Butterfly Distribution of Relativistic Electrons Driven by Parallel Propagating Lower Band Whistler Chorus Waves

We report results from a test particle simulation to reveal that electron scattering driven by lower band whistler chorus waves propagating along a magnetic field line plays an important role to produce the butterfly distribution of relativistic electrons. The results show that two nonlinear scattering processes, which are the phase trapping and the dislocation process, contribute to the formation of the butterfly distribution within a minute. We confirm that the quasilinear diffusion estimated from the whistler chorus waves are too slow to reproduce the butterfly distribution within a minute. The simulation results also show that there is the upper limit of rapid electron acceleration. We expect that the upper limit of the rapid flux enhancement is an evidence that the phase trapping process contributes to relativistic electron acceleration in the heart of the outer radiation belt.