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Computation of Nonlinear Fields and Orbit and Spin Transfer Maps of Electrostatic Elements using Differential Algebras

Abstract

Traditionally most large storage rings for nuclear and high energy physics use magnetic elements for focusing and bending. However, recent interest in the study of the possible existence of an electric dipole moment (EDM) of protons, deuterons and others requires the use of electrostatic elements in rings, and would even greatly benefit from the use of purely electrostatic lattices without any magnetic elements. Indeed the classical Thomas-BMT equation describing the motion of the spin due to a magnetic dipole moment coupling to magnetic fields can be augmented to analogously also describe the effects of a possibly present electric dipole moment coupling to electric fields, and the additional term would lead to detectable effects. We discuss how to address and resolve various problems appearing in the simulation of such lattices. We begin with methods that allow the computation of nonlinear fields of elements, and in particular their fringe fields, using DA-based PDE solvers, and proceed to the computation of high-order transfer maps, typically up to order 7 or 9. We also discuss a problem arising in these rings, especially the possible non-conservation of the particle energies.

K. Makino, E. Valetov, M. Berz, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 168

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