Whistler turbulence: Particle-in-cell simulations

Abstract

Two-dimensional electromagnetic particle-in-cell simulations in a magnetized, homogeneous, collisionless electron-proton plasma demonstrate the forward cascade of whistler turbulence. The simulations represent decaying turbulence, in which an initial, narrowband spectrum of fluctuations at wavenumbers kc∕ωe≃0.1 cascades toward increased damping at kc∕ωe≃1.0, where c∕ωe is the electron inertial length. The turbulence displays magnetic energy spectra that are relatively steep functions of wavenumber and are anisotropic with more energy in directions relatively perpendicular to the background magnetic field Bo=x̂Bo than at the same wavenumbers parallel to Bo. In the weak turbulence regime, the primary new results of the simulations are as follows: (1) Magnetic spectra of the cascading fluctuations become more anisotropic with increasing fluctuation energy; (2) the wavevector dependence of the three magnetic energy ratios, ∣δBj∣2∕∣δB∣2 with j=x,y,z, show good agreement with linear dispersion theory for whistler fluctuations; (3) the magnetic compressibility summed over the cascading modes satisfies 0.3≲∣δBx∣2∕∣δB∣2≲0.6; and (4) the turbulence heats electrons in directions both parallel and perpendicular to Bo, with stronger heating in the parallel direction.

Anisotropy in solar wind plasma turbulence

“…Reasonable agreement between linear theory and observations is used to conclude in favour of one mode or another. The majority of studies cite KAWs as the most likely candidate, with whistlers typically (but not always [64]) being a poor fit to measurements [42,43,64,101,108,109,113,114]. Note that linear theory predictions are overwhelmingly determined using a uniform and constant global mean field, whereas recent observational results often employ space (or time)-dependent B loc 0 .…”

“…Moreover, these explanations all presume that the fluctuations are dominantly wave-like. Although there is some numerical support for the wave-based explanations of variance anisotropy, for example in particle-in-cell simulations [113] and gyrokinetic simulations [101], it remains unclear whether strong turbulence has this property, at either MHD scales or sub-ion ones [115][116][117]; cf. §3b.…”

Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer

“…Some authors argue that it does not [83][84][85][86][87][88][89] and argue that kinetic Alfvén waves provide the observed steepening, but some of these observations have been brought into question [90]. Dispersion is sometimes invoked as an explanation for the steepening of the power spectrum at ion dissipation scales [55,[91][92][93][94][95] and whistler waves are also discussed in the context of forming the dissipation range at ion scales [92,[96][97][98]. The central issue to that question rests with the dissipation processes that remove energy from the turbulence and produce heat.…”

Electromagnetic waves and electron anisotropies downstream of supercritical interplanetary shocks

“…Many theories [e.g., Gary et al, 1994;Vocks et al, 2005;Saito and Gary, 2007] of the evolution of electrons from the Sun to the Earth suggest WWs scatter strahl electrons into the halo, which may explain the observed changes [e.g., Štverák et al, 2009] in the relative densities of strahl versus halo electrons. Theories have also suggested that WWs constrain the heat flux carrying electrons [e.g., Gary et al, 1994Gary et al, , 1999, e.g., strahl, and the halo/core electron temperature anisotropies [e.g., Vocks and Mann, 2003;Saito et al, 2008]. The core electrons have been observed to isotropize due to binary collisions [e.g., Salem et al, 2003], while halo electrons appear to be constrained by the whistler anisotropy and firehose instabilities in the slow solar wind [e.g., Štverák et al, 2008].…”