Self-consistent simulation studies of non-linear electron-whistler wave-particle interactions

We present results from self-consistent one-dimensional electromagnetic particle-in-cell simulation studies of non-linear electron-whistler wave-particle interactions. In contrast to analytical treatments that assume a constant amplitude, monochromatic wave field, effects on the wave fields due to an evolving electron distribution are self-consistently represented in our simulations (over a wide frequency range from 0.04 omega(ce) to similar to 100 omega(ce)). We analyse the phase space trajectories of the entire set of simulation electrons (many thousands) through application of the delay-coordinate technique. This enables us to establish the trapping frequencies of electrons directly from the trajectories. Additional details in the phase space structure and dynamical changes in the properties of the trajectories are also obtained. Results from two different simulations, in which the wave spectrum is eventually dominated by a single whistler wave mode of relatively large amplitude (B-w/B-o similar to 0.2 - 0.3), show: (i) the phase space trapping of large numbers of simulation electrons (thousands) with characteristic frequencies around the expected primary trapping resonance frequency estimated from the observed wave amplitude; (ii) more than one strong characteristic frequency component in trapped electron phase space motion; (iii) the dynamics of the trapped process is time dependent, there being an evolutionary shift in time of trapped electron phase space trajectories towards lower characteristic frequencies. We suspect that (ii) is due to the presence of higher order trapping resonances under the relatively large wave amplitude, whilst (iii) is not explained by time independent analytical treatments that neglect the effects of particles on the wave field