Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

Electron acceleration by the lower-hybrid-drift instability at Mercury: an extended quasilinear model

<p>Density inhomogeneities are ubiquitous in space and astrophysical plasmas, in particular at contact boundaries between different media. They often correspond to regions that exhibits strong dynamics on a wide range of spatial and temporal scales. Indeed, density inhomogeneities are a source of free energy that can drive various plasma instabilities such as, for instance, the lower-hybrid-drift instability<strong> </strong>which in turn transfers energy to the particles through wave-particle interactions and eventually heats the plasma. Here, we address the role of this instability in the Hermean plasma environment were kinetic processes of this fashion are expected to be crucial in the plasma dynamics and have so far eluded the measurements of past missions (Mariner-X and MESSENGER) to Mercury. <br />The goal of our work is to quantify the efficiency of the lower-hybrid-drift instability to accelerate and/or heat electrons parallel to the ambient magnetic field.<br />To reach this goal, we combine two complementary methods: full-kinetic and quasilinear models.<br />We report self-consistent evidence of electron acceleration driven by the development of the lower-hybrid-drift instability using 3D-3V full-kinetic numerical simulations. The efficiency of the observed acceleration cannot be explained by standard quasilinear theory. For this reason, we develop an extended quasilinear model able to quantitatively predict the interaction between lower-hybrid fluctuations and electrons on long time scales, now in agreement with full-kinetic simulations results. Finally, we apply this new, extended quasilinear model to a specific inhomogeneous space plasma boundary: the magnetopause of Mercury, and we discuss our quantitative predictions of electron acceleration in support to future BepiColombo observations.</p>

Electron pitch angle diffusion and rapid transport/advection during nonlinear interactions with whistler-mode waves

<p>Radiation belt numerical models utilize diffusion codes that evolve electron dynamics due to resonant wave-particle interactions. It is not known how to best incorporate electron dynamics in the case of a wave power spectrum that varies considerably on a 'sub-grid' timescale shorter than the computational time-step Δt, particularly if the wave amplitude reaches high values. Timescales associated with the growth rate, γ, of thermal instabilities are very short, and typically Δt>>1/γ. We use a kinetic code to study electron interactions with whistler-mode waves in the presence of a background plasma with thermally anisotropic components, as frequently occur within the magnetosphere. For low values of anisotropy, thermal instabilities are not triggered and we observe similar results to those obtained in Allanson et al. (2020, https://doi.org/10.1029/2020JA027949), for which the diffusion matched the quasilinear theory over short timescales inversely proportional to wave power. For high levels of anisotropy, wave growth via instability is triggered. Dynamics are not well described by the quasilinear theory when calculated using the average wave power. During the growth phase (~0.1s) we observe strong diffusive and advective components, which both saturate as the wave power saturates at ~ 1nT. The advective motions dominate over the diffusive processes. The growth phase facilitates significant transport in electron pitch angle space via successive resonant interactions with waves of different frequencies. This motivates future work on the longer-time impact of very short timescale processes in radiation belt modelling, and on the indirect effects of anisotropic background plasma components on electron scattering. We suggest that this rapid advective transport during nonlinear wave growth phase may have a role to play in the electron microburst mechanism.</p><p><em>[Allanson et al, JGR Space Physics, 2021 (under review)]</em></p>

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann (Phys. Fluids, vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

Theoretical plasma physics

These lecture notes were presented by Allan N. Kaufman in his graduate plasma theory course and a follow-on special topics course (Physics 242A, B, C and Physics 250 at the University of California Berkeley). The notes follow the order of the lectures. The equations and derivations are as Kaufman presented, but the text is a reconstruction of Kaufman’s discussion and commentary. The notes were transcribed by Bruce I. Cohen in 1971 and 1972, and word processed, edited and illustrations added by Cohen in 2017 and 2018. The series of lectures is divided into four major parts: (i) collisionless Vlasov plasmas (linear theory of waves and instabilities with and without an applied magnetic field, Vlasov–Poisson and Vlasov–Maxwell systems, Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) eikonal theory of wave propagation); (ii) nonlinear Vlasov plasmas and miscellaneous topics (the plasma dispersion function, singular solutions of the Vlasov–Poisson system, pulse-response solutions for initial-value problems, Gardner’s stability theorem, gyroresonant effects, nonlinear waves, particle trapping in waves, quasilinear theory, nonlinear three-wave interactions); (iii) plasma collisional and discreteness phenomena (test-particle theory of dynamic friction and wave emission, classical resistivity, extension of test-particle theory to many-particle phenomena and the derivation of the Boltzmann and Lenard–Balescu equations, the Fokker–Planck collision operator, a general scattering theory, nonlinear Landau damping, radiation transport and Dupree’s theory of clumps); (iv) non-uniform plasmas (adiabatic invariance, guiding-centre drifts, hydromagnetic theory, introduction to drift-wave stability theory).

Quasilinear approach of the cumulative whistler instability in fast solar wind: Constraints of electron temperature anisotropy

Context. Solar outflows are a considerable source of free energy that accumulates in multiple forms such as beaming (or drifting) components, or temperature anisotropies, or both. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the electron temperature (T) in fast solar winds are not explained yet. Aims. This paper provides an advanced quasilinear description of the whistler instability driven by the anisotropic electrons in conditions typical for the fast solar winds. The enhanced whistler-like fluctuations may constrain the upper limits of temperature anisotropy A ≡ T⊥/T∥ > 1, where ⊥, ∥ are defined with respect to the magnetic field direction. Methods. We studied self-generated whistler instabilities, cumulatively driven by the temperature anisotropy and the relative (counter)drift of electron populations, for example, core and halo electrons. Recent studies have shown that quasi-stable states are not bounded by linear instability thresholds but an extended quasilinear approach is necessary to describe these quasi-stable states in this case. Results. Marginal conditions of stability are obtained from a quasilinear theory of cumulative whistler instability and approach the quasi-stable states of electron populations reported by the observations. The instability saturation is determined by the relaxation of both the temperature anisotropy and relative drift of electron populations.