Vlasov Hybrid Simulation—An Efficient and Stable Algorithm for the Numerical Simulation of Collision‐Free Plasma

Abstract

This paper presents a highly efficient and stable algorithm for the numerical simulation of collision‐free plasma. The algorithm has been successfully used to numerically model nonlinear electron cyclotron resonance in VLF band radio waves in space, and has produced simulations of triggered VLF band radio emissions and for the first time simulations of VLF “dawn chorus.” More recently the algorithm has been successfully applied to the classical problem of nonlinear instability of electrostatic waves in the presence of a weak electron beam.

The algorithm fills the phase box with simulation particles which represent phase space trajectories. Particle trajectories are followed forward continuously in time without restarts, and these particles are followed until either the simulation ends or the particles exit from the phase box. Liouville's theorem states that distribution function F is conserved along these trajectories, and so F is known at the phase space points represented by the particle positions. No phase space volume is associated with these particles. At each time step F is interpolated, and not distributed from particles to the regular phase space grid, for diagnostic purposes and to calculate plasma charge and current fields. For this operation a cheap low order interpolation suffices. The algorithm is simple, stable, robust and efficient. The large diffusion of distribution function in phase space due to restarting trajectories at phase space grid points is absent. Also, fine structure in F is merely undersampled and does not cause algorithm instability. Regions of phase space where F=0 are cost free as no particles need be provided. The algorithm readily accomodates situations where phase fluid flows into or out of the phase box.

The paper presents the latest simulations of VLF chorus and VLF triggered emissions from the VHS/VLF code, which are in excellent agreement with observations.

Keywords:

• Plasma
• Vlasov simulation
• VLF chorus
• wave particle interactions
• nonlinear effects in plasma

Acknowledgments

The author wishes to firstly thank J Manninen from Sodankyla Geophysical Observatory, Finland, for the provision of VLF ground data, and secondly Dr Santolik from Charles University, Prague, for the provision of VLF chorus data from the Cluster satellites.