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1	<?xml version="1.0" encoding="ISO-8859-1" ?>
2	<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
3	"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
4	<html xmlns="http://www.w3.org/1999/xhtml">
5	<head>
6	<meta name="author" content="Valery Kapin & Frank Schmidt" />
7	<meta name="description" content="MADX PTC_TWISS Module" />
8	<meta name="keywords" content="MADX MAD-X PTC PTC_TWISS TWISS Twiss-parameters Ripken TWISS3" />
9	<link rel="stylesheet" type="text/css" href="madxdoc.css" />
10	<title>MAD-X PTC_TWISS Module</title>
11	<!-- Created by: Valery KAPIN, 21-Mar-2006 -->
12	<!-- Changed by: Frank Schmidt 04-Apr-2006 -->
13	<style>
14	<!--
15	div.Section1
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17	span.SpellE
18	{}
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22
23	<body bgcolor="#ffffff">
24
25	<div style="text-align:center;">
26	<center>
27	EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
28	<img SRC="http://cern.ch/madx/icons/mx7_25.gif" align="right" alt="MAD-X Logo" />
29	<h1>PTC_TWISS Module <br>
30	(Ripken Optics Parameters)</h1>
31	</center>
32	</div>
33
34	<div class="madxdocContent">
35
36	<div>
37	<p align="left">
38	The <b>PTC_TWISS module</b> of MAD-X [<a href="#F._Schmidt">a</a>] is based on
39	the PTC code. It
40	is a supplementary to the TWISS module. The Twiss parameters are calculated in  Ripken's style (invented by G. Ripken in 1970 [31] and most accessible in
41	Ref.<font face="Times New Roman"> [<a href="#G. Ripken">b</a>]</font>).
42	These parameters were available in MAD8 using the TWISS3 command. This module is
43	a typical example of the advantages when using PTC and its Normal Form technique
44	(and of course the object-oriented Fortran90 coding): once the rather modest
45	programming has been performed the Twiss calculation will always be
46	automatically correct for all machine conditions like closed orbit, coupling or
47	after a new element has been introduced into the code. In a traditional coding
48	like in MAD8 this depends on reprogramming and modifying the code at various
49	places which is inherently error-prone.</p>
50	<p align="left">
51	The PTC_TWISS tracks a special representation of the beam in three degrees of
52	freedom. It works on the coupled lattice functions defined in Ref.<font face="Times New Roman">[<a href="#G. Ripken">b</a>]</font>,
53	which are essentially the projections of the lattice functions for the
54	eigen-modes on the three planes. The PTC_TWISS lists the projections of the
55	ellipses of motion onto the three planes (<i>x</i>, <i>p<sub>x</sub></i>), (<i>y</i>,
56	<i>p<sub>y</sub></i>), (<i>t</i>, <i>p<sub>t</sub></i>) expressed them via the
57	Ripken's parameters <i><font face="Symbol">b</font><sub>k</sub></i><sub>,<i>j</i></sub>,
58	<i><font face="Symbol">a</font><sub>k</sub></i><sub>,<i>j, </i></sub><i>
59	<font face="Symbol">g</font><sub>k</sub></i><sub>,<i>j</i></sub> along with the
60	phase advances   <i><font face="Symbol">m</font></i><sub><i>j</i></sub>
61	in selected positions, where index <font color="#FF0000"> <i>k</i>=1...3</font> refers
62	<font color="#FF0000">to the plane (<i>x</i>, <i>y</i>,...)</font>, and
63	the index <font color="#FF0000"> <i>j</i>=1...3 denotes the eigen-mode</font>. The PTC_TWISS also calculates the
64	dispersion values <i>D</i><sub>1</sub>,...,<i>D</i><sub>4</sub>. In the MAD-X
65	commands and tables, these parameters are denoted as <code>beta11,...,beta33,
66	alfa11,...,alfa33, gama11,...,gama33, mu1,...,mu3, disp1,...,disp4</code>,
67	respectively.</p>
68
69	<p>The Ripken parametrization can be transformed into the Edwards-Teng
70	parametrization (used in twiss proper) using the formulae of
71	Ref.<font face="Times New Roman"> [<a
72	href="#V.A. Lebedev">d</a>]</font>. The parameters are noted as
73	<code>betx, bety, alfx, alfy</code> and the coupling matrix: R11, R12,
74	R21 and R22. In absence of coupling it holds:
75	<code>betx=beta11</code>, <code>bety=beta22</code>,
76	<code>alfx=alfa11</code> and <code>alfy=alfa22</code>.</p>
77
78	<p>PTC_TWISS can also compute the deltap/p-dependency of the Twiss
79	parameters. The column names <code>beta11p,...,beta33p,
80	alfa11p...,alfa33p, gama11p,...,gama33p</code> denote the derivatives
81	of the optics parameters w.r.t. deltap/p. <font color="#FF0000">If one
82	is interested in evaluating deltap/p-dependency of the Twiss
83	parameters, one must ensure that the order (no) of the map is set to 2
84	at least.</font>. The derivatives of the dispersion w.r.t. deltap/p
85	have column names: <code>disp1p,...,disp4p</code>. Second and third
86	order derivatives have respective column names:
87	<code>disp1p2,...,disp4p2</code> for the second order, and
88	<code>disp1p3,...,disp4p3</code> for the third order.</p>
89
90	<p>
91	In addition, we compute momentum compaction factor <font
92	face="Symbol">a</font><sub>c</sub> up to 1st order (for icase=5) or
93	3rd order (for icase=56). The values appear in the header of the
94	ptc_twiss output file (zero means the value has not been
95	computed). This feature is currently only available in the development
96	version.</p>
97	<p align="left">
98	For clarification: <font color="#FF0000">in the 4-D case, there is the
99	following correspondence between MAD-X and the Ripken's notations: <code>beta11</code><font face="Symbol"><code><font face="Symbol">®</font></code></font><i><font face="Symbol">b</font></i><sub><i>x</i>I</sub>, <code>beta12</code><font face="Symbol"><code><font face="Symbol">®</font></code></font><i><font face="Symbol">b</font></i><sub><i>x</i>II</sub>, <code>beta21</code><font face="Symbol"><code><font face="Symbol">®</font></code></font><i><font face="Symbol">b</font></i><sub><i>y</i>I</sub>, <code>beta22</code><font face="Symbol"><code><font face="Symbol">®</font></code></font><i><font face="Symbol">b</font></i><sub><i>y</i>II</sub>, </font>
100	while in the uncoupled 4-D case <code>beta11</code> is the same as
101	the classical <i><font face="Symbol">b</font><sub>x </sub></i>(<code>betx</code>)
102	and  <code>beta22 </code>is <i><font face="Symbol">b</font><sub>y </sub></i>
103	(<code>bety</code>), while  <code>beta12 </code>and  <code>beta21 </code>
104	are zero. When there is coupling all <code>betaNN </code>are non-zero and <code>
105	beta11</code> , <code>beta22 </code>are distinctively different from  <i><font face="Symbol">b</font><sub>x </sub></i>
106	, <i><font face="Symbol">b</font><sub>y</sub></i>, respectively.</p>
107	<p align="left">
108	PTC_TWISS also tracks the eigenvectors and prints them to Twiss table according to the SELECT command
109	(flag=ptc_twiss). Either all 36 components or
110	particular components of the eigenvectors can be selected with
111	<font face="Courier New">eign</font> or <font face="Courier New">eign<i>ij</i></font>,
112	respectively  (<font color="#FF0000"><i>j</i></font> = number of eigenvector,
113	<font color="#FF0000"><i>i</i></font> = number of
114	coordinate {<i>x</i>, <i>
115	p<sub>x</sub></i>, <i>y</i>, <i>p<sub>y</sub></i>, <i>t</i>,<i>
116	p<sub>t</sub></i>}).</p>
117
118	<p>
119	For ring lattices, PTC_TWISS computes momentum compaction, transition energy, as well as other one-turn characteristics such as the tunes (Q1,Q2 and if icase=6 with cavity Qs) and chromaticities (for no>=2).
120	</p>
121	</div>
122
123	<hr />
124
125	<div>
126	<dl>
127	<dt>Synopsis</dt>
128	<dd><i><code>PTC_CREATE_UNIVERSE;</code></i></dd>
129	<dd><i><code>PTC_CREATE_LAYOUT, model=integer,method=integer,
130	nst=integer, [exact];</code></i></dd>
131	<dd><code>..............................<br>
132	SELECT, flag=ptc_twiss, clear;</code></dd>
133	<dd><code>SELECT, flag=ptc_twiss, column=name, s,
134	<br>
135	beta11,...,beta33,alfa11,..., alfa33,gama11,...,gama33,
136	<br>
137	beta11p,...,beta33p,alfa11p,...,alfa33p,gama11p,...,gama33p,
138	<br>
139	mu1,...,mu3,
140	<br>
141	disp1,...,disp4,
142	<br>
143	disp1p,...,disp4p,
144	<br>
145	disp1p2,...,disp4p2,
146	<br>
147	disp1p3,...,disp4p3,
148	</code></dd>
149	<dd><code>[<font color="#FF0000">eign], eign11, ...,eign16,...,eign61,...,eign66;</font></code></dd>
150	<dd><code>..............................</code></dd>
151	<dd><code>PTC_TWISS;</code></dd>
152	<dd><code>..............................</code></dd>
153	<dd><i><code>PTC_END; </code></i></dd>
154	</dl>
155	</div>
156
157	<div>
158	<dl>
159	<dt>Commands</dt>
160	<dd>
161	<div>
162	<dl>
163	<dt class="command"><var><strong><b>PTC_TWISS, <br>
164	icase=</b>integer, </strong></var><strong>
165	<var class="option">deltap</var>=double, <b>closed_orbit</b>, <b>slice_magnets</b>, <b><br>
166	range=</b>string<b>, file[=</b>string<b>], table[=</b>string<b>],<br>
167	initial_matrix_table, initial_matrix_manual, initial_map_manual, beta0=</b>string<b>,
168	<br>
169	betx=</b>double,<b> alfx=</b>double<b>, mux=</b>double<b>,
170	<br>
171	bety=</b>double,<b> alfy=</b>double<b>, muy=</b>double<b>,
172	<br>
173	dx=</b>double,<b> dpx=</b>double,<b> dy=</b>double,<b> dpy=</b>double,<b><br>
174	</b><var class="option">x</var>=double, <var class="option">px</var>=double,
175	<var class="option">y</var>=double, <var class="option">py</var>=double,
176	<var class="option">t</var>=double, <var class="option">pt</var>=double,<br>
177	<b>re11</b>=double, <b>re12</b>=double, ... ,<b>re16</b>=double,<br>
178
179	................................................................<br>
180	<b>re61</b>=double, <b>re62</b>=double, ... ,<b>re66</b>=double;
181	</strong><var><strong>  </strong></var></dt>
182	<dd>
183	<div>
184	<dl>
185	<dt>Description</dt>
186	<dd>
187	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
188	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
189	The <var class="command">PTC_TWISS </var>command causes
190	computation of the Twiss parameters in
191	the Ripken's style. It operates on the working beam line defined in the latest
192	<a href="../control/general.html#use">
193	USE</a> command. Several options can be specified, the most
194	important being <var class="option">icase, deltap</var>,
195	<var class="option">closed_orbit, slice_magnets,</var> <var class="option">no,
196	</var>and
197	<var class="option">file, table</var>. (see the table below).
198	Other options should be specified for particular tasks.
199	Applications for the <var class="command">PTC_TWISS </var>
200	command are similar to the <var class="command">
201	<a href="../twiss/twiss.html">TWISS</a></var>-command.
202	The PTC_TWISS can be applied to two basic tasks. It can calculate
203	either a <a href="#Periodical_Solution">periodical solution</a>
204	or a <a href="#Initial_Conditions">solution with initial
205	conditions</a>.</dd>
206	<dt>Options</dt>
207	<dd>
208	<table cellspacing="0" cellpadding="3" border="1" id="table1" width="789">
209	<tr>
210	<th width="143">Option</th>
211	<th colspan="2">Meaning</th>
212	<th width="84">Default Value</th>
213	<th width="57">Value Type</th>
214	</tr>
215	<tr>
216	<td width="143"><a name="ICASE">ICASE</a></td>
217	<td colspan="2"><span lang="EN-US">the user-defined dimensionality
218	of the phase-space (4, 5 or 6). Note that the value is internally set to 56 when attempting to set icase=6 with no cavity.</span></td>
219	<td width="84">4</td>
220	<td width="57">integer</td>
221	</tr>
222	<tr>
223	<td width="143"><a name="NO">NO</a></td>
224	<td colspan="2"><span lang="EN-US">the order of the map, which is often
225	supplied as 1 but must be at least set to 2 to retrieve chromaticities
226	for instance.
227	For evaluating the Twiss parameters derivatives w.r.t. deltap/p, one
228	must pass order 2 at least.
229	</span></td>
230	<td width="84">1</td>
231	<td width="57">integer</td>
232	</tr>
233	<tr>
234	<td width="143">DELTAP</td>
235	<td colspan="2">
236	<p align="left">relative momentum offset for reference closed orbit.</td>
237	<td width="84">0.0</td>
238	<td width="57">double</td>
239	</tr>
240	<tr>
241	<td width="143">CLOSED_ORBIT</td>
242	<td colspan="2"><span lang="EN-US">the switch to turn on
243	the closed orbit calculation
244	(</span><a href="#Periodical_Solution">periodical solution</a>
245	ONLY)<span lang="EN-US">. </span></td>
246	<td width="84">.FALSE.</td>
247	<td width="57">logical</td>
248	</tr>
249	<tr>
250	<td width="143">DELTAP_DEPENDENCY</td>
251	<td colspan="2"><span lang="EN-US">the switch to turn on computation of the Twiss and dispersion derivatives w.r.t. deltap/p. Derivation formula assume that icase=5, so that deltap/p is supplied as a parameter.</span></td>
252	<td width="84">.FALSE.</td>
253	<td width="57">logical</td>
254	</tr>
255	<tr>
256	<td width="143">SLICE_MAGNETS</td>
257	<td colspan="2"><span lang="EN-US">the switch to turn on
258	the evaluation of Twiss parameters at each thin slice inside
259	successive magnets, instead of at the middle of each magnet.
260	Slices are located at the so-called
261	'integration nodes' determined by the number of steps (nst) selected
262	when creating the PTC layout. Note that extremities and fringes are skipped,
263	whereas only the inner slices are kept.</span>
264	</td>
265	<td width="84">.FALSE.</td>
266	<td width="57">logical</td>
267	</tr>
268	<tr>
269	<td width="143">CENTER_MAGNETS</td>
270	<td colspan="2"><span lang="EN-US">the switch to turn on
271	the evaluation of Twiss parameters at the middle of each magnet.
272	This relies on internal slicing and
273	'integration nodes' as determined by the number of steps (nst) selected
274	when creating the PTC layout. This number is assumed to be even otherwise the program issues a warning. </span>
275	</td>
276	<td width="84">.FALSE.</td>
277	<td width="57">logical</td>
278	</tr>
279
280	<tr>
281	<td rowspan="2" width="143">FILE</td>
282	<td width="79">omitted </td>
283	<td width="279">no output written to a file</td>
284	<td width="84"> </td>
285	<td width="57"> </td>
286	</tr>
287	<tr>
288	<td width="79">present</td>
289	<td width="279">the name of the file for printing
290	the PTC_TWISS
291	output.</td>
292	<td width="84">ptc_twiss</td>
293	<td width="57">string</td>
294	</tr>
295	<tr>
296	<td width="143" rowspan="2">TABLE</td>
297	<td>omitted </td>
298	<td>no output written to a internal table</td>
299	<td width="84"> </td>
300	<td width="57"> </td>
301	</tr>
302	<tr>
303	<td>present</td>
304	<td>the name of the internal PTC_TWISS table </td>
305	<td width="84">ptc_twiss</td>
306	<td width="57">string</td>
307	</tr>
308	<tr>
309	<td rowspan="2" width="143">SUMMARY_FILE</td>
310	<td width="79">omitted </td>
311	<td width="279">no output written to a file</td>
312	<td width="84"> </td>
313	<td width="57"> </td>
314	</tr>
315	<tr>
316	<td width="79">present</td>
317	<td width="279">the name of the file for printing
318	the PTC_TWISS_SUMMARY table
319	output.</td>
320	<td width="84">ptc_twiss_summary</td>
321	<td width="57">string</td>
322	</tr>
323	<tr>
324	<td width="143" rowspan="2">SUMMARY_TABLE</td>
325	<td>omitted </td>
326	<td>no output written to a internal table</td>
327	<td width="84"> </td>
328	<td width="57"> </td>
329	</tr>
330	<tr>
331	<td>present</td>
332	<td>the name of the internal PTC_TWISS_SUMMARY table </td>
333	<td width="84">ptc_twiss_summary</td>
334	<td width="57">string</td>
335	</tr>
336	<tr>
337	<td width="143">
338	<a href="../Introduction/ranges.html#range">
339	RANGE</a></td>
340	<td colspan="2">specifies a segment of beam-line for <br>
341	the PTC_TWISS calculation</td>
342	<td width="84">#s/#e</td>
343	<td width="57">string</td>
344	</tr>
345	<tr>
346	<td width="143">
347	INITIAL_MATRIX_TABLE</td>
348	<td colspan="2"><span lang="EN-US">Reading
349	the transfer matrix from the
350	map-table in memory (preceding </span> <var class="command">
351	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var> command
352	needed).</td>
353	<td width="84">.FALSE.</td>
354	<td width="57">logical</td>
355	</tr>
356	<tr>
357	<td width="143">
358	INITIAL_MATRIX_MANUAL</td>
359	<td colspan="2"><span lang="EN-US">Using the input
360	variables RE11,...,RE66 (see next entry) as the transfer matrix. </span></td>
361	<td width="84">.FALSE.</td>
362	<td width="57">logical</td>
363	</tr>
364	<tr>
365	<td width="143">
366	INITIAL_MAP_MANUAL</td>
367	<td colspan="2"><span lang="EN-US">Using the input map stored beforehand
368	in file fort.18 (e.g. by some initial run of
369	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a>).
370	</span></td>
371	<td width="84">.FALSE.</td>
372	<td width="57">logical</td>
373	</tr>
374	<tr>
375	<td width="143">
376	RE11,..., RE66</td>
377	<td colspan="2">Values of the 6x6 transfer matrix. </td>
378	<td width="84">unit matrix</td>
379	<td width="57">double</td>
380	</tr>
381	<tr>
382	<td width="143">
383	BETA0</td>
384	<td colspan="2"><span lang="EN-US">The name of the </span>
385	<var class="command">BETA0</var><span lang="EN-US">-block,
386	which contains the Twiss parameters for the
387	input. When icase=6, this information must be complemented
388	by supplying a value for 'betz' on the ptc_twiss command line.</span></td>
389	<td width="84">beta0</td>
390	<td width="57">string</td>
391	</tr>
392	<tr>
393	<td width="143">
394	betx, alfx, mux, bety, alfy, muy,
395	dx,dpx,dy, dpy</td>
396	<td colspan="2"><span lang="EN-US">
397	<a href="../twiss/twiss.html">Twiss and dispersion parameters</a> </span><i>
398	<font face="Symbol">b</font><sub>x,y</sub></i>,
399	<i><font face="Symbol">a</font><sub>x</sub></i><sub>,<i>y,
400	</i></sub><i><font face="Symbol">g</font><sub>x,y,
401	</sub></i><span lang="EN-US"><i>D<sub>x</sub></i>,
402	<i>D<sub>px</sub></i>, <i>D<sub>y</sub></i>, <i>
403	D<sub>py</sub></i> </span>
404	<a
405	href="../Introduction/bibliography.html#edwards">(Edwards and Teng)</a><span lang="EN-US">.</span></td>
406	<td width="84">0</td>
407	<td width="57">double</td>
408	</tr>
409	<tr>
410	<td width="143">
411	x, px, y, py, t, pt</td>
412	<td colspan="2">The
413	<a href="../Introduction/tables.html#canon">
414	<strong>canonical</strong></a> coordinates of
415	the initial orbit.</td>
416	<td width="84">0</td>
417	<td width="57">double</td>
418	</tr>
419	</table></dd>
420	<dt>Remarks</dt>
421	<dd><b>ICASE</b>:   <span lang="EN-US">It can be
422	internally corrected by the code. For example, if RF cavity has the voltage set to zero and
423	for <a href="#ICASE">icase</a>=6, the code sets
424	<a href="#ICASE">icase</a>=4.<br>
425	</span></dd>
426	</dl></div></dd>
427	</dl></div>
428	</dd>
429	<dt><a name="Periodical_Solution">Periodical Solution</a></dt>
430	<dd>
431	<div>
432	<dl>
433	<dt class="command"><var><strong><b>PTC_TWISS, <br>
434	icase=</b>integer, </strong></var><strong>
435	<var class="option">deltap</var>=double, <b>closed_orbit</b>, <b><br>
436	range=</b>string<b>, file[=</b>string<b>], table[=</b>string<b>];</b></strong></dt>
437	<dd>
438	<div>
439	<dl>
440	<dt>Description</dt>
441	<dd>
442	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
443	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
444	This is the simplest form of the <var class="command">PTC_TWISS</var>
445	command, which computes the periodic solution for a specified
446	beam line. It may accept  all basic options described in
447	the above table.</dd>
448	</dl></div></dd>
449	</dl></div>
450	</dd>
451
452	<dt><a name="Slicing_Magnets">Evaluation of Twiss parameters inside magnets</a></dt>
453	<dd>
454	<div>
455	<dl>
456	<dt class="command"><var><strong><b>PTC_TWISS, <br>
457	icase=</b>integer, </strong></var><strong>
458	<var class="option">deltap</var>=double, <b>closed_orbit</b>, <b> slice_magnets</b> <b><br>
459	range=</b>string<b>, file[=</b>string<b>], table[=</b>string<b>];</b></strong></dt>
460	<dd>
461	<div>
462	<dl>
463	<dt>Description</dt>
464	<dd>
465	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
466	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
467	This computes the periodic solution for a specified
468	beam line and evaluates the Twiss parameters at each thin-slice
469	(a.k.a "integration-node") inside magnets. The number of such integration-nodes
470	is given by the number of steps (nst) selected when creating the PTC layout.
471	All other basic options described in the above table may be selected
472	.</dd>
473
474	<dt>Example</dt>
475	<dd>An example is found in the
476	<a href="http://isscvs.cern.ch/cgi-bin/viewcvs-all.cgi/madX-examples/REF/ptc_twiss/SliceMagnets/?root=madx-examples">
477	<var class="command">PTC_TWISS</var> Examples'</a> repository.
478	.</dd>
479
480	</dl></div></dd>
481	</dl></div>
482	</dd>
483
484
485
486
487	<dt>Solution with <a name="Initial_Conditions">Initial Conditions</a></dt>
488	<dd>
489	<div>
490	<dl>
491	<dt class="command"><b>Code Logic:</b><strong><b>  </b></strong></dt>
492	<dd> </dd>
493	<dd>
494	<table border="1" width="39%" id="table11" bgcolor="#CCFFCC">
495	<tr>
496	<td>
497	<dl>
498	<dd>
499	<p class="important"><font size="2" face="Courier">IF
500	("initial_matrix_table"=ON .AND. <br>&    {the map-table exists})   THEN<font color="#000000">
501	<br>   (</font></font><font color="#000000"><font size="2">from
502	a <a href="#map-table">Map-Table</a></font><font size="2" face="Courier">)</font></font></dd>
503	<dd>
504	<p class="important"><font size="2" face="Courier">ELSEIF("initial_map_manual"=ON) THEN<font color="#000000"><br>   (</font></font><font color="#000000"><font size="2">from
505	a <a href="#Given_Map_File">Given Map File</a></font><font size="2" face="Courier">)</font></font></dd>
506	<dd>
507	<p class="important"><font size="2" face="Courier">ELSEIF("initial_matrix_manual"=ON) THEN<font color="#000000"><br>   (</font></font><font color="#000000"><font size="2">from
508	a <a href="#Given_Matrix">Given Matrix</a></font><font size="2" face="Courier">)</font></font></dd>
509	<dd>
510	<p class="important"><font size="2" face="Courier">ELSEIF(BETA0 block =ON) THEN
511	<font color="#000000"><br>   (</font></font><font color="#000000"><font size="2">from
512	Twiss Parameters via <a href="#BETA0-block">BETA0-block</a></font><font size="2" face="Courier">)</font></font></dd>
513	<dd>
514	<p class="important"><font size="2" face="Courier">ELSE<br>
515	<font color="#000000">   (</font></font><font color="#000000"><font size="2">from
516	<a href="#Given_Twiss">Given Twiss</a> Parameters</font><font size="2" face="Courier">)</font></font></dd>
517	<dd>
518	<p class="important"><font face="Courier" size="2">ENDIF</font></dd>
519	</dl></td>
520	</tr>
521	</table>
522	</dd>
523	</dl></div></dd>
524	</dl>
525	<dl>
526	<dd>
527	<div>
528	<dl>
529	<dl>
530	<dt class="command"><b><u><i>Initial Values from a
531	<font color="#FF0000"><a name="map-table">Map-Table</a></font></i></u></b><var><strong><b><u><i>
532	<br>
533	(obtainable by a preceding </i></u></b></strong></var> <var class="command">
534	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var><b><i>
535	</i></b><var><strong><b><u><i>command)</i></u></b></strong><b><i><strong><u>:<br>
536	</u></strong></i><strong>    PTC_TWISS,<br>        icase=</b>integer,
537	</strong></var><strong><var class="option">deltap</var>=double,
538	<b>closed_orbit</b>,  <b><br>        range=string, file[=</b>string<b>],
539	table[=</b>string<b>],<br>        initial_matrix_table</b>;
540	</strong><var><strong>  </strong></var></dt>
541	<dd>
542	<div>
543	<dl>
544	<dt>Description</dt>
545	<dd>
546	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
547	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
548	<var class="command">PTC_TWISS</var> calculates a solution
549	with initial conditions given as a map-table of
550	preceding ring or beam-line. It requires the input option
551	<var class="option">initial_matrix_table</var> and an existence of the map-table in
552	memory, which was generated
553	by a  preceding <var class="command">
554	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var> command.</dd>
555	<dt>Example</dt>
556	<dd>An example is found in the
557	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
558	<var class="command">PTC_TWISS</var> Examples</a> in
559	the folder
560	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss/Example3/">
561	"Example3"</a>.</dd>
562	</dl></div></dd>
563	</dl>
564
565
566
567
568
569
570	<!-- map-file entry -->
571
572	<dl>
573	<dt class="command"><b><u><i>Initial Values from a
574	<font color="#FF0000"><a name="Given_Map_File">Map-File</a></font></i></u></b><var><strong><b><u><i>
575	<br>
576	(obtainable by a preceding </i></u></b></strong></var> <var class="command">
577	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var><b><i>
578	</i></b><var><strong><b><u><i>command)</i></u></b></strong><b><i><strong><u>:<br>
579	</u></strong></i><strong>    PTC_TWISS,<br>        icase=</b>integer,
580	</strong></var><strong><var class="option">deltap</var>=double,
581	<b>closed_orbit</b>,  <b><br>        range=string, file[=</b>string<b>],
582	table[=</b>string<b>],<br>        initial_map_manual</b>;
583	</strong><var><strong>  </strong></var></dt>
584	<dd>
585	<div>
586	<dl>
587	<dt>Description</dt>
588	<dd>
589	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
590	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
591	<var class="command">PTC_TWISS</var> calculates a solution
592	with initial conditions given as a map-file fort.18 obtained from a
593	preceding ring or beam-line. It requires the input option
594	<var class="option">initial_map_manual</var> and an existence of the map-file named
595	a fort.18 file, which was generated
596	by a  preceding <var class="command">
597	<a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var> command.</dd>
598	<dt>Example</dt>
599	<dd>An example is found in the
600	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
601	<var class="command">PTC_TWISS</var> Examples</a> in
602	the folder
603	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss/Example3/">
604	"Example3"</a>.</dd>
605	</dl></div></dd>
606	</dl>
607
608
609	<!-- end of map-file entry -->
610
611
612
613
614
615
616	<dt class="command"><u><i><b>Initial Values from a
617	<font color="#FF0000"> <a name="Given_Matrix">
618	Given Matrix</a></font></b></i></u><var><strong><b><u><i>:</i></u><br>
619	PTC_TWISS,<br>
620	icase=</b>integer, </strong></var>
621	<strong><var class="option">deltap</var>=double, <b>closed_orbit</b>,
622	<b><br>
623	range=string, file=</b>string<b>,
624	table=</b>string<b>,<br>
625	initial_matrix_manual, <br>
626	re11</b>=double, <b>re12</b>=double,
627	... ,<b>re16</b>=double,<br>
628
629	................................................................<br>
630	<b>    re61</b>=double, <b>re62</b>=double,
631	... ,<b>re66</b>=double;</strong></dt>
632	<dd>
633	<div>
634	<dl>
635	<dt>Description</dt>
636	<dd>
637	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
638	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
639	<var class="command">PTC_TWISS</var> calculates a solution
640	with initial conditions given by the matrix, which is
641	"manually" entered on the command-line. It requires the
642	option <var class="option">initial_matrix_manual</var>.
643	MAD-X expects a symplectic 6x6 transfer matrix as input.  </dd>
644	<dt>Example</dt>
645	<dd>An example is found in the
646	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
647	<var class="command">PTC_TWISS</var> Examples</a> in the
648	folder
649	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss/Example4/">
650	"Example4"</a>.</dd>
651	</dl></div></dd>
652	<dt class="command"><u><i><b>Initial Values from Twiss Parameters via
653	<font color="#FF0000">
654	<a name="BETA0-block">BETA0-block</a></font></b></i></u><var><strong><b><u><i>:</i></u><br>
655	PTC_TWISS,<br>
656	icase=</b>integer, </strong></var>
657	<strong><var class="option">deltap</var>=double, <b>closed_orbit</b>,
658	<b><br>
659	range=string, file[=</b>string<b>],
660	table[=</b>string<b>],<br>
661	beta0=</b>string<b>;</b></strong></dt>
662	<dd>
663	<div>
664	<dl>
665	<dt>Description</dt>
666	<dd>
667	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
668	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
669	<var class="command">PTC_TWISS</var> calculates a solution
670	with initial conditions given by Twiss parameters, which
671	are transferred from  <span lang="EN-US">the </span>
672	<var class="command">BETA0</var><span lang="EN-US">-block.
673	</span> The data in the <span lang="EN-US">the
674	</span><var class="command">BETA0</var><span lang="EN-US">-block
675	have to be filled </span>by a combination of the
676	<a href="../control/general.html#savebeta">
677	SAVEBETA</a> and
678	<a href="../twiss/twiss.html">
679	TWISS</a> commands of a preceding ring or beam-line. Note, that
680	this case is limited to uncoupled motion of the preceding
681	machine.</dd>
682	<dt>Example</dt>
683	<dd>An example is found in the
684	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
685	<var class="command">PTC_TWISS</var> Examples</a> in the
686	folder
687	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss/Example1/">
688	"Example1"</a>.</dd>
689	</dl></div></dd>
690	<dt class="command"><u><i><b>Initial Values from the
691	<font color="#FF0000">
692	<a name="Given_Twiss">Given Twiss</a></font> Parameters</b></i></u><var><strong><b><u><i>:</i></u><br>
693	PTC_TWISS,<br>
694	icase=</b>integer, </strong></var>
695	<strong><var class="option">deltap</var>=double, <b>closed_orbit</b>,
696	<b><br>
697	range=string, file[=</b>string<b>],
698	table[=</b>string<b>],<br>
699	</b><b>betx=</b>double,<b> alfx=</b>double<b>,
700	mux=</b>double<b>, <br>
701	bety=</b>double,<b> alfy=</b>double<b>,
702	muy=</b>double<b>, <br>
703	dx=</b>double,<b> dpx=</b>double,<b> dy=</b>double,<b> dpy=</b>double,<b><br>
704	</b><var class="option">    x</var>=double,
705	<var class="option">px</var>=double, <var class="option">y</var>=double,
706	<var class="option">py</var>=double, <var class="option"><br>
707	t</var>=double, <var class="option">pt</var>=double;</strong></dt>
708	<dd>
709	<div>
710	<dl>
711	<dt>Description</dt>
712	<dd>
713	<!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
714	<strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> -->
715	<var class="command">PTC_TWISS</var> calculates a solution
716	with initial conditions given by the Twiss parameters,
717	which are explicitly typed  on the
718	command line. Note, that this case is also limited to
719	uncoupled motion of the preceding ring or beam-line.</dd>
720	<dt>Example</dt>
721	<dd>An example is found in the
722	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
723	<var class="command">PTC_TWISS</var> Examples</a> in the
724	folder
725	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss/Example2/">
726	"Example2"</a>.</dd>
727	</dl></div></dd>
728	</dl></div></dd>
729	</dl>
730	<dl>
731	<dt>References for PTC_TWISS</dt>
732	</dl>
733	<ol type="a">
734	<li><a name="F._Schmidt">F. Schmidt</a>, "`<a href="http://cern.ch/madx/doc/MPPE012.pdf">MAD-X PTC Integration</a>'',
735	Proc. of the 2005 PAC Conference in Knoxville, USA, pp.1272.</li>
736	<li><a name="G. Ripken">G. Ripken</a> and F. Willeke, "<a href="http://cern.ch/madx/doc/1988_Ripken.pdf">Methods of
737	Beam Optics</a>", DESY 88114, 1988.</li>
738	<li><a name="K._Zhang">K. Zhang</a>, "PTC twiss with initial TWISS
739	parameters",
740	<a href="http://cern.ch/frs/MAD-X_minutes/Meeting-13/minutes.html">
741	MAD-X Meeting 13 (04.07.2005)</a>,  <font color="#000000">slides in
742	<a href="http://cern.ch/frs/MAD-X_minutes/Meeting-13/Input_of_PTC_TWISS_module.ppt">
743	ppt</a>.</font></li>
744	<li><a name="V.A. Lebedev">V.A. Lebedev</a> and S.A. Bogacsz, "<a href="http://cern.ch/madx/doc/1748-0221_5_10_P10010.pdf">Betatron motion with coupling of horizontal and vertical degrees of motion</a>", Thomas Jefferson National Accelerator Facility 2010.</li>
745
746	</ol>
747	</div>
748	<div>
749	<dl>
750	<dt>See Also</dt>
751	<dd>
752	<var class="command">
753	<a href="../twiss/twiss.html">TWISS</a></var>,
754	<a href="http://cern.ch/frs/mad-X_examples/ptc_twiss">
755	<var class="command">PTC_TWISS</var> Examples</a>.</dd>
756	</dl>
757	</div>
758
759	</div>
760
761	<hr />
762	<address>
763	<span lang="EN-US">
764	<a style="color: blue; text-decoration: underline; text-underline: single" href="mailto:kapin@itep.ru">
765	V. <span class="SpellE">Kapin<span style="text-decoration: none"> </span></span>
766	</a></span>(ITEP) and <span lang="EN-US">
767	<a style="color: blue; text-decoration: underline; text-underline: single" href="mailto:Frank.Schmidt@cern.ch">
768	F. Schmidt</a>, </span>March 2006</address>
769
770	</body>
771	</html>

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