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Explicit high-order symplectic integrators for charged particles in general electromagnetic fields. (English) Zbl 1373.78048

Summary: 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 a 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.

MSC:

78A35 Motion of charged particles
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
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