Coherent interactions between whistler mode waves and energetic electrons in the earth's radiation belts [electronic resource]
Keywords: Electrical Engineering.

Near-Earth space can be best described as a large electromagnetic system dominated by fundamental plasma physical interactions. Specifically, high energy electrons and protons sourced from the solar wind are trapped in the Earth's magnetic field and form the radiation belts. The interaction between energetic particles in the Earth's radiation belts and electromagnetic waves plays an important role in the dynamics of the near-Earth space environment. In this work, we can consider the nonlinear gyro-resonant (doppler shifted cyclotron resonant) interaction between "whistler-mode" electromagnetic waves and energetic electrons in the radiation belts. Specifically, we address the amplification of whistler mode waves externally injected into the radiation belts as well as the subsequent precipitation of energetic electrons interacting with such waves. Modeling wave amplification due to gyro-resonant wave-particle interactions in the radiation belts requires the solution of the Vlasov-Maxwell system of equations in an inhomogeneous magneto-plasma. Previous works have employed Particle-In-Cell (PIC) methods or Eulerian solvers (such as the VHS code) to provide numerical solutions of this problem. In this report, we provide an alternative numerical approach by utilizing a first order finite difference upwind scheme. When coupled with the narrowband Maxwell's Equations, the model reproduces linear as well as nonlinear wave growth of coherent signals. Wave growth is nonlinear when the wave amplitude exceeds the minimum value for phase trapping of counter streaming resonant particles and is linear otherwise. The model also demonstrates free-running frequency variation for a case with a high linear growth rate. In addition, the model confirms the theoretical prediction of a stable "phase space hole" during the nonlinear growth process with higher resolution than that which was obtained in previously attempted simulations. The interaction between coherent whistler mode waves and energetic radiation belt electrons can also result in pitch angle scattering of electrons into the bounce loss cone and their subsequent precipitation onto the natural atmosphere. In order to capture the nonlinear effects of large amplitude coherent waves, we utilize a Vlasov-Liouville (VL) model which computes the precipitated phase-space particle distribution function directly using a characteristic based solution of the Vlasov equation. Previous work has shown that in the case of large amplitude coherent waves, phase-trapping can significantly perturb resonant particles from their adiabatic paths. We evaluate the importance of phase-trapping over a range of wave amplitudes (up to 200 pT); the percentage of particles that precipitate after being phase trapped is computed over a phase space grid in the loss cone. The results demonstrate that phase trapping contributes significantly to precipitation when a large amplitude wave (> 100 pT) is present. Additionally, linear theory can be valid over a broad range of amplitudes and the relative accuracy of linear theory in calculating the precipitated flux depends strongly on the initial particle distribution. We also demonstrate the ability of the VL model to calculate the time evolution of the precipitated flux due to short duration whistler mode pulses. The physical parameters used in the modeling effort presented here are typical of those associated with the Siple Station wave injection experiment, carried out over a 15 year period (1973 - 1988), using a dedicated and specifically designed VLF transmitter located over the thick Antarctic ice sheet.