Agapitov O. Resonance effects of wave-particle interaction in the near Earth space

ELF/VLF waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. Modeling of wave-particle interactions requires the best possible knowledge of wave energy and wave-normal directions distribution in L-shells for different magnetic latitudes and magnetic activity conditions. We show that whistler wave normals are directed approximately along the magnetic field (with the mean value about 10-15 degrees) in a vicinity of the geomagnetic equator on the basis of statistical study for ELF/VLF emissions using a whistler frequency range for ten years (2001-2010) of Cluster measurements. The distribution changes with magnetic latitude, the angle for a given frequency tends to the resonance cone and as a result at latitudes about 30 degrees, wave-normals become nearly perpendicular to the magnetic field. Above 20 degrees of latitude the field aligned wave population appears which is explained by Landau damping effects of waves propagation. The obtained results were proved by use of numerical ray tracing simulation. Distributions for the diffusion coefficients for day and night sectors and for different geomagnetic activity regimes are obtained and parametric model is developed. The diffusion coefficients from these distributions are compared with coefficients calculated under assumption of whistler parallel propagation with constant value of variance and wave amplitude along magnetic field line. The analytical validation of diffusion rates was made. The increase of the mean value and the variance of the wave vector distribution with latitude results in significant growth of the pitch-angle diffusion rates due to significant increase of the contribution of higher order cyclotron resonances at large latitudes, which is the most efficient for electrons with small equatorial pitch-angles. The new acceleration mechanism of radiation belts electron based on Landau resonance which explains energy gain up to 1 MeV has been developed.