[FFA_CEBAF_Collab] [EXTERNAL] Re: Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization

[Meot, Francois]

Hi All,   open access this NIM A one:

https://urldefense.proofpoint.com/v2/url?u=https-3A__www.sciencedirect.com_science_article_pii_S0168900222011214-3Fvia-253Dihub&d=DwIGaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=Ogg4WFNBwvADBq3fkmCLiJ7SaRDPYtawHzJElJMB0jE&m=fvtIf6kpzCXE5X0bbzMrTrJbR8kaZ9ghBqpXR5f5w48y5pAImTxmGzsW0XYMqeN_&s=TSS2SKzXYQu9hMX7QILU2odxTPCUbMTLz5yszaaMZ30&e= 

in case there would be plans for VFFAG arcs at CEBAF

François


​
François Méot
Brookhaven National Laboratory
Collider-Accelerator Department
--
Adjunct Professor
Physics & Astronomy
Stony Brook University - NYU
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From: FFA_CEBAF_Collab <ffa_cebaf_collab-bounces at jlab.org> on behalf of Jay Benesch via FFA_CEBAF_Collab <ffa_cebaf_collab at jlab.org>
Sent: Tuesday, December 6, 2022 7:32 AM
To: FFA_CEBAF_Collab <ffa_cebaf_collab at jlab.org>
Subject: [FFA_CEBAF_Collab] Convergence map with action-angle variables based on square matrix for nonlinear lattice optimization

seems relevant to FFA and EIC.  YMMV

https://urldefense.com/v3/__https://arxiv.org/abs/2212.01430__;!!P4SdNyxKAPE!F4GHAcoIl_gtMwfe56xHIp1BUnI-p1wTwVbdkgd9r6_YK-TQMKB-ViCf94JDNNCMFlQJF_Jf1EbrxaI5VbPSApuA2g$

Convergence map with action-angle variables based on square matrix for
nonlinear lattice optimization
Li Hua Yu, Yoshiteru Hidaka, Victor Smaluk  (BNL)

     To analyze nonlinear dynamic systems, we developed a new technique
based on the square matrix method. We propose this technique called the
\convergence map" for generating particle stability diagrams similar to
the frequency maps widely used in accelerator physics to estimate
dynamic aperture. The convergence map provides similar information as
the frequency map but in a much shorter computing time. The dynamic
equation can be rewritten in terms of action-angle variables provided by
the square matrix derived from the accelerator lattice. The convergence
map is obtained by solving the exact nonlinear equation iteratively by
the perturbation method using Fourier transform and studying
convergence. When the iteration is convergent, the solution is expressed
as a quasi-periodic analytical function as a highly accurate
approximation, and hence the motion is stable. The border of stable
motion determines the dynamical aperture. As an example, we applied the
new method to the nonlinear optimization of the NSLS-II storage ring and
demonstrated a dynamic aperture comparable to or larger than the nominal
one obtained by particle tracking. The computation speed of the
convergence map is 30 to 300 times faster than the speed of the particle
tracking, depending on the size of the ring lattice (number of
superperiods). The computation speed ratio is larger for complex
lattices with low symmetry, such as particle colliders.

Subjects:        Accelerator Physics (physics.acc-ph); Numerical Analysis
(math.NA)
Cite as:         arXiv:2212.01430 [physics.acc-ph]
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