Abstract
Dynamic aperture (DA) is one of the key nonlinear properties for a storage ring. Although there have been both analytical and numerical methods to find the aperture, the reverse problem of how to optimize it is still a challenging problem. A general and flexible way of optimizing the DA is highly demanded in accelerator design and operation. In this paper, we discuss the use of multiobjective optimization for DA. First we consider using objective functions based only on numerical tracking results. Data mining of these results demonstrated a correlation between DA and low-order nonlinear driving terms. Next we considered using objective functions which included both numerical tracking results and analytical estimates of low-order nonlinear driving terms. This resulted in faster convergence. The National Synchrotron Light Source II (NSLS-II) lattice was taken as an example to illustrate this method. This multiobjective approach is not limited by particular linear or nonlinear lattice settings, and can also be applied for optimizing other properties of a storage ring.
Highlights
Dynamic aperture (DA) is one of the key nonlinear properties of a storage ring lattice in both design and operation stages
In maximizing the DA area, we put a constraint for the DA boundary requiring that it should cover an ellipse defined by two half-axes lengths Ax and Ay
The first strategy uses the set of objective functions f1 and f2 characterizing the DA area of on-momentum and off-momentum particles: f1 1⁄4 Sð 1⁄4 0Þ f2 1⁄4 Sð 1⁄4 À2:5%Þ þ Sð 1⁄4 2:5%Þ; (6)
Summary
Dynamic aperture (DA) is one of the key nonlinear properties of a storage ring lattice in both design and operation stages. We considered using objective functions which included both numerical tracking results and analytical estimates of low-order nonlinear driving terms. It is found that including the tune shifts in the optimizer improves convergence speed Both approaches are illustrated using the NSLS-II lattice as an example. Gives more algorithm details on generating new children in the optimization iterations
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