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2<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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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_NORMAL Module" /> 
8  <meta name="keywords"    content="MADX MAD-X PTC PTC_NORMAL Non-Linear Machine Parameters" /> 
9  <link rel="stylesheet" type="text/css" href="madxdoc.css" /> 
10  <title>PTC_NORMAL Module (Non-Linear Machine Parameters)</title> 
11      <!-- Created by: Valery KAPIN, 21-Mar-2006 --> 
12      <!-- Changed by: ____________, ___________ --> 
13      <style> 
14<!-- 
15div.Section1 
16      {page:Section1;} 
17span.SpellE 
18      {} 
19--> 
20</style> 
21</head> 
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_NORMAL Module <br> 
30      (Non-Linear Machine Parameters)</h1> 
31</center> 
32</div> 
33 
34<div class="madxdocContent"> 
35       
36<div> 
37<p align="left"> 
38The <b>PTC_NORMAL module</b>&nbsp;of MAD-X [<a href="#F._Schmidt">a</a>,<a href="#d Amico">b</a>] is based on PTC 
39code. This module takes full advantage of the PTC Normal Form analysis which is 
40a&nbsp; considerable upgrade of what was available with the Lie Algebra 
41technique used in MAD8. It allows to calculate dispersions, chromaticities, 
42anharmonicities and Hamiltonian terms to very high order. In fact, the order is 
43only limited by the RAM memory of your computer and your patience to wait for 
44the results. </p> 
45<p align="left"> 
46The number of terms per order increases with some power law. The internal MAD-X 
47tables are not adequate to keep such large amounts of data. On the other hand, 
48only a reduced set of this data is actually needed by the user. Thus a much 
49easier and flexible solution is to gather the users  requirements with a series 
50of special MAD-X command called <var class="option">SELECT_PTC_NORMAL</var>. A 
51special MAD-X table is dynamically built using just those commands and it will 
52be filled by the next call to the&nbsp; <var class="option">PTC_NORMAL</var>-command. </p> 
53<p align="left"> 
54Another essential advantage of this table is the fact that it is structured to 
55facilitate exchange of Normal Form (including Hamiltonian terms of high order) 
56between MAD-X modules. The immediate goal is to use this table to allow 
57non-linear matching inside the present MAD-X MATCHING module.</p> 
58</div> 
59 
60<hr /> 
61 
62<div> 
63      <dl> 
64       <dt>Synopsis</dt> 
65       <dd><i><code>PTC_CREATE_UNIVERSE;</code></i></dd> 
66       <dd><i><code>PTC_CREATE_LAYOUT, model=integer,method=integer, 
67       nst=integer, [exact];</code></i></dd> 
68       <dd><code>..............................<br> 
69       SELECT_PTC_NORMAL, dx,..., gnfu;</code></dd> 
70       <dd><code>..............................</code></dd> 
71       <dd><code>PTC_NORMAL;<br> 
72       WRITE, table=normal_results, file=normal_results;</code></dd> 
73       <dd><code>..............................</code></dd> 
74       <dd><i><code>PTC_END; </code></i></dd> 
75</dl> 
76</div> 
77 
78<div> 
79      <dl> 
80       <dt>Commands</dt> 
81       <dd> 
82<div> 
83      <dl> 
84       <dt class="command"><var><strong><b>SELECT_PTC_NORMAL, <br> 
85       </b></strong></var><strong> 
86       <b> dx</b>=integer<b>, dpx</b>=integer<b>, dy</b>=integer<b>, dpy</b>=integer<b>,<br> 
87       q1</b>=0<b>, dq1</b>=integer<b>, q2</b>=0<b>, dq2</b>=integer<b>,
88       <br> 
89       anhx</b>=integer array, <b>anhy</b>=integer array<b>, <br> 
90       gnfu</b>=integer,0,0<b>, haml</b>=integer,0,0<b>,<br> 
91       <font color="#FF0000">eign</font></b><font color="#FF0000">=integer, 
92       integer</font><b>;</b></strong></dt> 
93       <dd> 
94       <div> 
95        <dl> 
96         <dt>Description</dt> 
97         <dd> 
98              <!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
99              <strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> --> 
100              The <var class="command">SELECT_PTC_NORMAL </var>command selects 
101         parameters to be calculated by the next <var class="command"> 
102         PTC_NORMAL </var>command. The dispersion and tune parameters are defined 
103         by a name and an integer number specifying their 
104         order. For example, the notation &quot;dx=2&quot; means 
105         the horizontal dispersion to second order <i>D<sub>x</sub></i><sup>(2)</sup>=<font face="Times New Roman">&#8706;</font><sup>(2)</sup><i>x</i><sub>co</sub>/<font face="Times New Roman">&#8706;<i>&#948;</i></font><sub><i>p</i></sub><sup>(2)</sup>, 
106         where &quot;co&quot; is abbreviation of &quot;closed orbit&quot;. The 
107         anharmonisities are defined by a name and three 
108         integer numbers: the first is the order of <font face="Times New Roman"><i>&#949;</i></font><sub>1</sub>, 
109         the second is the order of <font face="Times New Roman"><i>&#949;</i></font><sub>2</sub>, 
110         the third is the order of <font face="Times New Roman"><i>&nbsp;&#948;</i></font><sub><i>p</i></sub>. For example, the notation &quot;anhx=2,0,0&quot; 
111         means second order in <font face="Times New Roman"><i>&#949;</i></font><sub>1</sub>:
112         <font face="Times New Roman">&#8706;</font><sup>(2)</sup><i>q</i><sub>1</sub>/<font face="Times New Roman">&#8706;<i>&#949;</i></font><sub>1</sub><sup>(2)</sup>. </dd> 
113         <dd><font color="#FF0000">Components of the eigenvectors at the 
114         end of the structure can be specified by two integers: 
115         the first integer defines the&nbsp; eigenvector number, the 
116         second integer defines the coordinate {<i>x</i>, <i> 
117         p<sub>x</sub></i>, <i>y</i>, <i>p<sub>y</sub></i>, <i>t</i>,<i> 
118         p<sub>t</sub></i>}.</font></dd> 
119         <dd>The Generating Function can be specified by
120         <font face="Times New Roman">{ <i>n</i>, 0, 0}. </font>The positive and negative values of&nbsp; 
121         <i>n</i> 
122         define the order of upright or skew resonances, respectively. 
123         The integers <i>n</i><sub>2</sub> and <i>n</i><sub>3</sub> are 
124         reserved for a future upgrade.
125              For example, &quot;gnfu=-5, 0, 0&quot; will calculate all 
126         Generating Function terms for skew decapoles. In the output 
127         table, one finds the cosine, sine and amplitude coefficients as 
128         denoted by &quot;GNFC&quot;, &quot;GNFS&quot;, and &quot;GNFA&quot;, respectively.</dd> 
129         <dd>Similarily, the Hamiltonian terms can be specified by
130         <font face="Times New Roman">{ <i>n</i>, 0, 0}. </font>The positive and negative values of&nbsp; 
131         <i>n</i> define the order of upright or skew resonances, 
132         respectively.
133              For example, &quot;haml=3, 0, 0&quot; will calculate all 
134         Hamiltonian terms for upright sextupoles. In the output table, 
135         one finds the cosine, sine and amplitude coefficients as denoted 
136         by &quot;HAMC&quot;, &quot;HAMS&quot;, and &quot;HAMA&quot;, respectively.</dd> 
137        </dl></div></dd> 
138       <dd> 
139       <div> 
140        <dl> 
141        <dl> 
142         <dt>Parameters</dt> 
143         <dd> 
144         <table cellspacing="0" cellpadding="3" border="1" id="table3"> 
145          <tr> 
146           <th>Notation</th> 
147           <th>Meaning</th> 
148           <th>Value</th> 
149          </tr> 
150          <tr> 
151           <td>DX, DPX, <br> 
152           DY,DPY</td> 
153           <td>dispersions, <i>D<sub>x</sub></i><sup>(<i>n</i>)</sup>, <i>D<sub>px</sub></i><sup>(<i>n</i>)</sup>,
154           <i><br> 
155           D<sub>y</sub></i><sup>(<i>n</i>)</sup>, <i>D<sub>py</sub></i><sup>(<i>n</i>)</sup></td> 
156           <td> 
157           <p align="center"><i>n</i></td> 
158          </tr> 
159          <tr> 
160           <td>Q1, Q2</td> 
161           <td> 
162           <p align="left">horizontal and vertical <br> 
163           tunes <i>q</i><sub>1</sub><sup>(0)</sup>,
164           <i>q</i><sub>2</sub><sup>(0)</sup></td> 
165           <td> 
166           <p align="center">0</td> 
167          </tr> 
168          <tr> 
169           <td>DQ1, DQ2</td> 
170           <td>derivatives of horizontal <br> 
171           and
172           vertical tunes <font face="Times New Roman"><br> 
173           &#8706;</font><sup>(<i>n</i>)</sup><i>q</i><sub>1</sub>/<font face="Times New Roman">&#8706;<i>&#948;</i></font><sub><i>p</i></sub><sup>(<i>n</i>)</sup>, <font face="Times New Roman">&#8706;</font><sup>(<i>n</i>)</sup><i>q</i><sub>2</sub>/<font face="Times New Roman">&#8706;<i>&#948;</i></font><sub><i>p</i></sub><sup>(<i>n</i>)</sup> </td> 
174           <td> 
175           <p align="center"><i>n</i></td> 
176          </tr> 
177          <tr> 
178           <td>ANHX, ANHY</td> 
179           <td>Anharmonicities</td> 
180           <td> 
181           <p align="center"><i>n</i>(<font face="Times New Roman"><i>&#949;</i></font><sub>1</sub>),
182           <i>n</i>(<font face="Times New Roman"><i>&#949;</i></font><sub>2</sub>),
183           <i><br> 
184           n</i>(<font face="Times New Roman"><i>&#948;</i></font><sub><i>p</i></sub>)</td> 
185          </tr> 
186          <tr> 
187           <td>GNFU</td> 
188           <td>Generating Function&nbsp; </td> 
189           <td> 
190           <p align="center"><font face="Times New Roman"> <i>n</i>, 0, 0</font></td> 
191          </tr> 
192          <tr> 
193           <td>HAML</td> 
194           <td>Hamiltonian </td> 
195           <td> 
196           <p align="center"><font face="Times New Roman"> <i>n</i>, 0, 0</font></td> 
197          </tr> 
198          <tr> 
199           <td><font color="#FF0000">EIGN</font></td> 
200           <td><font color="#FF0000">Eigenvector (the <i>n</i><sub>2</sub>-th 
201           component <br> 
202           of the <i>n</i><sub>1</sub>-th eigenvector)</font></td> 
203           <td> 
204           <p align="center"><font color="#FF0000"><i>n</i><sub>1</sub>,
205           <i>n</i><sub>2</sub></font></td> 
206          </tr> 
207          </table></dd> 
208        </dl> 
209        </dl></div></dd> 
210       <dt class="command"><var><strong><b>PTC_NORMAL, <br> 
211&nbsp;&nbsp;&nbsp; icase=</b>integer, </strong></var><strong> 
212       <var class="option">normal</var>, <b>closed_orbit</b>, <b><br> 
213&nbsp;&nbsp;&nbsp; no</b>=integer,
214       <b>map_table, deltap</b>=double<b>;</b></strong></dt> 
215       <dd> 
216       <div> 
217        <dl> 
218         <dt>Description</dt> 
219         <dd> 
220              <!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br />
221              <strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> --> 
222              The calculation of the parameters 
223         specified by the preceding&nbsp; <var class="command">SELECT_PTC_NORMAL </var> 
224         commands is initiated by the <var class="command">PTC_NORMAL </var>command, 
225         which operates on the working beam line defined in the latest
226         <a href="../control/general.html#use"> 
227         USE</a> command. The options for <var class="command"> 
228         PTC_NORMAL </var>command are 
229         described in the table below. </dd> 
230         <dt>Options</dt> 
231         <dd> 
232         <table cellspacing="0" cellpadding="3" border="1" id="table1" width="571"> 
233          <tr> 
234           <th>Option</th> 
235           <th>Meaning</th> 
236           <th width="69">Default Value</th> 
237           <th width="57">Value Type</th> 
238          </tr> 
239          <tr> 
240           <td>ICASE</td> 
241           <td><span lang="EN-US">the user-defined dimensionality 
242           <br> 
243           of
244           the phase-space (4, 5 or 6)</span></td> 
245           <td width="69"> 
246           <p align="center">4</td> 
247           <td width="57">integer</td> 
248          </tr> 
249          <tr> 
250           <td>NO</td> 
251           <td>the order of the map.</td> 
252           <td width="69"> 
253           <p align="center">1</td> 
254           <td width="57">integer</td> 
255          </tr> 
256          <tr> 
257           <td>CLOSED_ORBIT</td> 
258           <td><span lang="EN-US">the switch to turn on <br> 
259           the closed 
260           orbit calculation.</span></td> 
261           <td width="69"> 
262           <p align="center">.FALSE.</td> 
263           <td width="57">logical</td> 
264          </tr> 
265          <tr> 
266           <td>DELTAP</td> 
267           <td> 
268           <p align="left">relative momentum offset <br> 
269           for reference closed orbit</td> 
270           <td width="69"> 
271           <p align="center">0.0</td> 
272           <td width="57">double</td> 
273          </tr> 
274          <tr> 
275           <td>MAPTABLE</td> 
276           <td>turn on the map-table in memory</td> 
277           <td width="69"> 
278           <p align="center">.FALSE.</td> 
279           <td width="57">logical</td> 
280          </tr> 
281          <tr> 
282           <td>NORMAL</td> 
283           <td>turn on the calculation of <br> 
284           the Normal 
285           Form</td> 
286           <td width="69"> 
287           <p align="center">.FALSE.</td> 
288           <td width="57">logical</td> 
289          </tr> 
290          </table></dd> 
291         <dt>Remarks</dt> 
292         <dd><p><b>MAPTABLE</b>:&nbsp;(requires no=1) creates the one-turn matrix which 
293         can be used by the next
294         <a href="../ptc_twiss/ptc_twiss.html"> 
295         PTC_TWISS</a> command.</dd> 
296           <dt>Example</dt> 
297           <dd>The simple example is located on the Web-page for the 
298           <a href="http://cern.ch/frs/mad-X_examples/ptc_normal"> 
299           <var class="command">PTC_NORMAL</var> example</a>.</dd> 
300        </dl></div></dd> 
301      </dl></div> 
302    </dd> 
303</dl> 
304      <dl> 
305       <dt>References for PTC_NORMAL</dt> 
306      </dl> 
307      <ol type="a"> 
308       <li><a name="F._Schmidt">F. Schmidt</a>, &quot;`<a href="http://cern.ch/madx/doc/MPPE012.pdf">MAD-X PTC Integration</a>'', 
309       Proc. of the 2005 PAC Conference in Knoxville, USA, pp.1272.</li> 
310       <li>E.T. <a name="d Amico">d Amico</a>, &quot;Nonlinear parameters from PTC&quot;,
311       <a href="http://cern.ch/frs/MAD-X_minutes/Meeting-7">MAD-X 
312       Meeting 7 (29.11.2004)</a>, notes (<a href="http://cern.ch/frs/MAD-X_minutes/Meeting-7/Nonlinear_parameters_from_PTC.doc">doc</a>-file).</li> 
313       <li><a name="A._Schoch">A. Schoch</a>, &quot;Theory of linear and non-linear 
314       perturbations of betatron oscillations in alternating-gradient 
315       synchrotrons &quot;,
316       <a href="http://cern.ch/madx/doc/yellow-report-1957.pdf">CERN-27-21</a>, 1958.</li> 
317      </ol> 
318</div> 
319<div> 
320      <dl> 
321       <dt>.See Also</dt> 
322       <dd> 
323       <a href="http://cern.ch/frs/mad-X_examples/ptc_normal"> 
324       <var class="command">PTC_NORMAL</var> example</a>,
325       <a href="../ptc_general/ptc_general.html">PTC 
326       Set-up Parameters</a>.</dd> 
327</dl> 
328</div> 
329 
330</div> 
331 
332<hr /> 
333<address> 
334<span lang="EN-US"> 
335<a style="color: blue; text-decoration: underline; text-underline: single" href="mailto:kapin@itep.ru"> 
336V.&nbsp;<span class="SpellE">Kapin<span style="text-decoration: none"> </span></span> 
337</a></span>(ITEP) and <span lang="EN-US"> 
338<a style="color: blue; text-decoration: underline; text-underline: single" href="mailto:Frank.Schmidt@cern.ch"> 
339F.&nbsp;Schmidt</a>, </span>March  2006</address> 
340 
341</body> 
342</html> 
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