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This article considers non-relativistic charged particle dynamics in bothstatic and non-static electromagnetic fields, which are governed bynonseparable, possibly time-dependent Hamiltonians. For the first time,explicit symplectic integrators of arbitrary high-orders are constructed foraccurate and efficient simulations of such mechanical systems. Performancessuperior to the standard non-symplectic method of Runge-Kutta are demonstratedon two examples: the first is on the confined motion of a particle in a statictoroidal magnetic field used in tokamak; the second is on how time-periodicperturbations to a magnetic field inject energy into a particle via parametricresonance at a specific frequency.

Explicit high-order symplectic integrators for charged particles in general electromagnetic fields