Leapfrog methods for relativistic charged-particle dynamics
Ernst Hairer, Christian Lubich, and Yanyan Shi,
Abstract. A basic leapfrog integrator and its energy-preserving and
variational / symplectic variants are proposed and studied for the numerical integration
of the equations of motion of relativistic charged particles in an electromagnetic field.
The methods are based on a four-dimensional formulation of the equations of motion.
Structure-preserving properties of the numerical methods are analysed, in particular
conservation and long-time near-conservation of energy and mass shell as well as
preservation of volume in phase space. In the non-relativistic limit, the considered
methods reduce to the Boris algorithm for non-relativistic charged-particle dynamics
and its energy-preserving and variational / symplectic variants.
Key Words. relativistic charged particle, leapfrog integrator,
structure preservation,
energy conservation, mass shell conservation,
backward error analysis.