Current Advance Method and Cyclic Leapfrog for 2D Multispecies Hybrid Plasma Simulations

Abstract

CAM-CL (current advance method and cyclic leapfrog) is a new algorithm for hybrid plasma simulations. In common with existing methods, its physical basis is a "hybrid" plasma model which treats the ions as particles and the electrons as a massless fluid. CAM-CL is distinguished from previous 2D hybrid algorithms by four main features: (1) Multiple ion species may be treated with only a single computational pass through the particle data: this is achieved without extrapolation of the electric field in time. The particles are advanced by a leapfrog procedure which requires the electric field to be a half time-step ahead of the particle velocities. The electric field depends on the ionic current density and hence the particle velocities. In order to avoid a time-consuming "pre-push" of the velocities, CAM advances the ionic current density a half-step with an appropriate equation of motion. This is similar in concept to the moment method (D. Winske and K. B. Quest, J. Geophys, Res.93 (A9), 9681 (1988), Appendix A), except for the next two features: (2) CAM advances the ionic current density, whereas the moment method advances the fluid velocity. Consequently, multiple ion species may be easily treated (3) A free-streaming ionic current density is collected (velocities are collected at positions a half time-step ahead). An equation of motion is then applied, in which the advective term and the ionic stress tensor in the moment method are not needed, since transport effects are included in the free-streaming current. (4) CL is a leapfrog scheme for advancing the magnetic field, an adaptation of the modified midpoint method described by W. H. Press et al. (Numerical Recipes (Cambridge Univ. Press, Cambridge, 1986)). It is stable and allows sub-stepping of the magnetic field (the magnetic field time-step may be different to the particle time-step). A two-dimensional version of the algorithm has been tested on a quiet plasma, MHD wave propagation, and ion beam instabilities, the results of which are discussed.