VLF chorus emissions modeling using EPOCH PIC code: Generation regimes and comparison with a backward wave oscillator theory

Abstract

We present the results of a numerical model for VLF chorus emissions generation based on the EPOCH PIC code. The initial distribution function of energetic elections is assumed to have a finite-width step-like deformation in the velocities parallel to the geomagnetic field. This allows us to verify and generalize the analytical and numerical results obtained earlier within the framework of a backward wave oscillator model in which a sharp step feature is assumed. We show that in the presence of a sharp or smooth step, chorus emissions can be generated for realistic flux of energetic electrons even if the initial velocity distribution (without the step) is isotropic. Simulated chorus emissions behave very similarly for both sharp and finite-width steps. In particular, the generation of repetitive chirping chorus elements occurs if the coupling parameter exceeds the linear generation threshold several times. For smaller threshold excess, quasi-stationary or relaxation oscillation regimes take place. For the first time, we systematically study the dependence of the chorus emissions properties on the energetic electron distribution parameters, in particular, on the step width and the effective wave-particle coupling parameter proportional to the energetic electron flux and step height. We show that the functional dependences of the linear growth rate on the coupling parameter is the same for a smooth step gradient as those obtained for the sharp step within the framework of the backward wave oscillator model. The threshold flux of energetic electrons, above which whistler mode waves are generated, increases very fast with increasing step width. With a fixed relative step height, the threshold flux is about an order of magnitude higher for a step width of 8% than for a sharp step.