Particle-in-cell experiments examine electron diffusion by whistler-mode waves: 2. Quasilinear and nonlinear dynamics

Test-particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode-waves can be adequately described by quasilinear theory. However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasilinear theory. Using the method that was introduced in Allanson et al. (2019, https://dx.doi.org/10.1029/2019JA027088), we track the dynamical response of electrons due to interactions with incoherent whistler-mode waves, across all energy and pitch angle space. We conduct 5 experiments each with different values of the electromagnetic wave amplitude. We find that the electron dynamics agree well with the quasilinear theory diffusion coefficients for low amplitude incoherent waves with $(B_{\text{w,rms}}/B_0)^2\approx 3.7\cdot 10^{-10}$, over a timescale $T$ of the order of 1000 gyroperiods. However the resonant interactions with higher amplitude waves cause significant non-diffusive dynamics as well as diffusive dynamics. When electron dynamics are extracted and analyzed over timescales shorter than $T$, we are able to isolate both the diffusive and non-diffusive (advective) dynamics. Interestingly, when considered over these appropriately shorter timescales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasilinear theory, even for wave amplitudes up to $(B_{\text{w,rms}}/B_0)^2\approx 5.8\cdot 10^{-6}$. Quasilinear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. Therefore, the proper description of electron dynamics in response to wave-particle interactions with higher amplitude whistler-mode waves may require Fokker-Planck equations that incorporate diffusive and advective terms