Hamiltonian preserving nonlinear optics

Abstract

An accelerator lattice could be considered as a map that transforms the phase space coordinates of a beam. Formally, such a transformation leads to a time-dependent effective Hamiltonian of the system, and this does not guarantee optimal dynamic properties. In this paper, we suggest a method of designing a nonlinear lattice in a way that it will conserve the Hamiltonian that is close to a given time-independent Hamiltonian in normalized coordinates, with a desired degree of accuracy. We establish a connection between the integrator of a Hamiltonian in normalized (canonical) coordinates and a real lens arrangement. We apply know algorithms of high-order symplectic integrators, to produce several nonlinear lattices and show that this approach could improves the design of the nonlinear insert considered at the IOTA and UMER facilities. We also suggest new lattice design based on the Yoshida integrator.

Novel Approaches to High-Power Proton Beams [Slides]

“…With several superperiodic nonlinear cells, the integrable lattice design seems to be compatible with extreme nonlinearity under realistic tune-shifts; however a systematic study has not been conducted for tune-shift tolerances as a function of nonlinearity. Separately, a framework for nonlinear integrable lattices based on distributed thin nonlinear elements has also been proposed [15].…”