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