Long-term analysis of exponential integrators for charged-particle dynamics in a strong and constant magnetic field

For the charged-particle dynamics under a strong and constant magnetic field, we consider and analyze exponential integrators in this paper. We derive two kinds of exponential integrators and study their long-time behavior by using the technique of modulated Fourier expansions. It is shown that a symmetric two-stage exponential integrator and some one-stage symplectic exponential integrators approximately conserve the energy and magnetic moment of the charged-particle dynamics over long times.