Self-sustaining sound in collisionless, high-β plasma

Abstract

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $\delta n/n_0 \gtrsim 2/\beta$ (where $\beta \gg {1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $\delta n/n_0 \gtrsim 2/\beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.

Particle energization in relativistic plasma turbulence: solenoidal versus compressive driving

“…We point out that qualitative differences may be expected the high-beta regime due to the effect of plasma microinstabilities such as the firehose and mirror instabilities, which arise from pressure anisotropy (Kunz et al 2014). In particular, it was recently suggested that these microinstabilities may impede Landau damping of large-scale compressive fluctuations (Kunz et al 2020), which would have consequences on the results described here.…”

Observations of Cross Scale Energy Transfer in the Inner Heliosphere by Parker Solar Probe

“…In this picture the exchange between kinetic and magnetic fluctuations happens at relatively large scales in the inertial range. There are also suggestions that magnetic reconnection, and in some situations large scale instabilities, could potentially bypass the cascade and transfer energy directly into the kinetic range and into internal degrees of freedom [79][80][81].…”

A Measurement of the Effective Mean-Free-Path of Solar Wind Protons

“…The measured effective mean-free-path and mean proton thermal speed (measured with this data set) gives an effective collision frequency of ν eff = v p th /λ eff mfp = 1.11 ×10 −4 s −1 . The transition frequency, where ν eff ≃ ω can be estimated with ν eff = v p th /λ eff mfp and the ion-acoustic dispersion relation ω IA = k c s , giving the parallel transition wavenumber k trans = v p th /c s λ eff mfp [37,51,65]. Using the wavenumber model (Eq.…”

“…Effective collisional processes have long been studied theoretically and numerically [3,[68][69][70][71][72][73], but it is an open question as to the relevant role of the various mechanisms [2,[40][41][42][74][75][76]) and how they are activated [65,77,78]. Therefore, further studies are necessary to assess exactly what key physics of weakly collisional plasma leads to the measured effective collisionality, since most astrophysical plasmas, being multi-scale and turbulent, will support effective collision mechanisms [79].…”