Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

Discrete ELF/VLF (Extremely Low Frequency/Very Low Frequency) chorus emissions are one of the most intense electromagnetic plasma waves observed in radiation belts and in the outer terrestrial magnetosphere. These waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. The objective of our study is to reconstruct the realistic distribution of chorus wave-normals in radiation belts for all magnetic latitudes. To achieve this aim, the data from the electric and magnetic field measurements onboard Cluster satellite are used to determine the wave-vector distribution of the chorus signal around the equator region. Then the propagation of such a wave packet is modeled using three-dimensional ray tracing technique, which employs K. Rönnmark's WHAMP to solve hot plasma dispersion relation along the wave packet trajectory. The observed chorus wave distributions close to waves source are first fitted to form the initial conditions which then propagate numerically through the inner magnetosphere in the frame of the WKB approximation. Ray tracing technique allows one to reconstruct wave packet properties (electric and magnetic fields, width of the wave packet in k-space, etc.) along the propagation path. The calculations show the spatial spreading of the signal energy due to propagation in the inhomogeneous and anisotropic magnetized plasma. Comparison of wave-normal distribution obtained from ray tracing technique with Cluster observations up to 40° latitude demonstrates the reliability of our approach and applied numerical schemes.