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

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-BMT 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 analysed 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.

arXiv comment15 pages, 9 figures

References in corpus (13)

• Dynamics of spin 1/2 quantum plasmas
• Higher Order Decompositions of Ordered Operator Exponentials
• Spin polarization of electrons by ultraintense lasers
• A comprehensive comparison of relativistic particle integrators
• Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields
• Explicit high-order symplectic integrators for charged particles in general electromagnetic fields
• Symplectic Integration of Magnetic Systems
• High-order energy-conserving Line Integral Methods for charged particle dynamics
• High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields
• Collapse-and-revival dynamics of strongly laser-driven electrons
• An fully implicit scheme for numerical integration of the relativistic particle equation of motion
• Accurate and efficient spin integration for particle accelerators
• Why geometric integration?