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1<head>
2<title>Touschek</title>
3<!-- Changed by: Frank Zimmermann, 18-Jun-2002 -->
4<! IMG ISMAP SRC="http://cern.ch/Frank.Schmidt/dynap/icons/at_work.gif"height=90 Under construction and not yet reliable!!!!!>
5</head>
6
7<body bgcolor="#ffffff">
8
9EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
10<IMG SRC="http://cern.ch/madx/icons/mx7_25.gif" align=right>
11<h2>TOUSCHEK: Touschek Lifetime and Scattering Rates</h2>
12</center>
13
14<P>The TOUSCHEK module computes the Touschek lifetime and the scattering rates
15around a lepton or hadron storage ring, based on the formalism of Piwinski [A.
16Piwinski, &quot;The Touschek Effect in Strong Focusing Storage Rings,&quot; DESY-98-179;
17see also Piwinski's article on Touschek lifetime in the Handbook of Accelerator
18Physics and Engineering (A. Chao, M. Tigner, eds.), World Scientific, 1999] .</P>
19<P>The syntax of the TOUSCHEK command is: </P><PRE>TOUSCHEK, FILE;
20</PRE>TOUSCHEK should be called after a TWISS command. One or several cavities
21with rf voltages should be defined prior to calling TWISS and TOUSCHEK.
22[Warning: Calling EMIT between the TWISS and TOUSCHEK commands leads to TOUSCHEK using wrong beam parameters, even if the BEAM command is reiterated.]
23<p>The momentum acceptance is taken from the bucket size taking into account the
24energy loss per turn <i>U0 </i>from synchrotron radiation. The value of <i>U0</i> 
25is computed from the second synchrotron radiation integral <i>synch_2</i> in the
26TWISS summ table (<i>synch_2</i> is calculated only when the TWISS option 'chrom'
27is invoked), using Eq. (3.61) in Matt Sands' report SLAC-121, which was
28generalized to the case of several harmonic rf systems. If <i>synch_2=0</i>, not
29defined, or not calculated, zero energy loss is assumed. </p>
30<p>In the case of several&nbsp; rf systems with nonzero voltages, it is assumed
31that the lowest frequency system defines the phase of the outer point on the
32separatrix when calculating the momentum acceptance, and that all
33higher-harmonic systems are either in phase or in anti-phase to the lowest
34frequency system. (Note: if a storage rings really uses a different rf scheme,
35one would need to change the acceptance function in the routine <i>cavtousch </i>
36for that ring.) <br>
37&nbsp;</p>
38<P>The arguments have the following meaning: </P>
39<UL>
40  <LI>FILE: The name of the output file (default: 'touschek')
41  </UL>
42<P>Example: </P><PRE>BEAM,PARTICLE=PROTON,ENERGY=450,NPART=1.15e11,EX=7.82E-9,EY=7.82E-9,ET=5.302e-5,SIGE=7.164e-4,SIGT=0.1124,RADIATE=TRUE;
43</PRE>
44<PRE>...
45</PRE>
46<PRE>USE,PERIOD=FODO;   
47</PRE>
48<PRE>...       
49</PRE>
50<PRE>VRF=400;
51</PRE>
52<PRE>...
53</PRE>
54<PRE>SELECT,FLAG=TWISS,CLEAR;
55TWISS,CHROM,TABLE,FILE;
56</PRE>
57<PRE>TOUSCHEK,FILE;
58</PRE>
59<PRE>...
60</PRE>
61<br>
62
63The first command defines the beam parameters. It is essential that the
64longitudinal emittances and bunch length are set. The command <I>use</I> selects the beam
65line or sequence. The next command assign a value to the cavity rf voltage vrf
66(example name). The <i>select</i> clear previous assignments to the <i>twiss </i>module,
67<I>twiss
68</I>calculates and saves the values of all twiss parameters for all elements in
69the ring; the <i>touschek</i> command computes the Touschek lifetime and writes
70it to the file 'touschek' (default name).
71<P>The results are stored in the <I>TOUSCHEK </I>tables, and can be written to a
72file (with the default name 'touschek' in the example above), or values can be
73extracted from the table using the value command as follows </P>
74<P>value,table(touschek,name),table(touschek,s),table(touschek,tli),table(touschek,tliw),table(touschek,tlitot); </P>
75<P><font face="Times New Roman" size="3">where 'name' denotes the name of a
76beamline element, <i>s</i> the position of the center of the element,<i> tli</i> 
77the instanteneous Touschek loss rate within the element, and <i>tliw</i> the
78instantaneous rate weighted by the length of the element divided by the
79circumference (its contribution to the total loss rate), and<i> tlitot </i>the
80accumulated loss rate adding the rates over all beamline elements through the
81present position. The value of <i>tlitot</i> at the end of the beamline is the
82inverse of the Touschek lifetime in units of 1/s.</font></P>
83<P>Also, all results can be printed to a file using the command </P>
84<P>write,table=touschek,file;</P>
85<P>The MADX Touschek module was developed by
86<a href="mailto:catia.milardi@lnf.infn.it">Catia Milardi</a> and
87<a href="mailto:frank.zimmermann@cern.ch">Frank Zimmermann . </a><br>
88</P>
89<ADDRESS><A href="http://consult.cern.ch/xwho/people/62690">frankz</A> 
90        11.03.2008
91</ADDRESS></BODY></HTML>
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