Parametric interaction between ELF and VLF waves: 3D LSP simulation results

Abstract

We have investigated a non-linear parametric interaction between Extremely Low Frequency (ELF) and Very Low Frequency (VLF) waves using the Large Scale Plasma (LSP) simulation code in three dimensions. We have forced linear modes in the plasma at ELF and VLF frequencies through a direct excitation of the wave electric field. The modes are forced using traveling plane waves which propagate at specific values of the wave-vector and frequency consistent with the whistler and Fast Magnetosonic dispersion relations. We demonstrate, using a Lagrangian fluid model in LSP, that an electromagnetic ELF wave and a quasi-electrostatic VLF wave can parametrically couple to excite electromagnetic whistler waves. We also show the formation of multiple sidebands around the carrier VLF wave. This work serves to further validate a model developed in Sotnikov et al. [J. Geophys. Res. 99, 8917 (1994); J. Geophys. Res. 96, 11363 (1991)] and adapted by Mishin and Sotnikov [Plasma Phys. Controlled Fusion 59, 124003 (2017)] to explain the observations of whistler waves in the plasmasphere [E. Mishin and V. Sotnikov, Plasma Phys. Controlled Fusion 59, 124003 (2017) and Mishin et al., Geophys. Res. Lett. 38, L21101 (2011)].