The numerical simulation of VLF nonlinear wave-particle interactions in collision-free plasmas using the Vlasov hybrid simulation technique

Abstract

A novel scheme for the numerical simulation of wave-particle interactions in space plasmas has been developed. The method, termed VHS of Vlasov hybrid simulation, is applicable to hot collision-free plasmas in which the unperturbed distribution function is smooth and free of delta-function singularities. The particle population is described as a continuous Vlasov fluid in phase space — granularity and collisional effects beiing ignored. In traditional PIC/CIC codes the charge/current due to each simulation particle is assigned to a fixed spatial grid. In the VHS method the simulation particles sample the Vlasov fluid and provide information about the value of distribution function F( r , v ) at random points in phase space. Values of F are interpolated from the simulation particles onto a fixed grid in velocity/position or phase space. With the distribution function defined on a phase-space grid the plasma charge/current field is quickly calculated. The simulation particles serve only to provide information, and thus the particle population may be dynamic. Particles no longer resonant with the wave field may be discarded from the simulation, and new particles may be inserted into the Vlasov fluid where required. The VHS technique is particularly well suited to wave-particle interaction problems in inhomogeneous media where the resonance velocity may vary with both space and time. In this paper the VHS technique is applied to the problem of nonlinear wave-particle interactions in the VLF band, and used to simulate rising frequency emissions triggered by Siple pulses. The code produces stable reproducible emissions whose characteristics agree with experimental observations. The VHS codes are far more efficient than PIC/CIC codes, and considerably outperform previous Vlasov codes, which effect a discretization of the Vlasov equation. It is expected that the VHS simulation method will be widely applicable to hot plasma simulation problems in space.