Spatial spreading of magnetospherically reflected chorus elements in the inner magnetosphere

Chorus-type whistler waves are known to be generated in the vicinity of the magnetic equator, in the low-density plasma trough region. These wave packets propagate towards the magnetic poles, deviating from the magnetic field lines, before being eventually reflected at higher latitudes. Magnetospheric reflection of whistler waves results in bounce oscillations of these waves through the equator. Our study is devoted to the problem of geometrical spreading of these whistler-mode waves after their first magnetospheric reflection, which is crucial to determine where wave particle interactions occur. Recently, experimental studies stated that the relative intensity of the reflected signal was generally between 0.005 and 0.05 of the source signal We model such wave packets by means of ray tracing technique, using a warm plasma dispersion function along their trajectory and a realistic model of the inner magnetosphere. We reproduce the topology of the reflected energy distribution in the equatorial plane by modeling discrete chorus elements generated at the equator. Our calculations show that the spatial spreading is large and strongly dependent upon initial wave parameters, especially the chorus wave frequency. Thus, the divergence of each element ray trajectories can result in the filling of a large region (about 4 Earth radii around the source) of the magnetosphere and a reflected intensity of 0.005-0.06 of the source signal in the equatorial plane. These results are in good agreement with previous Cluster and THEMIS observations.