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

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 p ∣∣, , j j > ^ ( ∣∣ p ,j and p^,j represent the pressure of species j (electron or ion) parallel and perpendicular to B). Linear theory indicates that, for sufficiently large anisotropies, different velocity-space instabilities can be triggered. These instabilities in principle have the ability to pitch-angle scatter the particles, limiting the growth of the anisotropies. Our simulations focus on the nonlinear, saturated regime of the instabilities. This is done through the permanent decrease of ∣ ∣ B by an imposed plasma shear. We show that, in the regime 2   bj 20 (b p j º 8 pj ∣ ∣ B 2), the saturated ion and electron pressure anisotropies are controlled by the combined effect of the oblique ion firehose and the fast magnetosonic/whistler instabilities. These instabilities grow preferentially on the scale of the ion Larmor radius, and make Dpp pp ee i ∣∣ ∣∣ , , » D i (where D = - ^ ∣∣ pp p jj j , , ). We also quantify the thermal conduction of the plasma by directly calculating the mean free path of electrons, le, along the mean magnetic field, finding that le depends strongly 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.