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<p class="MsoNormal">Fantastic!<o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">FFA_CEBAF_Collab <ffa_cebaf_collab-bounces@jlab.org> on behalf of Meot, Francois via FFA_CEBAF_Collab <ffa_cebaf_collab@jlab.org><br>
<b>Date: </b>Wednesday, December 7, 2022 at 7:21 AM<br>
<b>To: </b>FFA_CEBAF_Collab <ffa_cebaf_collab@jlab.org>, Jay Benesch <benesch@jlab.org><br>
<b>Subject: </b>[FFA_CEBAF_Collab] [EXTERNAL] Re: Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization<o:p></o:p></span></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:black;background:white">Hi All, open access this NIM A one:</span></span><span style="font-size:12.0pt;color:black;background:white"><o:p></o:p></span></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:black;background:white"><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__www.sciencedirect.com_science_article_pii_S0168900222011214-3Fvia-253Dihub&d=DwMGaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=Ogg4WFNBwvADBq3fkmCLiJ7SaRDPYtawHzJElJMB0jE&m=fvtIf6kpzCXE5X0bbzMrTrJbR8kaZ9ghBqpXR5f5w48y5pAImTxmGzsW0XYMqeN_&s=TSS2SKzXYQu9hMX7QILU2odxTPCUbMTLz5yszaaMZ30&e=">https://www.sciencedirect.com/science/article/pii/S0168900222011214?via%3Dihub</a></span></span><span style="font-size:12.0pt;color:black;background:white"><o:p></o:p></span></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:black;background:white">in case there would be plans for VFFAG arcs at CEBAF
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:10.0pt;color:black;background:white">François</span></span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black;background:white"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt"></span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><br>
</span><span style="font-size:10.0pt">François Méot</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><br>
</span><span style="font-size:10.0pt">Brookhaven National Laboratory</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><br>
</span><span style="font-size:10.0pt">Collider-Accelerator Department</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt">--</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt">Adjunct Professor </span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif">
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<p class="MsoNormal"><span style="font-size:10.0pt">Physics & Astronomy</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt">Stony Brook University - NYU</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif">
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<p class="MsoNormal"><b><span style="color:black">From:</span></b><span style="color:black"> FFA_CEBAF_Collab <ffa_cebaf_collab-bounces@jlab.org> on behalf of Jay Benesch via FFA_CEBAF_Collab <ffa_cebaf_collab@jlab.org><br>
<b>Sent:</b> Tuesday, December 6, 2022 7:32 AM<br>
<b>To:</b> FFA_CEBAF_Collab <ffa_cebaf_collab@jlab.org><br>
<b>Subject:</b> [FFA_CEBAF_Collab] Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization</span>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">seems relevant to FFA and EIC. YMMV<br>
<br>
<a href="https://urldefense.com/v3/__https:/arxiv.org/abs/2212.01430__;!!P4SdNyxKAPE!F4GHAcoIl_gtMwfe56xHIp1BUnI-p1wTwVbdkgd9r6_YK-TQMKB-ViCf94JDNNCMFlQJF_Jf1EbrxaI5VbPSApuA2g$">https://urldefense.com/v3/__https://arxiv.org/abs/2212.01430__;!!P4SdNyxKAPE!F4GHAcoIl_gtMwfe56xHIp1BUnI-p1wTwVbdkgd9r6_YK-TQMKB-ViCf94JDNNCMFlQJF_Jf1EbrxaI5VbPSApuA2g$</a>
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<br>
Convergence map with action-angle variables based on square matrix for <br>
nonlinear lattice optimization<br>
Li Hua Yu, Yoshiteru Hidaka, Victor Smaluk (BNL)<br>
<br>
To analyze nonlinear dynamic systems, we developed a new technique <br>
based on the square matrix method. We propose this technique called the <br>
\convergence map" for generating particle stability diagrams similar to <br>
the frequency maps widely used in accelerator physics to estimate <br>
dynamic aperture. The convergence map provides similar information as <br>
the frequency map but in a much shorter computing time. The dynamic <br>
equation can be rewritten in terms of action-angle variables provided by <br>
the square matrix derived from the accelerator lattice. The convergence <br>
map is obtained by solving the exact nonlinear equation iteratively by <br>
the perturbation method using Fourier transform and studying <br>
convergence. When the iteration is convergent, the solution is expressed <br>
as a quasi-periodic analytical function as a highly accurate <br>
approximation, and hence the motion is stable. The border of stable <br>
motion determines the dynamical aperture. As an example, we applied the <br>
new method to the nonlinear optimization of the NSLS-II storage ring and <br>
demonstrated a dynamic aperture comparable to or larger than the nominal <br>
one obtained by particle tracking. The computation speed of the <br>
convergence map is 30 to 300 times faster than the speed of the particle <br>
tracking, depending on the size of the ring lattice (number of <br>
superperiods). The computation speed ratio is larger for complex <br>
lattices with low symmetry, such as particle colliders.<br>
<br>
Subjects: Accelerator Physics (physics.acc-ph); Numerical Analysis <br>
(math.NA)<br>
Cite as: arXiv:2212.01430 [physics.acc-ph]<br>
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