Phase-Space Dynamic of Coherent Wave-Particle Interaction in the Radiation Belts

Modeling the interaction between coherent whistler mode waves and radiation belt electrons is an important component of space weather dynamics. Two main aspects of the wave-particle interaction are, the amplification of coherent VLF waves by an unstable radiation belt electron distribution and the precipitation and/or acceleration of these particles by the waves. The solution of the full problem requires a numerical self-consistent code which captures both effects simultaneously. Unfortunately, self-consistent codes of nonlinear phenomena are computationally intensive and the results can be challenging to interpret. To quantify the effect of waves on particles, we employ a novel approach wherein the particle trajectories are traced backward in time. The validity of this method is based on conservation of phase space density formalized in Liouville's theorem. The model resolves in high resolution the formation of a depletion in the region of phase-space known as a phase space hole that is associated with nonlinear wave growth.