PIC Simulations of Velocity-Space Instabilities in a Decreasing Magnetic Field: Viscosity and Thermal Conduction

TL;DR

This study uses PIC simulations to investigate how velocity-space instabilities in a decreasing magnetic field influence plasma viscosity and thermal conduction, with implications for astrophysical low-collisionality plasmas.

Contribution

It demonstrates the nonlinear saturation of instabilities controlling pressure anisotropies and quantifies electron mean free paths in decreasing magnetic fields.

Findings

Pressure anisotropies are limited by oblique ion firehose and FM/W instabilities.

Ion and electron anisotropies become nearly equal in saturated state.

Electron mean free path depends strongly on magnetic field variation direction.

Abstract

We use particle-in-cell (PIC) simulations of a collisionless, electron-ion plasma with a decreasing background magnetic field, $B$, to study the effect of velocity-space instabilities on the viscous heating and thermal conduction of the plasma. If $B$ decreases, the adiabatic invariance of the magnetic moment gives rise to pressure anisotropies with $p_{||,j} > p_{\perp,j}$ ($p_{||,j}$ and $p_{\perp,j}$ represent the pressure of species $j$ ($=i$ or $e$) parallel and perpendicular to the magnetic field). Linear theory indicates that, for sufficiently large anisotropies, different velocity-space instabilities can be triggered. These instabilities, which grow on scales comparable to the electron and ion Larmor radii, in principle have the ability to pitch-angle scatter the particles, limiting the growth of the anisotropies. Our PIC simulations focus on the nonlinear, saturated regime of the instabilities. This is done through the permanent decrease of the magnetic field by an imposed shear in the plasma. Our results show that, in the regime $2 \lesssim \beta_j \lesssim 20$ ($\beta_j \equiv 8\pi p_j/B^2$), the saturated ion and electron pressure anisotropies are controlled by the combined effect of the oblique ion firehose (OIF) and the fast magnetosonic/whistler (FM/W) instabilities. These instabilities grow preferentially on the ion Larmor radius scale, and make the ion and electron pressure anisotropies nearly equal: $\Delta p_e/p_{||,e} \approx \Delta p_i/p_{||,i}$ (where $\Delta p_j=p_{\perp,j} - p_{||,j}$). We also quantify the thermal conduction of the plasma by directly calculating the mean free path of electrons along the mean magnetic field, which we find strongly depends on whether $B$ decreases or increases. Our results can be applied in studies of low collisionality plasmas such as the solar wind, the intracluster medium, and some accretion disks around black holes.