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

[Jay Benesch]

seems relevant to FFA and EIC.  YMMV

https://arxiv.org/abs/2212.01430

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]