Explicit volume-preserving numerical schemes for relativistic trajectories and 
spin dynamics

Cabrera, Renan; G. Campos, Andre; Bondar I, Denys; MacLean, Steve; Fillion-Gourdeau, Francois

doi:10.1103/PhysRevE.103.043310

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Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics

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G. Campos, Andre
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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Citation

Cabrera, R., G. Campos, A., Bondar I, D., MacLean, S., & Fillion-Gourdeau, F. (2021). Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics. Physical Review E, 103(4): 043310. doi:10.1103/PhysRevE.103.043310.

Cite as: https://hdl.handle.net/21.11116/0000-000A-3B3E-0

Abstract

A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz–Bargmann-Michel-Telegdi equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy conserving, volume conserving, and second-order convergent. These properties are analyzed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long-time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane-wave field configuration.