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In low-collisionality plasmas, velocity-space instabilities are a keymechanism providing an effective collisionality for the plasma. We useparticle-in-cell (PIC) simulations to study the interplay between electron andion-scale velocity-space instabilities and their effect on electron pressureanisotropy, viscous heating, and thermal conduction. The adiabatic invarianceof the magnetic moment in low-collisionality plasmas leads to pressureanisotropy, $p_{\perp,j} > p_{||,j}$, if the magnetic field $\vec{B}$ isamplified ($p_{\perp,j}$ and $p_{||,j}$ denote the pressure of species $j$[electron, ion] perpendicular and parallel to $\vec{B}$). If the resultinganisotropy is large enough, it can in turn trigger small-scale plasmainstabilities. Our PIC simulations explore the nonlinear regime of the mirror,ion-cyclotron, and electron whistler instabilities, through continuousamplification of the magnetic field $|\vec{B}|$ by an imposed shear in theplasma. In the regime $1 \lesssim \beta_j \lesssim 20$ ($\beta_j \equiv 8\pip_j/|\vec{B}|^2$), the saturated electron pressure anisotropy, $\Deltap_e/p_{||,e}$, is determined mainly by the (electron-lengthscale) whistlermarginal stability condition, with a modest factor of $\sim 1.5-2$ decrease dueto the trapping of electrons by the mirrors. We explicitly calculate the meanfree path of the electrons and ions along the mean magnetic field and provide asimple physical prescription for the mean free path and thermal conductivity inlow-collisionality $\beta_j \gtrsim 1$ plasmas. Our results imply thatvelocity-space instabilities likely decrease the thermal conductivity of plasmain the outer parts of massive, hot, galaxy clusters. We also discuss theimplications of our results for electron heating and thermal conduction inlow-collisionality accretion flows onto black holes, including Sgr A* in theGalactic Center.

PIC Simulations of the Effect of Velocity Space Instabilities on Electron Viscosity and Thermal Conduction