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A class of explicit numerical schemes is developed to solve for therelativistic dynamics and spin of particles in electromagnetic fields, usingthe Lorentz-BMT equation formulated in the Clifford algebra representation ofBaylis. It is demonstrated that these numerical methods, reminiscent of theleapfrog and Verlet methods, share a number of important properties: they areenergy-conserving, volume-conserving and second order convergent. Theseproperties are analysed empirically by benchmarking against known analyticalsolutions in constant uniform electrodynamic fields. It is demonstrated thatthe numerical error in a constant magnetic field remains bounded for long timesimulations in contrast to the Boris pusher, whose angular error increaseslinearly with time. Finally, the intricate spin dynamics of a particle isinvestigated in a plane wave field configuration.

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