We use a simulation algorithm for collision free plasma termed the Vlasov method of kinetic phase point trajectories (Kazeminezhad et al, Phys Rev, 2003) also known as Vlasov Hybrid Simulation (Nunn, 1990, CPC). The method is simplicity itself. In the chosen phase space simulation box particles are followed continuously forwards in time, just as in PIC codes. However, applying Liouville’s theorem, we actually know the distribution function (F) at the phase points occupied by the particles. It only remains to INTERPOLATE F from particles to phase space grid, whence integration over V space enables the plasma charge/current field to be calculated. Armed with this and Maxwell’s equations the electromagnetic field may be pushed.
The method is stable, easily programmed, robust against filamentation of F, and does not invoke unphysical smoothing of F. Like all Vlasov methods it is low noise compared to PIC, and has a large advantage over PIC in that the simulation can be confined to limited regions of velocity space.
The technique is here applied to the simulation of VLF chorus generation, and is able to reproduce many phenomena in the VLF band, such as triggering of risers, fallers and hooks, chorus like waveforms, resonant sideband generation and so forth. Simple 1D electrostatic code has been written as a further demonstrator of the method and its accurate calculation of F.