Long Time-Step Particle Pushing in Drift Approximation without Orbit Averaging

Abstract

An alternative way to utilize the well known drift approximation for particle motion in electromagnetic fields is proposed. Contrary to the traditional approach, in which the motion of the guiding center of a particle is considered, in the suggested algorithm the coordinates and velocities of the particle itself are evaluated. This approach is found to give accurate results provided that the characteristic scales of the change of fields both in time and in space are large compared to the corresponding micro-scales of the particle motion in these fields (e.g., wavelength of radio wave is large compared to the particle gyroradius in the magnetic field of that wave). Under this condition an approximate analytical solution for the Newton–Lorentz Law, accurate within many characteristic micro-timescales of the particle motion, is derived. This approximation is exploited to advance a particle substantially within a single elementary step of the algorithm, which can extend for as long as ∼mi/me≃ 2000 times the traditional one for certain astrophysical plasmas. Utilization of this approach can give a boost of productivity for the existing and new PIC codes, in which substantial computational time is spent solving the Newton–Lorentz Law for superparticles. In the present work the approach is implemented for the ultrarelativistic case, with the magnetic field prevailing over, although being not necessarily much higher than the electric field. The relevant computer code is developed and used to simulate the motion of a particle in an electromagnetic field with a complicated profile. The results exhibit a good agreement with those, obtained by direct integration of the Newton–Lorentz law, using a conventional ODE solver.