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

Riquelme, Mario; Quataert, Eliot; Verscharen, Daniel

We use particle-in-cell (PIC) simulations of a collisionless, electron-ion plasma with a decreasing background magnetic field, {\boldsymbol{B}}, to study the effect of velocity-space instabilities on the viscous heating and thermal conduction of the plasma. If | {\boldsymbol{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 (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 | {\boldsymbol{B}}| by an imposed plasma shear. We show that, in the regime 2≲ {β }_{j}≲ 20 ({β }_{j}\equiv 8π {p}_{j}/| {\boldsymbol{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 {{∆ }}{p}_{e}/{p}_{| | ,e}≈ {{∆ }}{p}_{i}/{p}_{| | ,i} (where {{∆ }}{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, {λ }_{e}, along the mean magnetic field, finding that {λ }_{e} depends strongly on whether | {\boldsymbol{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.