Double Leap-Frog Method for Large-Time-Step Particle Simulation to Keep Larmor Radius Small

Abstract

A modified leap-frog (LF) scheme is presented that keeps the correct Larmor radius even in case of a large time step Δt compared to the cyclotron period Ω⁻¹, ΩΔt » 1, for the particle simulation of a plasma in the strong magnetic field. The Larmor radius simulated by the conventional LF method becomes very large for ΩΔt » 1, and such a numerical condition has been avoided in general. If the LF method is applicable to such situations, new particle simulation codes can be more easily developed for a wide area of plasma physics. By repeating the LF steps doubly and adopting the averaged velocity to advance the particle position, the Larmor radius is kept real independently of the ΩΔt value. Proper nature on the energy conservation, magnetic moment conservation and drift-velocity realization is safely inherited from the LF method.