The importance of amplitude modulation in nonlinear interactions between electrons and large amplitude whistler waves

Abstract

The effects of amplitude modulation on nonlinear interactions between a parallel propagating whistler wave and electrons in a dipole field are investigated in this work using a test particle code. Here we first use the test particle simulation to validate a previous single-wave nonlinear theory. Then we adopt a simple two-wave model to represent the recently observed amplitude modulation of a whistler wave field. By varying the frequency spacing between the two waves, we investigate the effects of different modulation frequencies on the nonlinear interactions. We demonstrate that when the resonance overlap condition is satisfied, the resulting change in the electron pitch angle and energy could be very different from what has been predicted by ideal single-wave nonlinear theories. Using a previously observed probability distribution of the subpacket modulation frequency of a chorus event, we obtain the probability distribution of different types of electron response. Our results indicate that the observed subpacket distribution produces particle responses in both non-overlapping and overlapping regimes. Our results suggest that the observed amplitude modulation should be considered when quantitatively treating interactions between electrons and recently observed large amplitude whistler waves or chorus waves.