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

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_⊥,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 ≲ β_j ≲ 20 (β_j ≡ 8πp_j |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 δpe/p_∥,e ≈ δpi/p_∥,i (where δpj = p_⊥j - p_∥j). We also quantify the thermal conduction of the plasma by directly calculating the mean free path of electrons, λ_e, along the mean magnetic field, finding that λ_e 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.