Interactions between H+ band EMIC waves and radiation belt relativistic electrons: Comparisons of test particle simulations with quasi-linear calculations

Abstract

We develop a general 3-D relativistic test particle (TP) simulation code to examine the trajectories and pitch angle variations of test electrons. We investigate the conditions when the electrons transit broadband, parallel propagating H+ band electromagnetic ion cyclotron (EMIC) waves to find whether the classical quasilinear theory (QLT) can be applied to interactions between H+ band EMIC waves and radiation belt relativistic (and ultra-relativistic) electrons. We find that to reach good consistency between TP scattering coefficients and QLT calculations, the wave-particle resonant interaction time (which indicates the time of particles traveling in the wave fields and being resonant with the wave fields) must be carefully calculated to ensure the validity of the linear diffusion process. This wave-particle resonant interaction time depends largely on the wave amplitude, the bandwidth, and the initial parameters of electrons for TP simulations; once the time of electrons traveling in the wave fields becomes large enough when the pitch angles of electrons scattered by wave fields reach the maximal value limited by the resonance condition and cannot be diffused any longer, the linear diffusion process of particles defined by QLT will not be valid any longer. When the resonant electrons start to travel through the wave field, they undergo the linear diffusion process resulting from the pitch angle scattering by the H+ band EMIC wave field. As the time of traveling in the wave fields increases, the test electrons will suffer effective pitch angle scattering and the pitch angles of these electrons will reach the maximum value limited by the resonance condition, which is determined by the wave and electron parameters. These electrons are then reflected by the wave fields and the linear wave-particle interactions defined by QLT will not be valid anymore. This kind of wave-particle interaction subsequently introduces considerable deviation of TP diffusion coefficients from those predicted by QLT calculations. Our results demonstrate that the general validity of QLT in describing how broadband EMIC waves affect radiation belt relativistic electrons is highly related to the time of electron traveling in the wave fields, which tends to increase for smaller wave power and broader wave frequency spectra.