Particle‐in‐cell Experiments Examine Electron Diffusion by Whistler‐mode Waves: 1. Benchmarking With a Cold Plasma

Abstract

Using a particle-in-cell code, we study the diffusive response of electrons due to wave-particle interactions with whistler-mode waves. The relatively simple configuration of field-aligned waves in a cold plasma is used in order to benchmark our novel method, and to compare with previous works that used a different modelling technique. In this boundary-value problem, incoherent whistler-mode waves are excited at the domain boundary, and then propagate through the ambient plasma. Electron diffusion characteristics are directly extracted from particle data across all available energy and pitch-angle space. The 'nature' of the diffusive response is itself a function of energy and pitch-angle, such that the rate of diffusion is not always constant in time. However, after an initial transient phase, the rate of diffusion tends to a constant, in a manner that is consistent with the assumptions of quasilinear diffusion theory. This work establishes a framework for future investigations on the nature of diffusion due to whistler-mode wave-particle interactions, using particle-in-cell numerical codes with driven waves as boundary value problems.Plain Language Summary 'Whistler-mode' plasma waves interact with electrons in the Earth's outer radiation belts. This wave-particle interaction plays a significant role in both electron acceleration, and in the loss of electrons to the atmosphere via 'pitch angle scattering'. Such processes are typically modelled using numerical diffusion codes, with electron diffusion coefficients that characterize the nature and the strength of the wave-particle interaction. These diffusion coefficients are calculated using a mixture of long-established theory and input parameters taken from data and/or empirical models. We present a novel method for the direct extraction of characteristics of the electron diffusion from particle-in-cell numerical experiments. Our results demonstrate that the rate of diffusion can be time-dependent at early times, but then tends to constant values in a manner that is consistent with quasilinear theory.

Particle‐in‐Cell Experiments Examine Electron Diffusion by Whistler‐Mode Waves: 2. Quasi‐Linear and Nonlinear Dynamics

“…In this paper we have used the novel experimental and analysis methods established in Allanson et al (2019) to analyze electron dynamics due to wave-particle interactions with broadband and incoherent whistler-mode waves, as a function of root-mean-square wave amplitude. Our findings are intended to provide a better understanding of the applicability of quasi-linear diffusion under the usual hypotheses of sufficiently low wave amplitude and broad wave spectrum, and in the simple case of a constant background magnetic field, for which the theory is actually derived (Kennel & Engelmann, 1966).…”

“…In a recent work, Allanson et al (2019) benchmarked a boundary value problem particle-in-cell method to analyze electron dynamics due to interactions with whistler-mode wave spectra. In particular, Allanson et al (2019) (hereafter referred to as "Paper 1") presented novel experimental and analysis techniques (using the EPOCH particle-in-cell code) to (a) excite electromagnetic whistler-mode waves within the interior of the domain, by perturbing a boundary; (b) extract diffusive characteristics of electrons across all energies and pitch angles, through the use of a distribution of noninteracting test particles embedded within the experiment.…”

“…of frequency 0.2f ce ("dash"), 0.3f ce ("solid"), and 0.4f ce ("dash-dot"). We can observe the following: (i) runs with higher amplitude waves give higher values of P α and P E ; (ii) P α > 0.5 is observed for Runs 3-5 and P E > 0.5 is observed for Runs 4-5; (iii) significant values of P α and P E are largely confined to the resonant regions, except for Run 5, which also interestingly includes drift in nonresonant regions; and mark the values of energy and pitch angle that are in "n = −1 resonance" (see Allanson et al, 2019) with waves of frequency 0.2f ce ("dash"), 0.3f ce ("solid"), and 0.4f ce ("dash-dot").…”

“…⟨Δα⟩ðE; αÞ¼⟨Δα⟩=ðα bin;max − α bin;min Þ; Allanson et al, 2019) with waves of frequency 0.2f ce ("dash"), 0.3f ce ("solid"), and 0.4f ce ("dash-dot").…”

Dependence of kinetic plasma waves on ion-to-electron mass ratio and light-to-Alfvén speed ratio

“…Nonlinear computations such as particle-in-cell, Eulerian-Vlasov, and hybrid simulations have become standard tools to model astrophysical plasma systems (Lapenta 2012;Kunz et al 2014;Markidis et al 2014;Melzani et al 2014a;Germaschewski et al 2016;Pezzi et al 2019). Computational constraints often prevent us from simulating realistic values for the multiple length scales and timescales involved in astrophysical plasma processes (Vásconez et al 2014;Franci et al 2015;Parashar et al 2015b;Allanson et al 2019;Cerri et al 2019;Pecora et al 2019;Pezzi et al 2019;Verscharen et al 2019;Matsukiyo et al 2020). In the solar wind at 1 au (Matthaeus & Goldstein 1982;McComas et al 2000;Marsch 2006;Klein & Vech 2019), for example, the energy-containing scale of the turbulence is of order L ∼ 10 6 km ∼ 10 11 cm, while the Debye length of species j,…”