  This article considers non-relativistic charged particle dynamics in both
static and non-static electromagnetic fields, which are governed by
nonseparable, possibly time-dependent Hamiltonians. For the first time,
explicit symplectic integrators of arbitrary high-orders are constructed for
accurate and efficient simulations of such mechanical systems. Performances
superior to the standard non-symplectic method of Runge-Kutta are demonstrated
on two examples: the first is on the confined motion of a particle in a static
toroidal magnetic field used in tokamak; the second is on how time-periodic
perturbations to a magnetic field inject energy into a particle via parametric
resonance at a specific frequency.
