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| 5 | <head> |
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| 6 | <meta name="author" content="Valery Kapin & Frank Schmidt" /> |
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| 7 | <meta name="description" content="MADX PTC_TWISS Module" /> |
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| 8 | <meta name="keywords" content="MADX MAD-X PTC PTC_TWISS TWISS Twiss-parameters Ripken TWISS3" /> |
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| 9 | <link rel="stylesheet" type="text/css" href="madxdoc.css" /> |
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| 10 | <title>MAD-X PTC_TWISS Module</title> |
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| 11 | <!-- Created by: Valery KAPIN, 21-Mar-2006 --> |
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| 12 | <!-- Changed by: Frank Schmidt 04-Apr-2006 --> |
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| 21 | </head> |
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| 23 | <body bgcolor="#ffffff"> |
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| 24 | |
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| 25 | <div style="text-align:center;"> |
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| 26 | <center> |
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| 27 | EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH |
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| 28 | <img SRC="http://cern.ch/madx/icons/mx7_25.gif" align="right" alt="MAD-X Logo" /> |
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| 29 | <h1>PTC_TWISS Module <br> |
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| 30 | (Ripken Optics Parameters)</h1> |
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| 31 | </center> |
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| 32 | </div> |
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| 33 | |
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| 34 | <div class="madxdocContent"> |
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| 35 | |
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| 36 | <div> |
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| 37 | <p align="left"> |
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| 38 | The <b>PTC_TWISS module</b> of MAD-X [<a href="#F._Schmidt">a</a>] is based on |
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| 39 | the PTC code. It |
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| 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 |
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| 41 | Ref.<font face="Times New Roman"> [<a href="#G. Ripken">b</a>]</font>). |
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| 42 | These parameters were available in MAD8 using the TWISS3 command. This module is |
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| 43 | a typical example of the advantages when using PTC and its Normal Form technique |
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| 44 | (and of course the object-oriented Fortran90 coding): once the rather modest |
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| 45 | programming has been performed the Twiss calculation will always be |
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| 46 | automatically correct for all machine conditions like closed orbit, coupling or |
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| 47 | after a new element has been introduced into the code. In a traditional coding |
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| 48 | like in MAD8 this depends on reprogramming and modifying the code at various |
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| 49 | places which is inherently error-prone.</p> |
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| 50 | <p align="left"> |
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| 51 | The PTC_TWISS tracks a special representation of the beam in three degrees of |
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| 52 | freedom. It works on the coupled lattice functions defined in Ref.<font face="Times New Roman">[<a href="#G. Ripken">b</a>]</font>, |
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| 53 | which are essentially the projections of the lattice functions for the |
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| 54 | eigen-modes on the three planes. The PTC_TWISS lists the projections of the |
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| 55 | ellipses of motion onto the three planes (<i>x</i>, <i>p<sub>x</sub></i>), (<i>y</i>, |
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| 56 | <i>p<sub>y</sub></i>), (<i>t</i>, <i>p<sub>t</sub></i>) expressed them via the |
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| 57 | Ripken's parameters <i><font face="Symbol">b</font><sub>k</sub></i><sub>,<i>j</i></sub>, |
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| 58 | <i><font face="Symbol">a</font><sub>k</sub></i><sub>,<i>j, </i></sub><i> |
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| 59 | <font face="Symbol">g</font><sub>k</sub></i><sub>,<i>j</i></sub> along with the |
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| 60 | phase advances <i><font face="Symbol">m</font></i><sub><i>j</i></sub> |
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| 61 | in selected positions, where index <font color="#FF0000"> <i>k</i>=1...3</font> refers |
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| 62 | <font color="#FF0000">to the plane (<i>x</i>, <i>y</i>,...)</font>, and |
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| 63 | the index <font color="#FF0000"> <i>j</i>=1...3 denotes the eigen-mode</font>. The PTC_TWISS also calculates the |
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| 64 | dispersion values <i>D</i><sub>1</sub>,...,<i>D</i><sub>4</sub>. In the MAD-X |
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| 65 | commands and tables, these parameters are denoted as <code>beta11,...,beta33, |
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| 66 | alfa11,...,alfa33, gama11,...,gama33, mu1,...,mu3, disp1,...,disp4</code>, |
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| 67 | respectively.</p> |
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| 68 | |
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| 69 | <p>The Ripken parametrization can be transformed into the Edwards-Teng |
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| 70 | parametrization (used in twiss proper) using the formulae of |
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| 71 | Ref.<font face="Times New Roman"> [<a |
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| 72 | href="#V.A. Lebedev">d</a>]</font>. The parameters are noted as |
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| 73 | <code>betx, bety, alfx, alfy</code> and the coupling matrix: R11, R12, |
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| 74 | R21 and R22. In absence of coupling it holds: |
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| 75 | <code>betx=beta11</code>, <code>bety=beta22</code>, |
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| 76 | <code>alfx=alfa11</code> and <code>alfy=alfa22</code>.</p> |
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| 77 | |
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| 78 | <p>PTC_TWISS can also compute the deltap/p-dependency of the Twiss |
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| 79 | parameters. The column names <code>beta11p,...,beta33p, |
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| 80 | alfa11p...,alfa33p, gama11p,...,gama33p</code> denote the derivatives |
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| 81 | of the optics parameters w.r.t. deltap/p. <font color="#FF0000">If one |
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| 82 | is interested in evaluating deltap/p-dependency of the Twiss |
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| 83 | parameters, one must ensure that the order (no) of the map is set to 2 |
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| 84 | at least.</font>. The derivatives of the dispersion w.r.t. deltap/p |
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| 85 | have column names: <code>disp1p,...,disp4p</code>. Second and third |
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| 86 | order derivatives have respective column names: |
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| 87 | <code>disp1p2,...,disp4p2</code> for the second order, and |
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| 88 | <code>disp1p3,...,disp4p3</code> for the third order.</p> |
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| 89 | |
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| 90 | <p> |
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| 91 | In addition, we compute momentum compaction factor <font |
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| 92 | face="Symbol">a</font><sub>c</sub> up to 1st order (for icase=5) or |
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| 93 | 3rd order (for icase=56). The values appear in the header of the |
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| 94 | ptc_twiss output file (zero means the value has not been |
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| 95 | computed). This feature is currently only available in the development |
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| 96 | version.</p> |
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| 97 | <p align="left"> |
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| 98 | For clarification: <font color="#FF0000">in the 4-D case, there is the |
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| 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> |
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| 100 | while in the uncoupled 4-D case <code>beta11</code> is the same as |
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| 101 | the classical <i><font face="Symbol">b</font><sub>x </sub></i>(<code>betx</code>) |
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| 102 | and <code>beta22 </code>is <i><font face="Symbol">b</font><sub>y </sub></i> |
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| 103 | (<code>bety</code>), while <code>beta12 </code>and <code>beta21 </code> |
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| 104 | are zero. When there is coupling all <code>betaNN </code>are non-zero and <code> |
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| 105 | beta11</code> , <code>beta22 </code>are distinctively different from <i><font face="Symbol">b</font><sub>x </sub></i> |
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| 106 | , <i><font face="Symbol">b</font><sub>y</sub></i>, respectively.</p> |
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| 107 | <p align="left"> |
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| 108 | PTC_TWISS also tracks the eigenvectors and prints them to Twiss table according to the SELECT command |
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| 109 | (flag=ptc_twiss). Either all 36 components or |
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| 110 | particular components of the eigenvectors can be selected with |
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| 111 | <font face="Courier New">eign</font> or <font face="Courier New">eign<i>ij</i></font>, |
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| 112 | respectively (<font color="#FF0000"><i>j</i></font> = number of eigenvector, |
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| 113 | <font color="#FF0000"><i>i</i></font> = number of |
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| 114 | coordinate {<i>x</i>, <i> |
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| 115 | p<sub>x</sub></i>, <i>y</i>, <i>p<sub>y</sub></i>, <i>t</i>,<i> |
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| 116 | p<sub>t</sub></i>}).</p> |
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| 117 | |
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| 118 | <p> |
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| 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). |
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| 120 | </p> |
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| 121 | </div> |
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| 122 | |
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| 123 | <hr /> |
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| 124 | |
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| 125 | <div> |
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| 126 | <dl> |
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| 127 | <dt>Synopsis</dt> |
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| 128 | <dd><i><code>PTC_CREATE_UNIVERSE;</code></i></dd> |
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| 129 | <dd><i><code>PTC_CREATE_LAYOUT, model=integer,method=integer, |
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| 130 | nst=integer, [exact];</code></i></dd> |
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| 131 | <dd><code>..............................<br> |
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| 132 | SELECT, flag=ptc_twiss, clear;</code></dd> |
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| 133 | <dd><code>SELECT, flag=ptc_twiss, column=name, s, |
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| 134 | <br> |
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| 135 | beta11,...,beta33,alfa11,..., alfa33,gama11,...,gama33, |
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| 136 | <br> |
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| 137 | beta11p,...,beta33p,alfa11p,...,alfa33p,gama11p,...,gama33p, |
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| 138 | <br> |
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| 139 | mu1,...,mu3, |
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| 140 | <br> |
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| 141 | disp1,...,disp4, |
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| 142 | <br> |
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| 143 | disp1p,...,disp4p, |
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| 144 | <br> |
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| 145 | disp1p2,...,disp4p2, |
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| 146 | <br> |
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| 147 | disp1p3,...,disp4p3, |
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| 148 | </code></dd> |
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| 149 | <dd><code>[<font color="#FF0000">eign], eign11, ...,eign16,...,eign61,...,eign66;</font></code></dd> |
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| 150 | <dd><code>..............................</code></dd> |
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| 151 | <dd><code>PTC_TWISS;</code></dd> |
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| 152 | <dd><code>..............................</code></dd> |
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| 153 | <dd><i><code>PTC_END; </code></i></dd> |
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| 154 | </dl> |
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| 155 | </div> |
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| 156 | |
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| 157 | <div> |
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| 158 | <dl> |
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| 159 | <dt>Commands</dt> |
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| 160 | <dd> |
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| 161 | <div> |
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| 162 | <dl> |
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| 163 | <dt class="command"><var><strong><b>PTC_TWISS, <br> |
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| 164 | icase=</b>integer, </strong></var><strong> |
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| 165 | <var class="option">deltap</var>=double, <b>closed_orbit</b>, <b>slice_magnets</b>, <b><br> |
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| 166 | range=</b>string<b>, file[=</b>string<b>], table[=</b>string<b>],<br> |
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| 167 | initial_matrix_table, initial_matrix_manual, initial_map_manual, beta0=</b>string<b>, |
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| 168 | <br> |
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| 169 | betx=</b>double,<b> alfx=</b>double<b>, mux=</b>double<b>, |
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| 170 | <br> |
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| 171 | bety=</b>double,<b> alfy=</b>double<b>, muy=</b>double<b>, |
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| 172 | <br> |
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| 173 | dx=</b>double,<b> dpx=</b>double,<b> dy=</b>double,<b> dpy=</b>double,<b><br> |
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| 174 | </b><var class="option">x</var>=double, <var class="option">px</var>=double, |
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| 175 | <var class="option">y</var>=double, <var class="option">py</var>=double, |
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| 176 | <var class="option">t</var>=double, <var class="option">pt</var>=double,<br> |
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| 177 | <b>re11</b>=double, <b>re12</b>=double, ... ,<b>re16</b>=double,<br> |
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| 178 | |
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| 179 | ................................................................<br> |
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| 180 | <b>re61</b>=double, <b>re62</b>=double, ... ,<b>re66</b>=double; |
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| 181 | </strong><var><strong> </strong></var></dt> |
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| 182 | <dd> |
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| 183 | <div> |
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| 184 | <dl> |
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| 185 | <dt>Description</dt> |
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| 186 | <dd> |
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| 187 | <!-- <strong>TRACK, DELTAP= double, ONEPASS, DUMP, ONETABLE, FILE= string;</strong> (MADX version 1)<br /> |
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| 188 | <strong>TRACK, DELTAP= double, ONEPASS, DAMP, QUANTUM, DUMP, ONETABLE, FILE= string;</strong> (MADX version 2)<br /> --> |
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| 189 | The <var class="command">PTC_TWISS </var>command causes |
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| 190 | computation of the Twiss parameters in |
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| 191 | the Ripken's style. It operates on the working beam line defined in the latest |
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| 192 | <a href="../control/general.html#use"> |
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| 193 | USE</a> command. Several options can be specified, the most |
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| 194 | important being <var class="option">icase, deltap</var>, |
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| 195 | <var class="option">closed_orbit, slice_magnets,</var> <var class="option">no, |
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| 196 | </var>and |
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| 197 | <var class="option">file, table</var>. (see the table below). |
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| 198 | Other options should be specified for particular tasks. |
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| 199 | Applications for the <var class="command">PTC_TWISS </var> |
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| 200 | command are similar to the <var class="command"> |
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| 201 | <a href="../twiss/twiss.html">TWISS</a></var>-command. |
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| 202 | The PTC_TWISS can be applied to two basic tasks. It can calculate |
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| 203 | either a <a href="#Periodical_Solution">periodical solution</a> |
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| 204 | or a <a href="#Initial_Conditions">solution with initial |
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| 205 | conditions</a>.</dd> |
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| 206 | <dt>Options</dt> |
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| 207 | <dd> |
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| 208 | <table cellspacing="0" cellpadding="3" border="1" id="table1" width="789"> |
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| 209 | <tr> |
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| 210 | <th width="143">Option</th> |
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| 211 | <th colspan="2">Meaning</th> |
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| 212 | <th width="84">Default Value</th> |
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| 213 | <th width="57">Value Type</th> |
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| 214 | </tr> |
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| 215 | <tr> |
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| 216 | <td width="143"><a name="ICASE">ICASE</a></td> |
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| 217 | <td colspan="2"><span lang="EN-US">the user-defined dimensionality |
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| 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> |
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| 219 | <td width="84">4</td> |
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| 220 | <td width="57">integer</td> |
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| 221 | </tr> |
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| 222 | <tr> |
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| 223 | <td width="143"><a name="NO">NO</a></td> |
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| 224 | <td colspan="2"><span lang="EN-US">the order of the map, which is often |
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| 225 | supplied as 1 but must be at least set to 2 to retrieve chromaticities |
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| 226 | for instance. |
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| 227 | For evaluating the Twiss parameters derivatives w.r.t. deltap/p, one |
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| 228 | must pass order 2 at least. |
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| 229 | </span></td> |
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| 230 | <td width="84">1</td> |
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| 231 | <td width="57">integer</td> |
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| 232 | </tr> |
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| 233 | <tr> |
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| 234 | <td width="143">DELTAP</td> |
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| 235 | <td colspan="2"> |
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| 236 | <p align="left">relative momentum offset for reference closed orbit.</td> |
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| 237 | <td width="84">0.0</td> |
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| 238 | <td width="57">double</td> |
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| 239 | </tr> |
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| 240 | <tr> |
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| 241 | <td width="143">CLOSED_ORBIT</td> |
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| 242 | <td colspan="2"><span lang="EN-US">the switch to turn on |
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| 243 | the closed orbit calculation |
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| 244 | (</span><a href="#Periodical_Solution">periodical solution</a> |
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| 245 | ONLY)<span lang="EN-US">. </span></td> |
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| 246 | <td width="84">.FALSE.</td> |
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| 247 | <td width="57">logical</td> |
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| 248 | </tr> |
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| 249 | <tr> |
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| 250 | <td width="143">DELTAP_DEPENDENCY</td> |
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| 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> |
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| 252 | <td width="84">.FALSE.</td> |
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| 253 | <td width="57">logical</td> |
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| 254 | </tr> |
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| 255 | <tr> |
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| 256 | <td width="143">SLICE_MAGNETS</td> |
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| 257 | <td colspan="2"><span lang="EN-US">the switch to turn on |
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| 258 | the evaluation of Twiss parameters at each thin slice inside |
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| 259 | successive magnets, instead of at the middle of each magnet. |
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| 260 | Slices are located at the so-called |
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| 261 | 'integration nodes' determined by the number of steps (nst) selected |
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| 262 | when creating the PTC layout. Note that extremities and fringes are skipped, |
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| 263 | whereas only the inner slices are kept.</span> |
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| 264 | </td> |
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| 265 | <td width="84">.FALSE.</td> |
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| 266 | <td width="57">logical</td> |
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| 267 | </tr> |
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| 268 | <tr> |
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| 269 | <td width="143">CENTER_MAGNETS</td> |
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| 270 | <td colspan="2"><span lang="EN-US">the switch to turn on |
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| 271 | the evaluation of Twiss parameters at the middle of each magnet. |
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| 272 | This relies on internal slicing and |
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| 273 | 'integration nodes' as determined by the number of steps (nst) selected |
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| 274 | when creating the PTC layout. This number is assumed to be even otherwise the program issues a warning. </span> |
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| 275 | </td> |
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| 276 | <td width="84">.FALSE.</td> |
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| 277 | <td width="57">logical</td> |
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| 278 | </tr> |
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| 279 | |
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| 280 | <tr> |
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| 281 | <td rowspan="2" width="143">FILE</td> |
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| 282 | <td width="79">omitted </td> |
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| 283 | <td width="279">no output written to a file</td> |
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| 284 | <td width="84"> </td> |
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| 285 | <td width="57"> </td> |
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| 286 | </tr> |
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| 287 | <tr> |
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| 288 | <td width="79">present</td> |
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| 289 | <td width="279">the name of the file for printing |
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| 290 | the PTC_TWISS |
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| 291 | output.</td> |
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| 292 | <td width="84">ptc_twiss</td> |
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| 293 | <td width="57">string</td> |
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| 294 | </tr> |
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| 295 | <tr> |
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| 296 | <td width="143" rowspan="2">TABLE</td> |
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| 297 | <td>omitted </td> |
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| 298 | <td>no output written to a internal table</td> |
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| 299 | <td width="84"> </td> |
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| 300 | <td width="57"> </td> |
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| 301 | </tr> |
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| 302 | <tr> |
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| 303 | <td>present</td> |
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| 304 | <td>the name of the internal PTC_TWISS table </td> |
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| 305 | <td width="84">ptc_twiss</td> |
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| 306 | <td width="57">string</td> |
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| 307 | </tr> |
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| 308 | <tr> |
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| 309 | <td rowspan="2" width="143">SUMMARY_FILE</td> |
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| 310 | <td width="79">omitted </td> |
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| 311 | <td width="279">no output written to a file</td> |
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| 312 | <td width="84"> </td> |
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| 313 | <td width="57"> </td> |
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| 314 | </tr> |
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| 315 | <tr> |
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| 316 | <td width="79">present</td> |
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| 317 | <td width="279">the name of the file for printing |
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| 318 | the PTC_TWISS_SUMMARY table |
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| 319 | output.</td> |
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| 320 | <td width="84">ptc_twiss_summary</td> |
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| 321 | <td width="57">string</td> |
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| 322 | </tr> |
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| 323 | <tr> |
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| 324 | <td width="143" rowspan="2">SUMMARY_TABLE</td> |
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| 325 | <td>omitted </td> |
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| 326 | <td>no output written to a internal table</td> |
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| 327 | <td width="84"> </td> |
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| 328 | <td width="57"> </td> |
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| 329 | </tr> |
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| 330 | <tr> |
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| 331 | <td>present</td> |
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| 332 | <td>the name of the internal PTC_TWISS_SUMMARY table </td> |
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| 333 | <td width="84">ptc_twiss_summary</td> |
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| 334 | <td width="57">string</td> |
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| 335 | </tr> |
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| 336 | <tr> |
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| 337 | <td width="143"> |
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| 338 | <a href="../Introduction/ranges.html#range"> |
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| 339 | RANGE</a></td> |
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| 340 | <td colspan="2">specifies a segment of beam-line for <br> |
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| 341 | the PTC_TWISS calculation</td> |
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| 342 | <td width="84">#s/#e</td> |
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| 343 | <td width="57">string</td> |
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| 344 | </tr> |
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| 345 | <tr> |
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| 346 | <td width="143"> |
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| 347 | INITIAL_MATRIX_TABLE</td> |
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| 348 | <td colspan="2"><span lang="EN-US">Reading |
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| 349 | the transfer matrix from the |
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| 350 | map-table in memory (preceding </span> <var class="command"> |
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| 351 | <a href="../ptc_normal/ptc_normal.html">PTC_NORMAL</a></var> command |
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| 352 | needed).</td> |
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| 353 | <td width="84">.FALSE.</td> |
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| 354 | <td width="57">logical</td> |
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| 355 | </tr> |
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| 356 | <tr> |
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| 357 | <td width="143"> |
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| 358 | INITIAL_MATRIX_MANUAL</td> |
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| 359 | <td colspan="2"><span lang="EN-US">Using the input |
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| 360 | variables RE11,...,RE66 (see next entry) as the transfer matrix. </span></td> |
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| 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> |
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| 720 | <dt>Example</dt> |
---|
| 721 | <dd>An example is found in the |
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| 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>'', |
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| 735 | Proc. of the 2005 PAC Conference in Knoxville, USA, pp.1272.</li> |
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| 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> |
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| 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> |
---|