# Hamiltonian preserving nonlinear optics

## TL;DR

This paper introduces a method for designing nonlinear accelerator lattices that approximately preserve a Hamiltonian integral of motion, enhancing the stability and performance of particle accelerators.

## Contribution

It presents a novel approach linking Hamiltonian integrators with real lens arrangements, improving nonlinear lattice design for accelerators.

## Key findings

- Improved nonlinear lattice designs for IOTA and UMER facilities.
- Application of high-order symplectic integrators to accelerator lattices.
- Proposal of new lattice design using Yoshida integrator.

## Abstract

In this paper we present a method of constructing a nonlinear accelerator lattice that has an approximate integral of motion that is given upfront. The integral under consideration is a Hamiltonian in normalized (canonical) coordinates that is preserved by a lattice with a given accuracy. We establish a connection between the integrator of a Hamiltonian in normalized coordinates and a real lens arrangement. We apply known algorithms of high-order symplectic integrators, to produce several nonlinear lattices and show that this approach could improve the design of the nonlinear insert considered at the IOTA and UMER facilities. We also suggest new lattice design based on the Yoshida integrator.