Formation process of relativistic electron flux through interaction with chorus emissions in the Earth\textquoterights inner magnetosphere

We perform test particle simulations of energetic electrons interacting with whistler mode chorus emissions. We compute trajectories of a large number of electrons forming a delta function with the same energy and equatorial pitch angle. The electrons are launched at different locations along the magnetic field line and different timings with respect to a pair of chorus emissions generated at the magnetic equator. We follow the evolution of the delta function and obtain a distribution function in energy and equatorial pitch angle, which is a numerical Green\textquoterights function for one cycle of chorus wave-particle interaction. We obtain the Green\textquoterights functions for the energy range 10 keV\textendash6 MeV and all pitch angles greater than the loss cone angle. By taking the convolution integral of the Green\textquoterights functions with the distribution function of the injected electrons repeatedly, we follow a long-time evolution of the distribution function. We find that the energetic electrons are accelerated effectively by relativistic turning acceleration and ultrarelativistic acceleration through nonlinear trapping by chorus emissions. Further, these processes result in the rapid formation of a dumbbell distribution of highly relativistic electrons within a few minutes after the onset of the continuous injection of 10\textendash30 keV electrons.