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.