12/11. +</p> +</div> +<div><head>How does it work?</head> +<p> +PassiveTeX relies heavily on work by David Carlisle +(his namespace-aware XML parser written in +TeX, <code>xmltex</code>), and was developed from my +<xref url="http://www.tug.org/applications/jadetex/">JadeTeX</xref> +macros for processing DSSSL via Jade. +</p> +<p> +Taking the XML version of the TEI Lite guidelines +(<xref url="test/teiu5.xml">teiu5.xml</xref>, with DTD +<xref url="test/teixlite.dtd">teixlite.dtd</xref>), we apply an XSL stylesheet +(see my page of <xref url="http://users.ox.ac.uk/~rahtz/tei">TEI style sheets</xref>), +and run it through James Clark's XT XSL processor: +<eg> + java com.jclark.xsl.sax.Driver teiu5.xml tei.xsl teiu5.fo +</eg> +(assuming you have <code>xt.jar</code>, <code>xp.jar</code> and <code>sax.jar</code> +on your CLASSPATH ). This creates the new XML file +<xref url="test/teiu5.fo">teiu5.fo</xref>. We now run XMLTeX on this +<eg> + pdfxmltex teiu5.fo +</eg> +which creates <xref url="test/teiu5.pdf">teiu5.pdf</xref>. Voila! +Actually, we need to do +<eg> + pdfxmltex teiu5.fo +</eg> +again, to resolve page-number references in the table of contents. For a comparison +with an HTML rendering of the same document (using XSL again), +see <xref url="http://users.ox.ac.uk/~rahtz/tei/teiu5.html">teiu5.html</xref> +on my TEI page. </p> +</div> +<div> +<head>Installation</head> +<p> +The PassiveTeX macros should be downloaded (as a ZIP file, +<xptr url="passivetex.zip"/>), unpacked, and installed in a TeX system (eg in +<code>texmf/tex/latex/passivetex</code>) in the normal place where you put +macros. Consult your local documentation or local expert if you do not know +how to install a new package; on a web2c-based system, don't forget to + run <code>mktexlsr</code> when you have the files in place, + to update the file lookup table. +</p> +<p> +What about that <code>pdfxmltex</code> command we saw in the last section? +You don't have it on your system? You need to download +<xref url="ftp://ftp.tex.ac.uk/tex-archive/macros/xmltex/base.zip">xmltex</xref> +(that link gives you a ZIP archive of the system) and install it in the your TeX system. +It too is just a set of TeX macro packages. +Then you can use it on a file called (eg) <code>teiu5.fo</code> in one of two ways: +<list type="ordered"> +<item>Build an <code>xmltex</code> format file for pdfTeX with +<eg> +pdftex -ini "&pdflatex" pdfxmltex.ini +</eg> +and process your file with +<eg> +pdflatex "&pdfxmltex" teiu5.fo +</eg> +Or, +</item> +<item> +Make a wrapper file called (eg) <code>teiu5.tex</code> looking like this: +<eg> +\def\xmlfile{teiu5.fo} +\input xmltex +</eg> +and run pdfTeX on it as normal with +<eg> +pdflatex teiu5.tex +</eg> +</item> +</list> +Do not worry, <code>xmltex</code> knows how to find the PassiveTeX macros as +it needs them. You will likely need to increase TeX memory +values (in the file <code>texmf.cnf</code> if you use a Web2c-based TeX); +I use: +<eg> +main_memory = 2500000 +param_size = 1500 +stack_size = 1500 +hash_extra = 50000 +string_vacancies = 45000 +pool_free = 47500 +nest_size = 500 +save_size = 10000 +pool_size = 500000 +max_strings = 55000 +</eg> +</p> +<p> +For reference, the PassiveTeX package consists of the following files: +<list> +<item>The core xmltex `style' files for XSL FO XML: +<eg> + fotex.xmt + fotex.sty +</eg> +</item> +<item> +Support for direct formatting of TEI XML with xmltex +<eg> + tei.xmt + teixml.sty +</eg> +</item> +<item> +Some support files, shared with JadeTeX: +<eg> + unicode.sty + ucharacters.sty + mlnames.sty + dummyels.sty +</eg> +</item> +</list> +</p> +<p> +NOTE: TeX has a limit +on the length of line it can read, +and some .fo files you generate may cause +TeX to die with an message about increasing buf_size. +If you get that, edit your +<code>texmf.cnf</code> file, increase the size of <code>buf_size</code> (mine is +200000), and remake any format files. +</p> +<div><head>LaTeX package dependencies</head> +<p>This setup assumes you have a decent modern TeX setup. The TeX Live 5 CD-ROM +is what I use, and it is up to date +(see <xptr url="http://www.tug.org/texlive/"/>). +</p> +<p> Here is a + list of the packages loaded in a typical run of + PassiveTeX, with their version numbers where known: +<table rend="rules"> +<row><cell> amsbsy.sty </cell><cell> 1999/11/29 v1.2d</cell></row> +<row><cell>amsfonts.sty </cell><cell> 1997/09/17 v2.2e</cell></row> +<row><cell> amsgen.sty </cell><cell> 1999/11/30 v2.0</cell></row> +<row><cell> amsmath.sty </cell><cell> 2000/03/29 v2.08 AMS math features</cell></row> +<row><cell> amsopn.sty </cell><cell> 1999/12/14 v2.01 operator names</cell></row> +<row><cell> amssymb.sty </cell><cell> 1996/11/03 v2.2b</cell></row> +<row><cell> amstext.sty </cell><cell> 1999/11/15 v2.0</cell></row> +<row><cell> array.sty </cell><cell> 1998/05/13 v2.3m Tabular extension package (FMi)</cell></row> +<row><cell> article.cls </cell><cell> 1999/09/10 v1.4a Standard LaTeX document class</cell></row> +<row><cell> bm.sty </cell><cell> 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi)</cell></row> +<row><cell> color.sty </cell><cell> 1999/02/16 v1.0i Standard LaTeX Color (DPC)</cell></row> +<row><cell> fontenc.sty </cell><cell> (version not available)</cell></row> +<row><cell>graphics.sty </cell><cell> 1999/02/16 v1.0l Standard LaTeX Graphics (DPC,SPQR)</cell></row> +<row><cell>graphicx.sty </cell><cell> 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)</cell></row> +<row><cell> hpdftex.def </cell><cell> 2000/05/08 v6.70f Hyperref driver for pdfTeX</cell></row> +<row><cell>hyperref.sty </cell><cell> 2000/05/08 v6.70f Hypertext links for LaTeX</cell></row> +<row><cell> ifthen.sty </cell><cell> 1999/09/10 v1.1b Standard LaTeX ifthen package (DPC)</cell></row> +<row><cell> keyval.sty </cell><cell> 1999/03/16 v1.13 key=value parser (DPC)</cell></row> +<row><cell>longtable.sty </cell><cell> 1998/05/13 v4.09 Multi-page Table package (DPC)</cell></row> +<row><cell>multicol.sty </cell><cell> 1999/10/21 v1.5w multicolumn formatting (FMi)</cell></row> +<row><cell> nameref.sty </cell><cell> 2000/05/08 v2.18 Cross-referencing by name of section</cell></row> +<row><cell> ot1phv.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 scalable font definitions for OT1/phv.</cell></row> +<row><cell> pd1enc.def </cell><cell> 2000/05/08 v6.70f Hyperref: PDFDocEncoding definition (HO)</cell></row> +<row><cell> pifont.sty </cell><cell> 2000/01/12 PSNFSS-v8.1 Pi font support (SPQR) </cell></row> +<row><cell>rotating.sty </cell><cell> 1997/09/26, v2.13 Rotation package</cell></row> +<row><cell> size10.clo </cell><cell> 1999/09/10 v1.4a Standard LaTeX file (size option)</cell></row> +<row><cell>stmaryrd.sty </cell><cell> 1994/03/03 St Mary's Road symbol package</cell></row> +<row><cell> t1enc.def </cell><cell> 1999/12/08 v1.9x Standard LaTeX file</cell></row> +<row><cell> t1phv.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 scalable font definitions for T1/phv.</cell></row> +<row><cell> t1ptm.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for T1/ptm.</cell></row> +<row><cell> t2acmr.fd </cell><cell> 1999/01/07 v1.0 Computer Modern Cyrillic font definitions</cell></row> +<row><cell> t2aenc.def </cell><cell> 1999/11/29 v1.0c Cyrillic encoding definition file</cell></row> +<row><cell> t3enc.def </cell><cell> (version not available)</cell></row> +<row><cell>textcomp.sty </cell><cell> 1999/12/08 v1.9x Standard LaTeX package</cell></row> +<row><cell> times.sty </cell><cell> 2000/01/12 PSNFSS-v8.1 Times font as default roman (SPQR) </cell></row> +<row><cell> tipa.sty </cell><cell> 1996/06/10 TIPA version 1.0</cell></row> +<row><cell> trig.sty </cell><cell> 1999/03/16 v1.09 sin cos tan (DPC)</cell></row> +<row><cell> ts1cmr.fd </cell><cell> 1999/05/25 v2.5h Standard LaTeX font definitions</cell></row> +<row><cell> ts1enc.def </cell><cell> 1998/06/12 v3.0d (jk/car/fm) Standard LaTeX file</cell></row> +<row><cell> ts1ptm.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for TS1/ptm.</cell></row> +<row><cell> ulem.sty </cell><cell> 1997/04/21</cell></row> +<row><cell> umsa.fd </cell><cell> 1995/01/05 v2.2e AMS font definitions</cell></row> +<row><cell> umsb.fd </cell><cell> 1995/01/05 v2.2e AMS font definitions</cell></row> +<row><cell> upsy.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for U/psy.</cell></row> +<row><cell> upzd.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for U/pzd.</cell></row> +<row><cell> url.sty </cell><cell> 1999/03/28 ver 1.5x Verb mode for urls, etc.</cell></row> +<row><cell> Ustmry.fd </cell><cell> (version not available)</cell></row> +<row><cell> uwasy.fd </cell><cell> 1999/05/13 v1.0iWasy-2 symbol font definitions</cell></row> +<row><cell> wasysym.sty </cell><cell> 1999/05/13 v1.0i Wasy-2 symbol support package</cell></row> +</table> +</p> +</div> +</div> + + +<div> +<head>Extensions</head> +<p> +PassiveTeX interprets MathML natively (elements must use the MathML namespace). +I also support a <code>bookmark</code> element in the +<code>fotex</code> namespace, used to make PDF bookmarks. Usage is like this: +<eg> +<xsl:template match="div2"> + <xsl:apply-templates select="head"/> + <fotex:bookmark + xmlns:fotex="http://www.tug.org/fotex" + fotex-bookmark-level="2" + fotex-bookmark-label="{@id}"> + <xsl:value-of select="head"/> + </fotex:bookmark> + </fo:block> +</xsl:template> +</eg> +</p> +</div> + + +<div> +<head>Notes on conformance to the XSL draft specification of November 2000</head> +&properties; +</div> + +<div> +<head>Sample files</head> +<p> +<list> +<item> The TEI Lite description (<xref +url="test/teiu5.xml">teiu5.xml</xref>) converted PDF as <xref +url="test/teiu5.pdf">teiu5.pdf</xref></item> +<item> A TEI test file (<xref +url="test/exercise.xml">exercise.xml</xref>) +converted to PDF as <xref +url="test/exercise.pdf">exercise.pdf</xref></item> +<item> A physics paper (<xref url="test/latextei.xml">latextei.xml</xref>) containing a fair + amount of MathML markup, originally + translated from LaTeX into XML. + It is used extensively as an example in the + <xref url="http://cseng.awl.com/bookpage.taf?ISBN=0-201-43311-7&ptype=0&catid=&navmin=&ctype=author&catpage=&seriesid=">LaTeX Web Companion</xref>. +Here we see it + converted to <xref url="test/latextei.pdf">latextei.pdf</xref> using + <xref url="test/latextei.xsl">test/latextei.xsl</xref></item> +<item> James Tauber prepared a simple XSL spec (<xref +url="test/darkness.xsl">darkness.xsl</xref>) for Joseph Conrad's +<xref url="test/darkness.xml"><emph>Heart of +Darkness</emph></xref>, which I ran to PDF as <xref +url="test/darkness.pdf">darkness.pdf</xref></item> +</list> +</p> +</div> + +<div> +<head>Concerns and problems</head> +<p> +Some points to bear in mind +<list type="ordered"> + <item> Obviously, the XSL FO spec is still a draft. + And this system is not conforming + precisely to the current draft. </item> + <item> This is an experiment system to check whether the + idea works. Expect something more polished eventually.</item> + <item> You need a modern TeX setup (like + <xref url="http://www.tug.org/teTeX/">teTeX</xref> or + <xref url="http://www.tug.org/texlive/">TeX Live</xref>) +to get to grips with it.</item> + <item> Quite a few flow objects and characteristics are not dealt with yet. + I will add support for more things as needed or requested.</item> + <item> I do not have any objective check that what I think XSL FOs are + supposed to do is actually right :-}</item> + <item> I have only worked so far with the TEI Lite (XML version) and + Docbook DTDs, and probably misinterpreted half of what they say.</item> +</list> +</p> +</div> + +<div> +<head>Things for LaTeX users to remember</head> +<p> +<list type="unordered"> +<item> No use is made of LaTeX high-level constructs. No sections, + no lists, no cross-refs, no bibliographies; on the other hand, + some extensions in the <code>fotex:</code> namespace are supported +(eg to get Acrobat bookmarks) +</item> +<item> XSL FO's underlying character set is Unicode; by default, + entities are mapped to their Unicode position; +</item> +<item> All vertical and horizontal space is explicit in the + specification +</item> +<item> Page and line breaking is left to TeX: the rest is up to you. +</item> +</list> +</p> +</div> + +<div> +<head>Future directions</head> +<p> +<list type="unordered"> +<item>Complete the MathML handling</item> +<item>Handle more variety in property values (eg colors, fonts) </item> +<item>Deal with more complex tables</item> +<item>Support SVG. How? + <list type="unordered"> + <item>By direct intepretation and mapping to raw PDF</item> + <item>By translation to MetaPost, and spawning a MetaPost process</item> + <item>By pre-processing to existing TeX graphics languages</item> + </list> +In any case, SVG fragments need to be recognized directly to perform in-line +graphical functions (setting text at an angle?) +</item> +<item>Use Unicode-based TeX variant (Omega) to handle non-Latin material +more naturally</item> +</list> +</p> +<p> +I will be very glad to discuss details with anyone. Contact me (Sebastian Rahtz) as +<xref url="mailto:sebastian.rahtz@oucs.ox.ac.uk">sebastian.rahtz@oucs.ox.ac.uk</xref> +</p> +</div> +</body> +</text> +</TEI.2> + diff --git a/Master/texmf-dist/doc/xmltex/passivetex/properties.xml b/Master/texmf-dist/doc/xmltex/passivetex/properties.xml new file mode 100644 index 00000000000..85cd904b3c0 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/properties.xml @@ -0,0 +1,592 @@ +<!-- +0. done +1. more or less OK +2. not done, but pending when for when I need it +3. not done, cannot see how to do it +4. N/A +--> +<p> +The following general limitations apply to most of the PassiveTeX + implementation of XSL FO: +<list type="ordered"> +<item>The `px' unit is not recognised</item> +<item>Absolute dimensions always work, but proportional ones +are often not recognized </item> +<item>The functions allowed in attribute values are usually not + recognized</item> +<item>There is no error checking at all, and all properies are + recognized; do not assume that they do anything...</item> +</list> +</p> +<p> +Most of the formatting objects are implemented more or less; the +following are not implemented at all: +<list type="ordered"> +<item><code>fo:bidi-override</code></item> +<item><code>fo:color-profile</code></item> +<item><code>fo:declarations</code></item> +<item><code>fo:initial-property-set</code></item> +<item><code>fo:instream-foreign-object</code></item> +<item><code>fo:multi-case</code></item> +<item><code>fo:multi-properties</code></item> +<item><code>fo:multi-property-set</code></item> +<item><code>fo:multi-switch</code></item> +<item><code>fo:multi-toggle</code></item> +<item><code>fo:region-end</code></item> +<item><code>fo:region-start</code></item> +<item><code>fo:table-footer</code></item> +</list> +</p> +<div><head>Properties needed for basic conformance</head> +<p> +<table rend="rules"> +<row><cell>alignment-adjust</cell><cell>auto | percentage | length | inherit</cell><cell>Basic</cell> +<cell>2. should be possible </cell></row> + +<row><cell>azimuth</cell><cell>angle | [[ left-side | far-left | left | center-left | center | center-right | right | far-right | right-side +] || behind ] | leftwards | rightwards | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>background-color</cell><cell>color | transparent | inherit</cell><cell>Basic</cell> <cell>3. does not really map in TeX </cell></row> + +<row><cell>baseline-identifier</cell><cell>baseline | before-edge | text-before-edge | middle | after-edge +| text-after-edge | ideographic | alphabetic | hanging | mathematical +| inherit</cell><cell>Basic</cell> +<cell>3. not at all sure where to start </cell></row> + +<row><cell>baseline-shift</cell><cell>baseline | sub | super | percentage | length | inherit</cell><cell>Basic</cell> +<cell>1. basically works </cell></row> + +<row><cell>block-progression-dimension</cell><cell>auto | length | percentage | length-range | inherit</cell><cell>Basic</cell> +<cell>3. do not really understand it </cell></row> + +<row><cell>border-after-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-after-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-after-width</cell><cell>border-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-before-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-before-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-before-width</cell><cell>border-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-bottom-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-bottom-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>1. used in places </cell></row> + +<row><cell>border-bottom-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-end-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-end-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-end-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-left-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-left-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-left-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-right-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-right-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-right-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-start-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-start-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-start-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-top-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>border-top-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>1. used in places </cell></row> + +<row><cell>border-top-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row> + +<row><cell>break-after</cell><cell>auto | column | page | even-page | odd-page | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row> + +<row><cell>break-before</cell><cell>auto | column | page | even-page | odd-page | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row> + +<row><cell>character</cell><cell>character</cell><cell>Basic</cell> <cell>0. should be working </cell></row> + +<row><cell>clip</cell><cell>shape | auto | inherit</cell><cell>Basic</cell> <cell>2. theoretically possible </cell></row> + +<row><cell>color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>1. more or less complete </cell></row> + +<row><cell>column-number</cell><cell>number</cell><cell>Basic</cell> <cell>0. OK </cell></row> + +<row><cell>column-width</cell><cell>length</cell><cell>Basic</cell> <cell>0. OK </cell></row> + +<row><cell>content-type</cell><cell>string | auto</cell><cell>Basic</cell> <cell>4. N/A, I think </cell></row> + +<row><cell>cue-after</cell><cell>uri | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>cue-before</cell><cell>uri | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>direction</cell><cell>ltr | rtl | inherit</cell><cell>Basic</cell> <cell>3. waiting for extended TeX </cell></row> + +<row><cell>display-align</cell><cell>auto | before | center | after | inherit</cell><cell>Basic</cell> +<cell>0. working </cell></row> + +<row><cell>dominant-baseline</cell><cell>auto | autosense-script | no-change | reset-size | ideographic | alphabetic | hanging | mathematical +| inherit</cell><cell>Basic</cell> +<cell>3. dont know where to begin </cell></row> + +<row><cell>elevation</cell><cell>angle | below | level | above | higher | lower | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>end-indent</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>0. working </cell></row> + +<row><cell>flow-name</cell><cell>name</cell><cell>Basic</cell> <cell>0. working </cell></row> + +<row><cell>font-family</cell><cell>[[ family-name | generic-family ],]* [family-name | generic-family] | inherit</cell><cell>Basic</cell> +<cell>1. more or less OK </cell></row> + +<row><cell>font-size</cell><cell>absolute-size | relative-size | length | percentage | inherit</cell><cell>Basic</cell> +<cell>1. more or less all implemented </cell></row> + +<row><cell>font-style</cell><cell>normal | italic | oblique | backslant | inherit</cell><cell>Basic</cell> <cell>1. no oblique or backslant </cell></row> + +<row><cell>font-variant</cell><cell>normal | small-caps | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row> + +<row><cell>font-weight</cell><cell>normal | bold | bolder | lighter | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | inherit</cell><cell>Basic</cell> +<cell>1. normal and bold only at present, others to follow</cell></row> + +<row><cell>format</cell><cell>string</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row> + +<row><cell>grouping-separator</cell><cell>character</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row> + +<row><cell>grouping-size</cell><cell>number</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row> + +<row><cell>height</cell><cell>length | percentage | auto | inherit</cell><cell>Basic</cell> <cell>2. should be OK, waiting for a need </cell></row> + +<row><cell>id</cell><cell> id</cell><cell>Basic</cell> <cell>0. used </cell></row> + +<row><cell>initial-page-number</cell><cell>auto | auto-odd | auto-even | number | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row> + +<row><cell>inline-progression-dimension</cell><cell>auto | length | percentage | length-range | inherit</cell><cell>Basic</cell> +<cell>3. have not considered at all </cell></row> + +<row><cell>keep-with-next</cell><cell>keep | inherit</cell><cell>Basic</cell> <cell>1. done in theory, not working 100%</cell></row> + +<row><cell>keep-with-previous</cell><cell>keep | inherit</cell><cell>Basic</cell> <cell>1. done in theory, not working 100% </cell></row> + +<row><cell>leader-length</cell><cell>length-range | inherit</cell><cell>Basic</cell> <cell>2. waiting to do soon </cell></row> + +<row><cell>leader-pattern</cell><cell>space | rule | dots | use-content | inherit</cell><cell>Basic</cell> <cell>2. waiting to do soon </cell></row> + +<row><cell>letter-value</cell><cell>auto | alphabetic | traditional</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row> + +<row><cell>line-height</cell><cell>normal | length | number | percentage | space | inherit</cell><cell>Basic</cell> +<cell>1. largely done </cell></row> + +<row><cell>line-stacking-strategy</cell><cell>line-height | font-height | max-height | inherit</cell><cell>Basic</cell> <cell>3. untouched </cell></row> + +<row><cell>margin-bottom</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row> + +<row><cell>margin-left</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row> + +<row><cell>margin-right</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row> + +<row><cell>margin-top</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row> + +<row><cell>master-name</cell><cell>name</cell><cell>Basic</cell> <cell>0. ok </cell></row> + +<row><cell>max-height</cell><cell>length | percentage | none | inherit </cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>max-width</cell><cell>length | percentage | none | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>min-height</cell><cell>length | percentage | inherit </cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>min-width</cell><cell>length | percentage | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>number-columns-repeated</cell><cell>number</cell><cell>Basic</cell> + <cell>2. doable in theory </cell></row> + +<row><cell>number-columns-spanned</cell><cell>number</cell><cell>Basic</cell> <cell>2. doable in theory </cell></row> + +<row><cell>number-rows-spanned</cell><cell>number</cell><cell>Basic</cell> <cell>2. doable in theory </cell></row> + +<row><cell>orphans</cell><cell>integer | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>overflow</cell><cell>visible | hidden | scroll | auto | inherit</cell><cell>Basic</cell> <cell>2. theoretically </cell></row> + +<row><cell>padding-after</cell><cell>padding-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-before</cell><cell>padding-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-bottom</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-end</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-left</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-right</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-start</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>padding-top</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row> + +<row><cell>page-break-after</cell><cell>auto | always | avoid | left | right | inherit</cell><cell>Basic</cell> <cell>1. Mostly implemented </cell></row> + +<row><cell>page-break-before</cell><cell>auto | always | avoid | left | right | inherit</cell><cell>Basic</cell> <cell>1. Mostly implemented </cell></row> + +<row><cell>page-height</cell><cell>auto | indefinite | length | inherit</cell><cell>Basic</cell> <cell>1. not all possibilities</cell></row> + +<row><cell>page-width</cell><cell>auto | indefinite | length | inherit</cell><cell>Basic</cell> <cell>1. not all possibilities</cell></row> + +<row><cell>pause-after</cell><cell>time | percentage | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>pause-before</cell><cell>time | percentage | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>pitch</cell><cell>frequency | x-low | low | medium | high | x-high | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>pitch-range</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>play-during</cell><cell>uri mix? repeat? | auto | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>precedence</cell><cell>true | false | inherit</cell><cell>Basic</cell> <cell>3. do not know where to start </cell></row> + +<row><cell>provisional-distance-between-starts</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>1. does something, probably wrong </cell></row> + +<row><cell>provisional-label-separation</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>1. does something, probably wrong </cell></row> + +<row><cell>ref-id</cell><cell>idref | inherit</cell><cell>Basic</cell> <cell>0. used in pagenumber </cell></row> + +<row><cell>reference-orientation</cell><cell> 0 | 90 | 180 | 270 | -90 | -180 | -270 | inherit</cell><cell>Basic</cell> <cell>2. doable for most objects </cell></row> + +<row><cell>region-name</cell><cell>xsl-region-body | xsl-region-start | xsl-region-end | xsl-region-before | xsl-region-after | xsl-before-float-separator +| xsl-footnote-separator | name</cell><cell>Basic</cell> +<cell>0. done </cell></row> + +<row><cell>relative-align</cell><cell>before | baseline | inherit</cell><cell>Basic</cell> +<cell>3. have not got to grips with this </cell></row> + +<row><cell>richness</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>role</cell><cell>string | none | inherit</cell><cell>Basic</cell> <cell>4. N/A what should I do with it?</cell></row> + +<row><cell>rule-style</cell><cell>none | dotted | dashed | solid | double | groove | ridge | inherit</cell><cell>Basic</cell> +<cell>1. done as far as possible </cell></row> + +<row><cell>rule-thickness</cell><cell>length</cell><cell>Basic</cell> <cell>0. done </cell></row> + +<row><cell>source-document</cell><cell>uri+ | none | inherit</cell><cell>Basic</cell> <cell>4. N/A not sure what to do with it</cell></row> + +<row><cell>space-after</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row> + +<row><cell>space-before</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row> + +<row><cell>space-end</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row> + +<row><cell>space-start</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row> + +<row><cell>speak</cell><cell>normal | none | spell-out | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>speak-header</cell><cell>once | always | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>speak-numeral</cell><cell>digits | continuous | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>speak-punctuation</cell><cell>code | none | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>speech-rate</cell><cell>number | x-slow | slow | medium | fast | x-fast | faster | slower | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>src</cell><cell> uri | inherit</cell><cell>Basic</cell> <cell>0. implemented </cell></row> + +<row><cell>start-indent</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row> + +<row><cell>stress</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row> + +<row><cell>text-align</cell><cell>start | center | end | justify | inside | outside | left | right | string | inherit</cell><cell>Basic</cell> +<cell>0. done </cell></row> + +<row><cell>text-indent</cell><cell>length | percentage | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row> + +<row><cell>visibility</cell><cell>visible | hidden | collapse | inherit</cell><cell>Basic</cell> <cell>2. I think can do this </cell></row> + +<row><cell>voice-family</cell><cell>[[specific-voice | generic-voice ],]* [specific-voice | generic-voice ] | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>volume</cell><cell>number | percentage | silent | x-soft | soft | medium | loud | x-loud | inherit</cell><cell>Basic</cell> +<cell>4. N/A </cell></row> + +<row><cell>widows</cell><cell>integer | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row> + +<row><cell>width</cell><cell>length | percentage | auto | inherit</cell><cell>Basic</cell> <cell>2. should be OK, waiting for a need </cell></row> + +<row><cell>wrap-option</cell><cell>no-wrap | wrap | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row> + +<row><cell>writing-mode</cell><cell>lr-tb | rl-tb | tb-rl | lr | rl | tb | inherit</cell><cell>Basic</cell> <cell>3. will need an extended TeX </cell></row> + +<row><cell>z-index</cell><cell>auto | integer | inherit</cell><cell>Basic</cell> <cell>3. dont know where to start </cell></row> +</table> +</p> +</div> + + +<div><head>Properties needed for full conformance</head> +<p> +<table rend="rules"> +<row><cell>absolute-position</cell><cell>auto | absolute | fixed | inherit</cell><cell>Complete</cell> <cell>2. should be doable </cell></row> + +<row><cell>background</cell><cell>[background-color || background-image +|| background-repeat || background-attachment || background-position +| ]]inherit</cell><cell>Complete</cell> +<cell>1. implemented but very fragile </cell></row> + +<row><cell>background-position</cell><cell>[ [percentage | length ]{1,2} | [ [top | center | bottom] || [left | center | right] ] ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border</cell><cell>[ border-width || border-style || color ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border-bottom</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border-color</cell><cell>color{1,4} | transparent | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>border-left</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border-right</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border-spacing</cell><cell>length length? | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>border-style</cell><cell>border-style{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>border-top</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>border-width</cell><cell>border-width{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>caption-side</cell><cell>before | after | start | end | top | bottom | left | right | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>cue</cell><cell>cue-before || cue-after | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>font</cell><cell>[ [ font-style || font-variant || font-weight ]? font-size [ / line-height]? font-family +] | caption | icon | menu | message-box | small-caption | status-bar +| inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>margin</cell><cell>margin-width{1,4} | inherit </cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>padding</cell><cell>padding-width{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>page-break-inside</cell><cell>avoid | auto | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>pause</cell><cell>[time | percentage]{1,2} | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>position</cell><cell>static | relative | absolute | fixed | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>size</cell><cell>length{1,2} | auto | landscape | portrait | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>vertical-align</cell><cell>baseline | middle | sub | super | text-top | text-bottom | percentage | length | top | bottom | inherit</cell><cell>Complete</cell> +<cell> </cell></row> + +<row><cell>white-space</cell><cell>normal | pre | nowrap | inherit</cell><cell>Complete</cell> <cell> </cell></row> + +<row><cell>xml:lang</cell><cell>country-language | inherit</cell><cell>Complete</cell> <cell>2. not done yet, but will be </cell></row> +</table> +</p> +</div> + +<div><head>Properties needed for extended conformance</head> +<p> +<table rend="rules"> +<row><cell>table-layout</cell><cell>auto | fixed | inherit</cell><cell>Extended.Fallback: fixed</cell> <cell> </cell></row> + +<row><cell>background-attachment</cell><cell>scroll | fixed | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. I can see where I might start </cell></row> + +<row><cell>background-image</cell><cell>uri | none | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. I can see where I might start </cell></row> + +<row><cell>background-position-horizontal</cell><cell>percentage | length | left | center | right | inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell>2. I can see where I might start </cell></row> + +<row><cell>background-position-vertical</cell><cell>percentage | length | top | center | bottom | inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell>2. I can see where I might start </cell></row> + +<row><cell>border-collapse</cell><cell>collapse | separate | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>border-separation</cell><cell>length-bp-ip-direction | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>column-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. implemented </cell></row> + +<row><cell>content-height</cell><cell>auto | length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>1. done for graphics </cell></row> + +<row><cell>content-width</cell><cell>auto | length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>1. done for graphics </cell></row> + +<row><cell>country</cell><cell>none | country | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. waiting to find a use for it </cell></row> + +<row><cell>empty-cells</cell><cell>show | hide | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>ends-row</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>font-height-override-after</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row> + +<row><cell>font-height-override-before</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row> + +<row><cell>font-size-adjust</cell><cell>number | none | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable, I think </cell></row> + +<row><cell>font-stretch</cell><cell>normal | wider | narrower | ultra-condensed | extra-condensed | condensed | semi-condensed | semi-expanded | +expanded | extra-expanded | ultra-expanded |inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell>0. should be OK </cell></row> + +<row><cell>glyph-orientation-horizontal</cell><cell>angle | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row> + +<row><cell>glyph-orientation-vertical</cell><cell>auto | angle | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row> + +<row><cell>hyphenate</cell><cell>false | true | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. done </cell></row> + +<row><cell>keep-together</cell><cell>keep | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>language</cell><cell>none | language | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. done, if underlying TeX system OK </cell></row> + +<row><cell>last-line-end-indent</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>leader-alignment</cell><cell>none | reference-area | page | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>leader-pattern-width</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>letter-spacing</cell><cell>normal | length | space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable in limited circumstances </cell></row> + +<row><cell>line-height-shift-adjustment</cell><cell>consider-shifts | disregard-shifts | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>linefeed-treatment</cell><cell>ignore | preserve | treat-as-space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable, if tiresome </cell></row> + +<row><cell>relative-position</cell><cell>auto | static | relative | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>scaling</cell><cell>uniform | non-uniform | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. ok </cell></row> + +<row><cell>scaling-method</cell><cell>auto | integer-pixels | resample-any-method | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>4. N/A, I think </cell></row> + +<row><cell>score-spaces</cell><cell>true | false | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. dont think I can do this </cell></row> + +<row><cell>space-treatment</cell><cell>ignore | preserve | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. seems to work </cell></row> + +<row><cell>span</cell><cell>none | all | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. proving hard </cell></row> + +<row><cell>starts-row</cell><cell>yes | + no</cell><cell>Extended.Fallback: Initial value</cell> + <cell>0. works</cell></row> + +<row><cell>suppress-at-line-break</cell><cell>auto | suppress | retain | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>table-omit-footer-at-break</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>table-omit-header-at-break</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>text-align-last</cell><cell>relative | start | center | end | justify | inside | outside | left | right | string | inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell>1. works, usually </cell></row> + +<row><cell>text-decoration</cell><cell>none | [ [ underline | no-underline] || [ overline | no-overline ] || [ line-through | no-line-through ] || [ blink | no-blink ] ] + +| inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell>1. done for some possibilities, not all </cell></row> + +<row><cell>text-shadow</cell><cell>none | [color || length length length? ,]* [color || length length length?] | inherit</cell><cell>Extended.Fallback: Initial value</cell> +<cell> </cell></row> + +<row><cell>text-transform</cell><cell>capitalize | uppercase | lowercase | none | </cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable </cell></row> + +<row><cell>treat-as-word-space</cell><cell>auto | yes | no | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>white-space-collapse</cell><cell>false | true | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. Done </cell></row> + +<row><cell>word-spacing</cell><cell>normal | length | space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row> + +<row><cell>bottom</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row> + +<row><cell>left</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row> + +<row><cell>right</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row> + +<row><cell>top</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row> + +<row><cell>column-gap</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: N/A due to fallback for column-count</cell> <cell>1. implemented (not for all value types) </cell></row> + +<row><cell>hyphenation-character</cell><cell>character | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. need to think about how to do this </cell></row> + +<row><cell>hyphenation-keep</cell><cell>auto | column | page | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. not sure how to do this </cell></row> + +<row><cell>hyphenation-ladder-count</cell><cell>no-limit | number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. I dont see how to do this </cell></row> + +<row><cell>hyphenation-push-character-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>2. I think this maps in TeX </cell></row> + +<row><cell>hyphenation-remain-character-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>2. I think this maps in TeX </cell></row> + +<row><cell>color-profile-name</cell><cell>name | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:color-profile</cell> <cell>3. would need a lot of thought </cell></row> + +<row><cell>rendering-intent</cell><cell>auto | perceptual | relative-colorimetric | saturation | absolute-colorimetric | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:color-profile</cell> <cell>3. not sure how to do this </cell></row> + +<row><cell>clear</cell><cell>start | end | left | right | both | none | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:float</cell> <cell> </cell></row> + +<row><cell>float</cell><cell>before | start | end | left | right | none | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:float</cell> <cell> </cell></row> + +<row><cell>marker-class-name</cell><cell>name</cell><cell>Extended.Fallback: N/A use fallback for fo:marker</cell> <cell> </cell></row> + +<row><cell>active-state</cell><cell>link | visited | active | hover | focus</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-properties</cell> <cell> </cell></row> + +<row><cell>auto-restore</cell><cell>yes | no</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row> + +<row><cell>case-name</cell><cell>name</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row> + +<row><cell>case-title</cell><cell>string</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row> + +<row><cell>starting-state</cell><cell>show | hide</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row> + +<row><cell>switch-to</cell><cell>xsl-preceding | xsl-following | xsl-any | name[ name]*</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row> + +<row><cell>extent</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:region-before, fo:region-after, fo:region-start, and fo:region-end</cell> <cell> </cell></row> + +<row><cell>blank-or-not-blank</cell><cell>blank | not-blank | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell>3. dont want to think about it </cell></row> + +<row><cell>odd-or-even</cell><cell>odd | even | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell> </cell></row> + +<row><cell>page-position</cell><cell>first | last | rest | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell> </cell></row> + +<row><cell>maximum-repeats</cell><cell>number | no-limit | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-reference and fo:repeatable-page-master-alternatives</cell> <cell> </cell></row> + +<row><cell>retrieve-boundary</cell><cell>page | page-sequence | document</cell><cell>Extended.Fallback: N/A use fallback for fo:retrieve-marker</cell> <cell> </cell></row> + +<row><cell>retrieve-class-name</cell><cell>name</cell><cell>Extended.Fallback: + N/A use fallback for fo:retrieve-marker</cell> <cell>1. works usually </cell></row> + +<row><cell>retrieve-position</cell><cell>first-starting-within-page | first-including-carryover | last-starting-within-page | last-ending-within-page</cell><cell>Extended.Fallback: N/A use fallback for fo:retrieve-marker</cell> +<cell> </cell></row> + +<row><cell>destination-placement-offset</cell><cell>length</cell><cell>Extended.Fallback: N/A use fallback for fo:simple-link</cell> <cell> </cell></row> + +<row><cell>external-destination</cell><cell>uri-reference</cell><cell>Extended.Fallback: + N/A use fallback for fo:simple-link</cell> <cell>0. works ok </cell></row> + +<row><cell>indicate-destination</cell><cell>yes | + no</cell><cell>Extended.Fallback: N/A use fallback for + fo:simple-link</cell> <cell>1. should work </cell></row> + +<row><cell>internal-destination</cell><cell>null string | + idref</cell><cell>Extended.Fallback: N/A use fallback for + fo:simple-link</cell> <cell>0. works </cell></row> + +<row><cell>show-destination</cell><cell>replace | new</cell><cell>Extended.Fallback: N/A use fallback for fo:simple-link</cell> <cell> </cell></row> + +<row><cell>force-page-count</cell><cell>auto | even | odd | end-on-even | end-on-odd | no-force | inherit</cell><cell>Extended.Fallback: no-force</cell> +<cell> </cell></row> + +<row><cell>background-repeat</cell><cell>repeat | repeat-x | repeat-y | no-repeat | inherit</cell><cell>Extended.Fallback: no-repeat</cell> <cell> </cell></row> + +<row><cell>script</cell><cell>none | auto | script | inherit</cell><cell>Extended.Fallback: none</cell> <cell>4. dont know what to do with it </cell></row> + +<row><cell>unicode-bidi</cell><cell>normal | embed | bidi-override | inherit</cell><cell>Extended.Fallback: See prose</cell> <cell> </cell> +</row> +</table> +</p> +</div> diff --git a/Master/texmf-dist/doc/xmltex/passivetex/test.xml b/Master/texmf-dist/doc/xmltex/passivetex/test.xml new file mode 100644 index 00000000000..321a22835d4 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/test.xml @@ -0,0 +1,280 @@ +<?xml version="1.0"?> +<!DOCTYPE TEI.2 SYSTEM "teixlite.dtd"> +<TEI.2> + <teiHeader> + <fileDesc> + <titleStmt> + <title>This and that</title> + </titleStmt> + <publicationStmt> + <p> </p> + </publicationStmt> + <sourceDesc> + <p></p> + </sourceDesc> + </fileDesc> + <revisionDesc> + <list> + <item><date>October 10th 1999</date>Initial version</item> + </list> + </revisionDesc> + </teiHeader> + <text> +<front> + <docTitle> + <titlePart type="main">Texts for beginners</titlePart> + </docTitle> +<docAuthor>A N Other</docAuthor> +<docDate>October 10th 1999</docDate> +</front> +<body> + +<div><head>The table in section 1</head> +<p> +Over the whine of the electric mixer, Mara heard her name called, but she +didn't bother to acknowledge it. Instead she added more sugar to the egg +whites and continued to beat them until they formed stiff peaks. She was +spooning the meringue on to the pie filling when she heard the hum of the +wheelchair approaching the kitchen. +</p><p> +`Mara, the mailman just drove by.' The chair rolled to a stop inside the +room. `I'm expecting some correspondence from Fitzgerald. Will you see if +it's come?' +</p><p> +Mara didn't turn around. I'm busy at the moment, Adam.' She continued to +spread the meringue thickly over the pie, ignoring the instant of tense +silence. +</p> +<div><head>The table in section 1</head> +<q rend="display"> +<table cols="3" rend="inline"> +<row><cell cols="3">AT&T Common Stock</cell></row> +<row><cell>Year </cell><cell> Price</cell><cell>Dividend</cell></row> +<row><cell>1971</cell><cell>41--54</cell><cell>$2.60</cell></row> +<row><cell> 2</cell><cell>41--54</cell><cell>2.70</cell></row> +<row><cell> 3</cell><cell>46--55</cell><cell>2.87</cell></row> +<row><cell> 4</cell><cell>40--53</cell><cell>3.24</cell></row> +<row><cell> 5</cell><cell>45--52</cell><cell>3.40</cell></row> +<row><cell> 6</cell><cell>51--59</cell><cell>.95*</cell></row> +<row><cell cols="3">(* first quarter only)</cell></row> +</table> +</q> + +<eg> +<![CDATA[ +<xsl:template match="eg"> + <fo:block font-family="{$typewriterFont}" + white-space-collapse="false" + wrap-option="no-wrap" + text-indent="0em" + start-indent="{$exampleMargin}" + text-align="start" + font-size="{$exampleSize}" + background="red" + color="white" + space-before.optimum="4pt" + space-after.optimum="4pt" + > + <xsl:value-of select="translate(.,' ',' ')"/> + </fo:block> +</xsl:template> +]]> +</eg> +</div> +</div> +<div><head>LOOMINGS</head> + +<p>Call me Ishmael. Some years ago—never mind how long +precisely —having little or no money in my purse, and nothing +particular to interest me on shore, I thought I would sail about a +little and see the watery part of the world. It is a way I have of +driving off the spleen, and regulating the circulation. Whenever I +find myself growing grim about the mouth; whenever it is a damp, +drizzly November in my soul; whenever I find myself involuntarily +pausing before coffin warehouses, and bringing up the rear of every +funeral I meet; and especially whenever my hypos get such an upper +hand of me, that it requires a strong moral principle to prevent me +from deliberately stepping into the street, and methodically knocking +people's hats off—then, I account it high time to get to sea as +soon as I can. This is my substitute for pistol and ball. With a +philosophical flourish Cato throws himself upon his sword; I quietly +take to the ship. There is nothing surprising in this. If they but +knew it, almost all men in their degree, some time or other, cherish +very nearly the same feelings towards the ocean with me. There now is +your insular city of the Manhattoes, belted round by wharves as Indian +isles by coral reefs—commerce surrounds it with her surf. Right +and left, the streets take you waterward. Its extreme down-town is +the battery, where that noble mole is washed by waves, and cooled by +breezes, which a few hours previous were out of sight of land. Look +at the crowds of water-gazers there. Circumambulate the city of a +dreamy Sabbath afternoon. Go from Corlears Hook to Coenties Slip, and +from thence, by Whitehall northward. What do you see?—Posted +like silent sentinels all around the town, stand thousands upon +thousands of mortal men fixed in ocean reveries. Some leaning against +the spiles; some seated upon the pier-heads; some looking over the +bulwarks glasses! of ships from China; some high aloft in the +rigging, as if striving to get a still better seaward peep. But these +are all landsmen; of week days pent up in lath and plaster—tied +to counters, nailed to benches, clinched to desks. How then is this? +Are the green fields gone? What do they here? But look! here come +more crowds, pacing straight for the water, and seemingly bound for a +dive. Strange! Nothing will content them but the extremest limit of +the land; loitering under the shady lee of yonder warehouses will not +suffice. No. They must get just as nigh the water as they possibly +can without falling in. And there they stand—miles of +them—leagues. </p> + +<p> Inlanders all, they come from lanes and alleys, streets and +avenues, —north, east, south, and west. Yet here they all +unite. Tell me, does the magnetic virtue of the needles of the +compasses of all those ships attract them thither? Once more. Say, +you are in the country; in some high land of lakes. Take almost any +path you please, and ten to one it carries you down in a dale, and +leaves you there by a pool in the stream. There is magic in it. Let +the most absent-minded of men be plunged in his deepest +reveries—stand that man on his legs, set his feet a-going, and +he will infallibly lead you to water, if water there be in all that +region. Should you ever be athirst in the great American desert, try +this experiment, if your caravan happen to be supplied with a +metaphysical professor. Yes, as every one knows, meditation and water +are wedded for ever. + But here is an artist. He desires to paint you the dreamiest, +shadiest, quietest, most enchanting bit of romantic landscape in all +the valley of the Saco. What is the chief element he employs? There +stand his trees, each with a hollow trunk, as if a hermit and a +crucifix were within; and here sleeps his meadow, and there sleep his +cattle; and up from yonder cottage goes a sleepy smoke. Deep into +distant woodlands winds a mazy way, reaching to overlapping spurs of +mountains bathed in their hill-side blue. But though the picture lies +thus tranced, and though this pine-tree shakes down its sighs like +leaves upon this shepherd's head, yet all were vain, unless the +shepherd's eye were fixed upon the magic stream before him. Go visit +the Prairies in June, when for scores on scores of miles you wade +knee-deep among Tiger-lilies—what is the one charm wanting? +—Water —there is not a drop of water there! Were Niagara +but a cataract of sand, would you travel your thousand miles to see +it? Why did the poor poet of Tennessee, upon suddenly receiving two +handfuls of silver, deliberate whether to buy him a coat, which he +sadly needed, or invest his money in a pedestrian trip to Rockaway +Beach? Why is almost every robust healthy boy with a robust healthy +soul in him, at some time or other crazy to go to sea? Why upon your +first voyage as a passenger, did you yourself feel such a mystical +vibration, when first told that you and your ship were now out of +sight of land? Why did the old Persians hold the sea holy? Why did +the Greeks give it a separate deity, and own brother of Jove? Surely +all this is not without meaning. And still deeper the meaning of that +story of Narcissus, who because he could not grasp the tormenting, +mild image he saw in the fountain, plunged into it and was drowned. +But that same image, we ourselves see in all rivers and oceans. It is +the image of the ungraspable phantom of life; and this is the key to +it all. Now, when I say that I am in the habit of going to sea +whenever I begin to grow hazy about the eyes, and begin to be over +conscious of my lungs, I do not mean to have it inferred that I ever +go to sea as a passenger. For to go as a passenger you must needs +have a purse, and a purse is but a rag unless you have something in +it. Besides, passengers get sea-sick —grow quarrelsome +—don't sleep of nights —do not enjoy themselves much, as a +general thing; —no, I never go as a passenger; nor, though I am +something of a salt, do I ever go to sea as a Commodore, or a Captain, +or a Cook. I abandon the glory and distinction of such offices to +those who like them. For my part, I abominate all honorable +respectable toils, trials, and tribulations of every kind whatsoever. +It is quite as much as I can do to take care of myself, without taking +care of ships, barques, brigs, schooners, and what not. And as for +going as cook, — though I confess there is considerable glory in +that, a cook being a sort of officer on ship-board —yet, +somehow, I never fancied broiling fowls; —though once broiled, +judiciously buttered, and judgmatically salted and peppered, there is +no one who will speak more respectfully, not to say reverentially, of +a broiled fowl than I will. It is out of the idolatrous dotings of +the old Egyptians upon broiled ibis and roasted river horse, that you +see the mummies of those creatures in their huge bake-houses the +pyramids. No, when I go to sea, I go as a simple sailor, right before +the mast, plumb down into the forecastle, aloft there to the royal +mast-head. True, they rather order me about some, and make me jump +from spar to spar, like a grasshopper in a May meadow. And at first, +this sort of thing is unpleasant enough. It touches one's sense of +honor, particularly if you come of an old established family in the +land, the van Rensselaers, or Randolphs, or Hardicanutes. And more +than all, if just previous to putting your hand into the tar-pot, you +have been lording it as a country schoolmaster, making the tallest +boys stand in awe of you. The transition is a keen one, I assure you, +from the schoolmaster to a sailor, and requires a strong decoction of +Seneca and the Stoics to enable you to grin and bear it. But even +this wears off in time. What of it, if some old hunks of a +sea-captain orders me to get a broom and sweep down the decks? What +does that indignity amount to, weighed, I mean, in the scales of the +New Testament? Do you think the archangel Gabriel thinks anything the +less of me, + because I promptly and respectfully obey that old hunks in that +particular instance? Who aint a slave? Tell me that. Well, then, +however the old sea-captains may order me about—however they may +thump and punch me about, I have the satisfaction of knowing that it +is all right; that everybody else is one way or other served in much +the same way — either in a physical or metaphysical point of +view, that is; and so the universal thump is passed round, and all +hands should rub each other's shoulder-blades, and be content. Again, +I always go to sea as a sailor, because they make a point of paying me +for my trouble, whereas they never pay passengers a single penny that +I ever heard of. On the contrary, passengers themselves must pay. +And there is all the difference in the world between paying and being +paid. The act of paying is perhaps the most uncomfortable infliction +that the two orchard thieves entailed upon us. But being paid, +—what will compare with it? The urbane activity with which a +man receives money is really marvellous, considering that we so +earnestly believe money to be the root of all earthly ills, and that +on no account can a monied man enter heaven. Ah! how cheerfully we +consign ourselves to perdition! Finally, I always go to sea as a +sailor, because of the wholesome exercise and pure air of the +forecastle deck. For as in this world, head winds are far more +prevalent than winds from astern (that is, if you never violate the +Pythagorean maxim), so for the most part the Commodore on the +quarter-deck gets his atmosphere at second hand from the sailors on +the forecastle. He thinks he breathes it first; but not so. In much +the same way do the commonalty lead their leaders in many other +things, at the same time that the leaders little suspect it. But +wherefore it was that after having repeatedly smelt the sea as a +merchant sailor, I should now take it into my head to go on a whaling +voyage; this the invisible police officer of the Fates, who has the +constant surveillance of me, and secretly dogs me, and influences me +in some unaccountable way —he can better answer than any one +else. And, doubtless, my going on this whaling + voyage, formed part of the grand programme of Providence that was drawn up a +long time ago. It came in as a sort of brief interlude and solo between more +extensive performances. I take it that this part of the bill must have run +something like this: +<list> +<item>Grand Contested Election for the Presidency of the +United States. </item> +<item>Whaling Voyage by one Ishmael. </item> +<item>Bloody Battle in Affghanistan.</item> +</list>Though I cannot tell why it was exactly that those stage +managers, the Fates, put me down for this shabby part of a whaling voyage, +when others were set down for magnificent parts in high tragedies, and short +and easy parts in genteel comedies, and jolly parts in farces —though I +cannot tell why this was exactly; yet, now that I recall all the +circumstances, I think I can see a little into the springs and motives which +being cunningly presented to me under various disguises, induced me to set +about +performing the part I did, besides cajoling me into the delusion that it was +a choice resulting from my own unbiased freewill and discriminating judgment. +chief among these motives was the overwhelming idea of the great whale +himself. Such a portentous and mysterious monster roused all my curiosity. +Then the wild and distant seas where he rolled his island bulk; the +undeliverable, nameless perils of the whale; these, with all the attending +marvels of a thousand Patagonian sights and sounds, helped to sway me to my +wish. With other men, perhaps, such things would not have been inducements; +but as for me, I am tormented with an everlasting itch for things remote. I +love to sail forbidden seas, and land on barbarous coasts. Not ignoring what +is good, I am quick to perceive a horror, and could still be social with +it—would they let me —since it is but well to be on friendly terms with all +the inmates of the place one lodges in. By reason of these things, then, the +whaling voyage was welcome; the great flood-gates of the wonder-world swung +open, and in the wild conceits that swayed me to my purpose, two and two +there floated into my inmost soul, endless processions of the whale, and, mid +most of them all, one grand hooded phantom, like a snow hill in the air. +</p> +</div> +</body> +</text> +</TEI.2> diff --git a/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml b/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml new file mode 100644 index 00000000000..df46cbc7896 --- /dev/null +++ b/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml @@ -0,0 +1,14 @@ +<xsa version="1.0"> + <vendor> + <name>Sebastian Rahtz</name> + <email>sebastian.rahtz@oucs.ox.ac.uk</email> + </vendor> + <product id="fotex"> + <name>Passive TeX</name> + <version>1.3, 10th December 2000</version> + <last-release>20001210</last-release> + <info-url>http://users.ox.ac.uk/~rahtz/passivetex/</info-url> + </product> +</xsa> + + |