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We use particle-in-cell (PIC) simulations of a collisionless, electron-ionplasma with a decreasing background magnetic field, $B$, to study the effect ofvelocity-space instabilities on the viscous heating and thermal conduction ofthe plasma. If $B$ decreases, the adiabatic invariance of the magnetic momentgives rise to pressure anisotropies with $p_{||,j} > p_{\perp,j}$ ($p_{||,j}$and $p_{\perp,j}$ represent the pressure of species $j$ ($=i$ or $e$) paralleland perpendicular to the magnetic field). Linear theory indicates that, forsufficiently large anisotropies, different velocity-space instabilities can betriggered. These instabilities, which grow on scales comparable to the electronand ion Larmor radii, in principle have the ability to pitch-angle scatter theparticles, limiting the growth of the anisotropies. Our PIC simulations focuson the nonlinear, saturated regime of the instabilities. This is done throughthe 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 arecontrolled by the combined effect of the oblique ion firehose (OIF) and thefast magnetosonic/whistler (FM/W) instabilities. These instabilities growpreferentially on the ion Larmor radius scale, and make the ion and electronpressure anisotropies nearly equal: $\Delta p_e/p_{||,e} \approx \Deltap_i/p_{||,i}$ (where $\Delta p_j=p_{\perp,j} - p_{||,j}$). We also quantify thethermal conduction of the plasma by directly calculating the mean free path ofelectrons along the mean magnetic field, which we find strongly depends onwhether $B$ decreases or increases. Our results can be applied in studies oflow collisionality plasmas such as the solar wind, the intracluster medium, andsome accretion disks around black holes.

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