Large-stepsize integrators for charged-particle dynamics over multiple time scales

Abstract The Boris algorithm, a closely related variational integrator and newly proposed filtered are studied when they used to numerically integrate the equations of motion charged particle in mildly non-uniform strong magnetic field, taking step sizes that much larger than period Larmor rotations. For algorithm standard (unfiltered) integrator, satisfactory behaviour is only obtained component initial velocity orthogonal field out. shows varying over multiple time scales: fast gyrorotation, guiding centre motion, slow perpendicular drift, near-conservation moment very long times conservation energy for all times. Using modulated Fourier expansions exact numerical solutions, it analysed which extent this reproduced by three integrators with large do not resolve gyrorotations.