A search for integrable four-dimensional nonlinear accelerator lattices

TL;DR

This paper explores the design of four-dimensional nonlinear accelerator lattices that are integrable, enabling stable, large-volume phase space motion to improve beam stability and reduce errors.

Contribution

It introduces new families of integrable lattices with one invariant and provides examples of realizable nonlinear accelerator lattices with separable variables.

Findings

Families of lattices with one invariant for stable motion

Examples of realizable integrable nonlinear lattices

Potential to suppress instabilities in accelerators

Abstract

Integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and/or electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents two examples of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.