Nonlinear whistler instability driven by a beamlike distribution of resonant electrons

Theory and simulation are used to study the instability of a coherent whistler parallel-propagating in a simplified model radiation belt with a background of cold electrons, as well as a ring distribution of energetic electrons. A nonlinear instability is initiated at the location z(+), where the electrons are cyclotron resonant with the wave, on the side of the equator (z=0) where the wave is propagating away from the equator. The instability propagates backward toward the equator, growing both spatially and temporally. As the instability develops, frequency falls in such a way as to keep the electrons nearly resonant with the waves over the entire region 0 < z < z(+). The instability causes a sharp drop in the pitch angle of the resonant electrons and eventually saturates with peak amplitude near the equator.