Diffusing loss effects of radiation belt energetic electrons caused by typical very low frequency electromagnetic wave

Radiation belt energetic electrons can interact with very low frequency (VLF) electromagnetic wave due to wave-particle resonance; then the particles are imposed to enter into the loss cone and sink to dense atmosphere resulting from changing of its pitch angle. To investigate the diffusion mechanism of interaction of VLF electromagnetic wave with radiation belt energetic electrons, according to quasi-linear diffusion theory, in this paper we use a physical model to calculate diffusion coefficients of Coulomb scatting and wave-particle resonance interaction. Bounce-averaged pitch angle diffusion coefficients of energetic electrons due to the interaction of wave-particle resonance with two groups of VLF electromagnetic waves are obtained. The influence of interaction caused by VLF electromagnetic wave and Coulomb scatting on diffusion of radiation belt energetic electrons for different L shells and various energies are analyzed. Take the case for example, where L equals 2.2 and electron energy E equals 0.5 MeV, the diffusion equation of energetic electrons are solved by using the finite difference method. The time evolutions of precipitation of directional particle flux and omnidirectional particle flux are analyzed. The results show that the resonance interaction caused by VLF electromagnetic wave plays a dominant role when E>0.5 MeV and L>1.6; the higher the L shell or electron energy value, the more significant the high order resonance interaction caused by the oblique propagation VLF electromagnetic wave will be; approximately, the omnidirectional particle flux of radiation belt energetic electrons decreases exponentially with time.