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Accelerator physics codes
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<h2 id="single-particle-dynamics-codes">Single particle dynamics codes</h2> <p>For many applications it is sufficient to track a single particle through the relevant electric and magnetic fields. Old codes no longer maintained by their original authors or home institutions include: BETA,<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> AGS, ALIGN, COMFORT, DESIGN, DIMAD, HARMON, LEGO, LIAR, MAGIC, MARYLIE, PATRICIA, PETROS, RACETRACK, SYNCH,<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> TRANSPORT, TURTLE, and UAL. Some legacy codes are maintained by commercial organizations for academic, industrial and medical accelerator facilities that continue to use those codes. TRACE 3-D and TURTLE are among the historic codes that are commercially maintained.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p><p>Major maintained codes include: </p> <table><tbody><tr><th></th><th>Single Particle Dynamics</th><th>Spin Tracking</th><th>Taylor Maps</th><th>Weak-Strong Beam-Beam Interaction</th><th>Electromagnetic Field Tracking</th><th>Higher Energy Collective Effects</th><th>Synchrotron Radiation Effects</th><th>Radiation Tracking</th><th>Wakefields</th><th>Extensible</th><th>Notes</th></tr><tr><th>Accelerator Toolbox (AT),<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></th><td>Yes</td><td>Yes<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td></td></tr><tr><th>ASTRA<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><th>For space-charge simulations</th></tr><tr><th>BDSIM<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><th>For particle-matter simulations.</th></tr><tr><th>Bmad (contains PTC)<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><th>Reproduces PTC's unique beam line structures. Simulates X-rays.</th></tr><tr><th>COSY INFINITY<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><th>Arbitrary-order differential-algebraic transfer maps</th></tr><tr><th>DYNAC<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td></td></tr><tr><th>Elegant<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td></td></tr><tr><th>MAD8 and MAD-X (includes PTC)<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></th><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td></td></tr><tr><th>MAD-NG<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></th><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><th>Extensible, embeds LuaJIT</th></tr><tr><th>MERLIN++<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a><a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a></th><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><th>Other: beam-matter interactions, sliced-macroparticle tracking</th></tr><tr><th>OCELOT<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td></td></tr><tr><th>OPA<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td></td></tr><tr><th>OPAL<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a></th><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><th>runs on laptops and on x 10k cores.</th></tr><tr><th>PLACET<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><th>LINAC including wakefields simulations.</th></tr><tr><th>Propaga<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td></td></tr><tr><th>PTC<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td></td></tr><tr><th>SAD<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></th><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td></td></tr><tr><th>SAMM<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></th><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td></td></tr><tr><th>SixTrack<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a></th><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><th>Can run on <a href="/facts/BOINC/RPaqqojG">BOINC</a></th></tr><tr><th>Xsuite<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a></th><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><th>Supports multi <a href="/facts/CPU/Jxp1bqMV">CPU</a> and <a href="/facts/GPU/PTK1RQVp">GPU</a> tracking</th></tr><tr><th>Zgoubi<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a><a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a></th><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><th></th></tr></tbody></table> <h3>Columns</h3> Spin Tracking Tracking of a particle's <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a>. Taylor Maps Construction of Taylor series maps to high order that can be used for simulating particle motion and also can be used for such things as extracting single particle resonance strengths. Weak-Strong Beam-Beam Interaction Can simulate the beam-beam interaction with the simplification that one beam is essentially fixed in size. See below for a list of strong-strong interaction codes. Electromagnetic Field Tracking Can track (ray trace) a particle through arbitrary electromagnetic fields. Higher Energy Collective effects The interactions between the particles in the beam can have important effects on the behavior, control and dynamics. Collective effects take different forms from <a href="/facts/Intrabeam_Scattering/MDWIenR6">Intrabeam Scattering</a> (IBS) which is a direct particle-particle interaction to wakefields which are mediated by the vacuum chamber wall of the machine the particles are traveling in. In general, the effect of direct particle-particle interactions is less with higher energy particle beams. At very low energies, space charge has a large effect on a particle beam and thus becomes hard to calculate. See below for a list of programs that can handle low energy space charge forces. Synchrotron radiation effects <p>Can simulate the effect of synchrotron radiation emission on the particles being tracked. </p> Radiation Tracking Ability to track the <a href="/facts/Synchrotron_radiation/mTsSKmRz">synchrotron radiation</a> (mainly <a href="/facts/X-ray/wseP79cN">X-rays</a>) produced by the acceleration of charged particles. <p>This is not the same as simulating the effect of synchrotron radiation emission on the particles being tracked. </p> Wakefields The electro-magnetic interaction between the beam and the vacuum chamber wall enclosing the beam are known as wakefields. Wakefields produce forces that affect the trajectory of the particles of the beam and can potentially destabilize the trajectories. Extensible Open source and object oriented coding to make it relatively easy to extend the capabilities. <h2 id="space-charge-codes">Space charge codes</h2> <p>The self interaction (e.g. space charge) of the charged particle beam can cause growth of the beam, such as with bunch lengthening, or intrabeam scattering. Additionally, space charge effects may cause instabilities and associated beam loss. Typically, at relatively low energies (roughly for energies where the relativistic gamma factor is less than 10 or so), the Poisson equation is solved at intervals during the tracking using <a href="/facts/Particle-in-cell/EF4cFzg0">particle-in-cell</a> algorithms. Space charge effects lessen at higher energies so at higher energies the space charge effects may be modeled using simpler algorithms that are computationally much faster than the algorithms used at lower energies. Codes that handle low energy space charge effects include: </p> <ul><li>ASTRA<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a></li> <li>Bmad</li> <li>CST Studio Suite<a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a></li> <li>GPT<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a></li> <li>IMPACT<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a></li> <li>ImpactX<a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a></li> <li>mbtrack<a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a></li> <li>ORBIT,<a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a> PyORBIT<a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a></li> <li>OPAL<a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a></li> <li>PyHEADTAIL<a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a></li> <li>Synergia<a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a></li> <li>TraceWin<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a></li> <li>Tranft<a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a></li> <li>VSim<a class="footnote-ref" id="fnref:43" href="#fn:43"><sup>43</sup></a></li> <li>Warp<a class="footnote-ref" id="fnref:44" href="#fn:44"><sup>44</sup></a></li> <li>Xsuite<a class="footnote-ref" id="fnref:45" href="#fn:45"><sup>45</sup></a></li></ul> <p>At higher energies, space charge effects include Touschek scattering and coherent synchrotron radiation (CSR). Codes that handle higher energy space charge include: </p> <ul><li>Bmad</li> <li>ELEGANT</li> <li>MaryLie</li> <li>SAD</li></ul> <h2 id="strong-strong-beam-beam-effects-codes">"Strong-strong" beam-beam effects codes</h2> <p>When two beams collide, the electromagnetic field of one beam will then have strong effects on the other one, called beam-beam effects. So called "weak-strong" simulations model one beam (called the "strong" beam since it affects the other beam) as a fixed distribution (typically a Gaussian distribution) which interacts with the particles of the other "weak" beam. This greatly simplifies the simulation. A full "strong-strong" simulation is more complicated and takes more simulation time. Strong-strong codes include </p> <ul><li>GUINEA-PIG<a class="footnote-ref" id="fnref:46" href="#fn:46"><sup>46</sup></a></li> <li>BeamBeam3D<a class="footnote-ref" id="fnref:47" href="#fn:47"><sup>47</sup></a></li> <li>Xsuite<a class="footnote-ref" id="fnref:48" href="#fn:48"><sup>48</sup></a></li></ul> <h2 id="impedance-computation-codes">Impedance computation codes</h2> <p>An important class of collective effects may be summarized in terms of the beams response to an "<a href="/facts/Impedance_(Accelerator_Physics)/wpllXGPd">impedance</a>". An important job is thus the computation of this impedance for the machine. Codes for this computation include </p> <ul><li>ABCI<a class="footnote-ref" id="fnref:49" href="#fn:49"><sup>49</sup></a></li> <li>ACE3P<a class="footnote-ref" id="fnref:50" href="#fn:50"><sup>50</sup></a></li> <li>CST Studio Suite<a class="footnote-ref" id="fnref:51" href="#fn:51"><sup>51</sup></a></li> <li>GdfidL<a class="footnote-ref" id="fnref:52" href="#fn:52"><sup>52</sup></a></li> <li>TBCI<a class="footnote-ref" id="fnref:53" href="#fn:53"><sup>53</sup></a></li> <li>VSim<a class="footnote-ref" id="fnref:54" href="#fn:54"><sup>54</sup></a></li></ul> <h2 id="magnet-and-other-hardware-modeling-codes">Magnet and other hardware-modeling codes</h2> <p>To control the charged particle beam, appropriate electric and magnetic fields must be created. There are software packages to help in the design and understanding of the magnets, RF cavities, and other elements that create these fields. Codes include </p> <ul><li>ACE3P<a class="footnote-ref" id="fnref:55" href="#fn:55"><sup>55</sup></a></li> <li>COMSOL Multiphysics<a class="footnote-ref" id="fnref:56" href="#fn:56"><sup>56</sup></a></li> <li>CST Studio Suite<a class="footnote-ref" id="fnref:57" href="#fn:57"><sup>57</sup></a></li> <li>OPERA<a class="footnote-ref" id="fnref:58" href="#fn:58"><sup>58</sup></a></li> <li>VSim<a class="footnote-ref" id="fnref:59" href="#fn:59"><sup>59</sup></a></li></ul> <h2 id="lattice-description-and-data-interchange-issues">Lattice description and data interchange issues</h2> <p>Given the variety of modeling tasks, there is not one common data format that has developed. For describing the layout of an accelerator and the corresponding elements, one uses a so-called "lattice file". There have been numerous attempts at unifying the lattice file formats used in different codes. One unification attempt is the Accelerator Markup Language, and the Universal Accelerator Parser.<a class="footnote-ref" id="fnref:60" href="#fn:60"><sup>60</sup></a> Another attempt at a unified approach to accelerator codes is the UAL or Universal Accelerator Library.<a class="footnote-ref" id="fnref:61" href="#fn:61"><sup>61</sup></a> As of 2023 neither of these formats are maintained. </p><p>The file formats used in MAD may be the most common, with translation routines available to convert to an input form needed for a different code. Associated with the Elegant code is a data format called SDDS, with an associated suite of tools. If one uses a Matlab-based code, such as Accelerator Toolbox, one has available all the tools within Matlab. </p><p>For the interchange of particle positions and electromagnetic fields, the OpenPMD<a class="footnote-ref" id="fnref:62" href="#fn:62"><sup>62</sup></a> standard defines a format which can then be implemented with a file format like <a href="/facts/Hierarchical_Data_Format/IaIFvRP1">HDF5</a>. </p> <h2 id="codes-in-applications-of-particle-accelerators">Codes in applications of particle accelerators</h2> <p>There are many applications of particle accelerators. For example, two important applications are elementary <a href="/facts/Particle_physics/YgIuyj2t">particle physics</a> and <a href="/facts/Synchrotron_radiation/mTsSKmRz">synchrotron radiation</a> production. When performing a modeling task for any accelerator operation, the results of charged particle beam dynamics simulations must feed into the associated application. Thus, for a full simulation, one must include the codes in associated applications. For particle physics, the simulation may be continued in a detector with a code such as <a href="/facts/Geant4/h8N7o86m">Geant4</a>. </p><p>For a synchrotron radiation facility, for example, the electron beam produces an x-ray beam that then travels down a <a href="/facts/Beamline/vrfaEtFt">beamline</a> before reaching the experiment. Thus, the electron beam modeling software must interface with the <a href="/facts/X-ray_optics/pTeyH8nt">x-ray optics</a> modelling software such as SRW,<a class="footnote-ref" id="fnref:63" href="#fn:63"><sup>63</sup></a> Shadow,<a class="footnote-ref" id="fnref:64" href="#fn:64"><sup>64</sup></a> McXTrace,<a class="footnote-ref" id="fnref:65" href="#fn:65"><sup>65</sup></a> or Spectra.<a class="footnote-ref" id="fnref:66" href="#fn:66"><sup>66</sup></a> Bmad<a class="footnote-ref" id="fnref:67" href="#fn:67"><sup>67</sup></a> can model both X-rays and charged particle beams. The x-rays are used in an experiment which may be modeled and analyzed with various software, such as the DAWN science platform.<a class="footnote-ref" id="fnref:68" href="#fn:68"><sup>68</sup></a> OCELOT<a class="footnote-ref" id="fnref:69" href="#fn:69"><sup>69</sup></a> also includes both synchrotron radiation calculation and x-ray propagation models. </p><p>Industrial and medical accelerators represent another area of important applications. A 2013 survey estimated that there were about 27,000 industrial accelerators and another 14,000 medical accelerators world wide,<a class="footnote-ref" id="fnref:70" href="#fn:70"><sup>70</sup></a> and those numbers have continued to increase since that time.<a class="footnote-ref" id="fnref:71" href="#fn:71"><sup>71</sup></a> Codes used at those facilities vary considerably and often include a mix of traditional codes and custom codes developed for specific applications. The Advanced Orbit Code (AOC)<a class="footnote-ref" id="fnref:72" href="#fn:72"><sup>72</sup></a> developed at <a href="/facts/Ion_Beam_Applications/GMmQEHwE">Ion Beam Applications</a> is an example. </p> <h2 id="see-also">See also</h2> <ul><li><a href="http://pbpl.physics.ucla.edu/Computing/Code_Overview/">List of codes from UCLA Particle Beam Physics Laboratory</a> <a href="https://web.archive.org/web/20180717231154/http://pbpl.physics.ucla.edu/Computing/Code_Overview/">Archived</a> 2018-07-17 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li> <li><a href="https://publications.nscl.msu.edu/thesis/Alt_2016_385.pdf#page=168">Comparison of Accelerator Codes</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Computer Codes for Particle Accelerator Design and Analysis: A Compendium, Second Edition, Helen Stokes Deaven and Kwok Chi Dominic Chen, Los Alamos National Laboratory report number LA-UR-90-1766, 290 pages (1990). <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>the CERN CARE/HHH website Archived December 13, 2012, at the Wayback Machine <a href="https://oraweb.cern.ch/pls/hhh/code_website.disp_allcat" target="_blank">https://oraweb.cern.ch/pls/hhh/code_website.disp_allcat</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>"user's guide" (PDF). Archived from the original (PDF) on 2018-07-04. Retrieved 2013-11-16. <a href="https://web.archive.org/web/20180704202245/http://care-hhh.web.cern.ch/care-hhh/Simulation-Codes/Optics/Literature/BETA_MANUAL.pdf" target="_blank">https://web.archive.org/web/20180704202245/http://care-hhh.web.cern.ch/care-hhh/Simulation-Codes/Optics/Literature/BETA_MANUAL.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>libtracy at sourceforge.net <a href="http://sourceforge.net/projects/libtracy/" target="_blank">http://sourceforge.net/projects/libtracy/</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>AccelSoft Inc. website <a href="http://www.accelsoftinc.com/" target="_blank">http://www.accelsoftinc.com/</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>ATcollab website <a href="https://github.com/atcollab/at" target="_blank">https://github.com/atcollab/at</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>See https://github.com/carmignani/festa <a href="https://github.com/carmignani/festa" target="_blank">https://github.com/carmignani/festa</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>ASTRA Homepage <a href="http://www.desy.de/~mpyflo/" target="_blank">http://www.desy.de/~mpyflo/</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>BDSIM Homepage <a href="http://www.pp.rhul.ac.uk/bdsim" target="_blank">http://www.pp.rhul.ac.uk/bdsim</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Bmad home page <a href="http://www.lepp.cornell.edu/bmad/" target="_blank">http://www.lepp.cornell.edu/bmad/</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>"COSY". <a href="http://www.cosyinfinity.org" target="_blank">http://www.cosyinfinity.org</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>"DYNAC". <a href="https://dynac.web.cern.ch/dynac/dynac.html" target="_blank">https://dynac.web.cern.ch/dynac/dynac.html</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>ELEGANT, a Flexible SDDS Compliant Code for Accelerator Simulation software <a href="https://www.aps.anl.gov/Accelerator-Operations-Physics/Software" target="_blank">https://www.aps.anl.gov/Accelerator-Operations-Physics/Software</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>"MAD - Methodical Accelerator Design". mad@cern.ch. Retrieved 2020-09-09. <a href="http://cern.ch/mad/" target="_blank">http://cern.ch/mad/</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>"MAD - Methodical Accelerator Design". mad@cern.ch. Retrieved 2020-09-09. <a href="http://cern.ch/mad/" target="_blank">http://cern.ch/mad/</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Appleby, Robert; Barlow, Roger J.; Bungau, Adriana; Fallon, James; Kruecker, Dirk; Molson, James; Rafique, Haroon; Rowan, Scott; Serluca, Maurizio; Sjøbæk, Kyrre Ness; Toader, Adina; Tygier, Sam; Walker, Nick; Wolski, Andy (2019-03-03). "Github Merlin-Collaboration/Merlin". doi:10.5281/zenodo.2598428. {{cite journal}}: Cite journal requires |journal= (help) <a href="https://github.com/Merlin-Collaboration/Merlin" target="_blank">https://github.com/Merlin-Collaboration/Merlin</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Appleby, Robert; Barlow, Roger J.; Bungau, Adriana; Fallon, James; Kruecker, Dirk; Molson, James; Rafique, Haroon; Rowan, Scott; Serluca, Maurizio; Sjøbæk, Kyrre Ness; Toader, Adina; Tygier, Sam; Walker, Nick; Wolski, Andy (2019). "Merlin++". doi:10.5281/zenodo.2598428. {{cite journal}}: Cite journal requires |journal= (help) <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>OCELOT collaboration on GitHub <a href="https://github.com/ocelot-collab/ocelot/" target="_blank">https://github.com/ocelot-collab/ocelot/</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>OPA website <a href="https://ados.web.psi.ch/opa/" target="_blank">https://ados.web.psi.ch/opa/</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>"Home · Wiki · OPAL / SRC". <a href="https://gitlab.psi.ch/OPAL/src/-/wikis/home" target="_blank">https://gitlab.psi.ch/OPAL/src/-/wikis/home</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>PLACET manual <a href="https://cds.cern.ch/record/2145365?ln=en" target="_blank">https://cds.cern.ch/record/2145365?ln=en</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>Propaga GitHub repository <a href="https://github.com/ALaDyn/Propaga" target="_blank">https://github.com/ALaDyn/Propaga</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>"GitHub - jceepf/fpp_book". GitHub. 2019-02-06. <a href="https://github.com/jceepf/fpp_book" target="_blank">https://github.com/jceepf/fpp_book</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>SAD home page at kek.jp <a href="http://acc-physics.kek.jp/SAD/" target="_blank">http://acc-physics.kek.jp/SAD/</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>SAMM, another Matlab based tracking code, at liv.ac.uk <a href="http://pcwww.liv.ac.uk/~awolski/main_links_computercodes.htm" target="_blank">http://pcwww.liv.ac.uk/~awolski/main_links_computercodes.htm</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>SixTrack home page at cern.ch <a href="http://sixtrack.web.cern.ch/SixTrack/" target="_blank">http://sixtrack.web.cern.ch/SixTrack/</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> <li id="fn:27"><p>Xsuite home page at cern.ch <a href="https://xsuite.web.cern.ch/" target="_blank">https://xsuite.web.cern.ch/</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li> <li id="fn:28"><p>Zgoubi home page at sourceforge.net <a href="https://sourceforge.net/projects/zgoubi/files/" target="_blank">https://sourceforge.net/projects/zgoubi/files/</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></p></li> <li id="fn:29"><p>Zgoubi Users' Guide <a href="https://sourceforge.net/p/zgoubi/code/HEAD/tree/trunk/guide/Zgoubi.pdf" target="_blank">https://sourceforge.net/p/zgoubi/code/HEAD/tree/trunk/guide/Zgoubi.pdf</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></p></li> <li id="fn:30"><p>ASTRA Homepage <a href="http://www.desy.de/~mpyflo/" target="_blank">http://www.desy.de/~mpyflo/</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></p></li> <li id="fn:31"><p>PIC solver at cst.com <a href="https://www.cst.com/solutions#SolverIds-Param%5B%5D=afcdc15d9d8a463c86193b62acc4b805" target="_blank">https://www.cst.com/solutions#SolverIds-Param%5B%5D=afcdc15d9d8a463c86193b62acc4b805</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></p></li> <li id="fn:32"><p>General Particle Tracer (GPT) from Pulsar Physics <a href="http://www.pulsar.nl/gpt/" target="_blank">http://www.pulsar.nl/gpt/</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></p></li> <li id="fn:33"><p>"IMPACT homepage at Berkeley Lab". Archived from the original on 2015-04-16. Retrieved 2015-04-09. <a href="https://web.archive.org/web/20150416205107/http://amac.lbl.gov/~jiqiang/impact/" target="_blank">https://web.archive.org/web/20150416205107/http://amac.lbl.gov/~jiqiang/impact/</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></p></li> <li id="fn:34"><p>ImpactX: an s-based beam dynamics code including space charge effects from Berkeley Lab <a href="https://github.com/ECP-WarpX/impactx" target="_blank">https://github.com/ECP-WarpX/impactx</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></p></li> <li id="fn:35"><p>THE MULTIPARTICLE TRACKING CODES SBTRACK AND MBTRACK. R. Nagaoka, PAC '09 paper here <a href="http://accelconf.web.cern.ch/accelconf/PAC2009/papers/fr5rfp046.pdf" target="_blank">http://accelconf.web.cern.ch/accelconf/PAC2009/papers/fr5rfp046.pdf</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></p></li> <li id="fn:36"><p>ORBIT home page at ornl.gov <a href="http://web.ornl.gov/~jzh/JHolmes/ORBIT.html" target="_blank">http://web.ornl.gov/~jzh/JHolmes/ORBIT.html</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></p></li> <li id="fn:37"><p>PyORBIT Collaboration <a href="https://github.com/PyORBIT-Collaboration" target="_blank">https://github.com/PyORBIT-Collaboration</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></p></li> <li id="fn:38"><p>OPAL homepage <a href="https://gitlab.psi.ch/OPAL/src/wikis/home" target="_blank">https://gitlab.psi.ch/OPAL/src/wikis/home</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></p></li> <li id="fn:39"><p>PyHEADTAIL wiki <a href="https://github.com/PyCOMPLETE/PyHEADTAIL/wiki" target="_blank">https://github.com/PyCOMPLETE/PyHEADTAIL/wiki</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></p></li> <li id="fn:40"><p>Synergia home page at fnal.gov <a href="https://web.fnal.gov/sites/Synergia/SitePages/Synergia%20Home.aspx" target="_blank">https://web.fnal.gov/sites/Synergia/SitePages/Synergia%20Home.aspx</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></p></li> <li id="fn:41"><p>TraceWin at CEA Saclay <a href="http://irfu.cea.fr/Sacm/logiciels/index3.php" target="_blank">http://irfu.cea.fr/Sacm/logiciels/index3.php</a> <a href="#fnref:41" class="footnote-back-ref">↩</a></p></li> <li id="fn:42"><p>TRANFT user's manual, BNL--77074-2006-IR http://www.osti.gov/scitech/biblio/896444 <a href="https://www.osti.gov/scitech/biblio/896444" target="_blank">https://www.osti.gov/scitech/biblio/896444</a> <a href="#fnref:42" class="footnote-back-ref">↩</a></p></li> <li id="fn:43"><p>VSim at Tech-X <a href="https://www.txcorp.com/vsim" target="_blank">https://www.txcorp.com/vsim</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></p></li> <li id="fn:44"><p>Warp wiki <a href="http://warp.lbl.gov" target="_blank">http://warp.lbl.gov</a> <a href="#fnref:44" class="footnote-back-ref">↩</a></p></li> <li id="fn:45"><p>Xsuite home page at cern.ch <a href="https://xsuite.web.cern.ch/" target="_blank">https://xsuite.web.cern.ch/</a> <a href="#fnref:45" class="footnote-back-ref">↩</a></p></li> <li id="fn:46"><p>"GUINEA-PIG Twiki". twiki.cern.ch. Archived from the original on 2022-01-20. Retrieved 2020-07-03. <a href="https://twiki.cern.ch/twiki/bin/view/ABPComputing/Guinea-Pig" target="_blank">https://twiki.cern.ch/twiki/bin/view/ABPComputing/Guinea-Pig</a> <a href="#fnref:46" class="footnote-back-ref">↩</a></p></li> <li id="fn:47"><p>"BeamBeam3D GitHub Repo"."J. Qiang, M. Furman, and R. Ryne, "A parallel particle-in-cell model for beam–beam interaction in high energy ring colliders"". J. Comp. Phys. 2004. doi:10.1016/j.jcp.2004.01.008. <a href="https://github.com/beam-beam/BeamBeam3D" target="_blank">https://github.com/beam-beam/BeamBeam3D</a> <a href="#fnref:47" class="footnote-back-ref">↩</a></p></li> <li id="fn:48"><p>Xsuite home page at cern.ch <a href="https://xsuite.web.cern.ch/" target="_blank">https://xsuite.web.cern.ch/</a> <a href="#fnref:48" class="footnote-back-ref">↩</a></p></li> <li id="fn:49"><p>ABCI home page at kek.jp <a href="http://abci.kek.jp/abci.htm" target="_blank">http://abci.kek.jp/abci.htm</a> <a href="#fnref:49" class="footnote-back-ref">↩</a></p></li> <li id="fn:50"><p>ACE3P at slac.stanford.gov <a href="https://portal.slac.stanford.edu/sites/ard_public/acd/Pages/Default.aspx" target="_blank">https://portal.slac.stanford.edu/sites/ard_public/acd/Pages/Default.aspx</a> <a href="#fnref:50" class="footnote-back-ref">↩</a></p></li> <li id="fn:51"><p>CST Archived 2018-07-29 at the Wayback Machine, Computer Simulation Technology at cst.com <a href="https://www.cst.com/" target="_blank">https://www.cst.com/</a> <a href="#fnref:51" class="footnote-back-ref">↩</a></p></li> <li id="fn:52"><p>GdfidL, Gitter drueber, fertig ist die Laube at gdfidl.de <a href="http://www.gdfidl.de/" target="_blank">http://www.gdfidl.de/</a> <a href="#fnref:52" class="footnote-back-ref">↩</a></p></li> <li id="fn:53"><p>T. Weiland, DESY <a href="#fnref:53" class="footnote-back-ref">↩</a></p></li> <li id="fn:54"><p>VSim at Tech-X <a href="https://www.txcorp.com/vsim" target="_blank">https://www.txcorp.com/vsim</a> <a href="#fnref:54" class="footnote-back-ref">↩</a></p></li> <li id="fn:55"><p>ACE3P at slac.stanford.gov <a href="https://portal.slac.stanford.edu/sites/ard_public/acd/Pages/Default.aspx" target="_blank">https://portal.slac.stanford.edu/sites/ard_public/acd/Pages/Default.aspx</a> <a href="#fnref:55" class="footnote-back-ref">↩</a></p></li> <li id="fn:56"><p>COMSOL home page at comsol.com <a href="http://www.comsol.com/" target="_blank">http://www.comsol.com/</a> <a href="#fnref:56" class="footnote-back-ref">↩</a></p></li> <li id="fn:57"><p>CST Electromagnetic Studio at cst.com <a href="https://archive.today/20131115111937/https://www.cst.com/Applications/Category/Magnetostatics" target="_blank">https://archive.today/20131115111937/https://www.cst.com/Applications/Category/Magnetostatics</a> <a href="#fnref:57" class="footnote-back-ref">↩</a></p></li> <li id="fn:58"><p>"OPERA at magnet-design-software.com". Archived from the original on 2013-12-24. Retrieved 2013-11-15. <a href="https://web.archive.org/web/20131224023436/http://magnet-design-software.com/webinar-introduction-magnet-design-opera/" target="_blank">https://web.archive.org/web/20131224023436/http://magnet-design-software.com/webinar-introduction-magnet-design-opera/</a> <a href="#fnref:58" class="footnote-back-ref">↩</a></p></li> <li id="fn:59"><p>VSim at Tech-X <a href="https://www.txcorp.com/vsim" target="_blank">https://www.txcorp.com/vsim</a> <a href="#fnref:59" class="footnote-back-ref">↩</a></p></li> <li id="fn:60"><p>Description of AML and UAP at cornell.edu <a href="http://www.lepp.cornell.edu/~dcs/aml/" target="_blank">http://www.lepp.cornell.edu/~dcs/aml/</a> <a href="#fnref:60" class="footnote-back-ref">↩</a></p></li> <li id="fn:61"><p>See references by N. Malitsky and Talman such as this manual from 2002. <a href="http://www.bnl.gov/isd/documents/24937.pdf" target="_blank">http://www.bnl.gov/isd/documents/24937.pdf</a> <a href="#fnref:61" class="footnote-back-ref">↩</a></p></li> <li id="fn:62"><p>OpenPMD GitHub repository. <a href="https://github.com/openPMD/openPMD-standard" target="_blank">https://github.com/openPMD/openPMD-standard</a> <a href="#fnref:62" class="footnote-back-ref">↩</a></p></li> <li id="fn:63"><p>SRW home page at esrf.eu <a href="http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/SRW" target="_blank">http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/SRW</a> <a href="#fnref:63" class="footnote-back-ref">↩</a></p></li> <li id="fn:64"><p>Shadow home page at esrf.eu <a href="http://www.esrf.eu/computing/scientific/raytracing/" target="_blank">http://www.esrf.eu/computing/scientific/raytracing/</a> <a href="#fnref:64" class="footnote-back-ref">↩</a></p></li> <li id="fn:65"><p>McXTrace home page at mcxtrace.org <a href="http://www.mcxtrace.org/" target="_blank">http://www.mcxtrace.org/</a> <a href="#fnref:65" class="footnote-back-ref">↩</a></p></li> <li id="fn:66"><p>"Spectra home page at riken.go.jp". Archived from the original on 2013-08-27. Retrieved 2013-11-15. <a href="https://web.archive.org/web/20130827221328/http://radiant.harima.riken.go.jp/spectra/" target="_blank">https://web.archive.org/web/20130827221328/http://radiant.harima.riken.go.jp/spectra/</a> <a href="#fnref:66" class="footnote-back-ref">↩</a></p></li> <li id="fn:67"><p>Bmad home page <a href="http://www.lepp.cornell.edu/bmad/" target="_blank">http://www.lepp.cornell.edu/bmad/</a> <a href="#fnref:67" class="footnote-back-ref">↩</a></p></li> <li id="fn:68"><p>DAWN science platform website <a href="http://www.dawnsci.org" target="_blank">http://www.dawnsci.org</a> <a href="#fnref:68" class="footnote-back-ref">↩</a></p></li> <li id="fn:69"><p>"An Introduction to Ocelot". GitHub. 16 December 2021. <a href="https://github.com/ocelot-collab/ocelot" target="_blank">https://github.com/ocelot-collab/ocelot</a> <a href="#fnref:69" class="footnote-back-ref">↩</a></p></li> <li id="fn:70"><p>R. W. Hamm and M. E. Hamm, Industrial Accelerators <a href="https://accelconf.web.cern.ch/IPAC2013/papers/weib201.pdf" target="_blank">https://accelconf.web.cern.ch/IPAC2013/papers/weib201.pdf</a> <a href="#fnref:70" class="footnote-back-ref">↩</a></p></li> <li id="fn:71"><p>session on accelerator business opportunities at IPAC-17 <a href="https://accelconf.web.cern.ch/ipac2017/talks/tuia2_talk.pdf" target="_blank">https://accelconf.web.cern.ch/ipac2017/talks/tuia2_talk.pdf</a> <a href="#fnref:71" class="footnote-back-ref">↩</a></p></li> <li id="fn:72"><p>AOC, A Beam Dynamics Code for Medical and Industrial Accelerators <a href="https://accelconf.web.cern.ch/ipac2016/papers/tupoy002.pdf" target="_blank">https://accelconf.web.cern.ch/ipac2016/papers/tupoy002.pdf</a> <a href="#fnref:72" class="footnote-back-ref">↩</a></p></li> </ol>