Hamiltonian preserving nonlinear optics

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.

14 pages, 13 figures

References in corpus (9)

• IOTA (Integrable Optics Test Accelerator): Facility and Experimental Beam Physics Program
• Tevatron Electron Lenses: Design and Operation
• Landau Damping of Beam Instabilities by Electron Lenses
• Single-Particle Dynamics in a Nonlinear Accelerator Lattice: Attaining a Large Tune Spread with Octupoles in IOTA
• Quasi-integrable optics for a small electron recirculator
• A study of coherent and incoherent resonances in high intensity beams using a linear Paul trap
• Beam Physics of Integrable Optics Test Accelerator at Fermilab
• High-order control for symplectic maps
• Complex Representation of Potentials and Fields for the Nonlinear Magnetic Insert of the Integrable Optics Test Accelerator