Effects of Pressure-Anisotropy-Driven Instabilities on the Electrical Resistivity of Collisionless, High-Beta Plasmas

Collisionless, high-beta plasmas are generally subject to pressure-anisotropy-driven instabilities, such as the firehose and mirror instabilities. These instabilities lead to the growth of persistent electromagnetic perturbations on the Larmor scales, causing scattering and trapping of particles. This process has been shown to regulate the effective viscosity of the plasma. In this study, we investigate whether these instabilities also impact the electrical resistivity of the plasma by formulating and solving the collisionless, high-beta version of the classic Spitzer-Haerm problem. We utilize an expanding-box framework within the fully kinetic particle-in-cell code TRISTAN-MP to drive a spatially constant pressure anisotropy that is unstable to firehose instability. Concurrently, we apply an external electric field and measure the resulting current through the plasma affected by the firehose instability. To ensure a steady-state solution, we employ novel boundary conditions that complete the circuit across the simulation domain. We find that the unstable plasma's effective resistivity depends on the plasma beta and the macroscopic timescale on which the pressure anisotropy is driven, and discuss to what extent this result may be understood within quasi-linear theory. This effective plasma resistivity can be implemented as a sub-grid model into magnetohydrodynamic simulations of high-beta plasmas in which the firehose instability would otherwise be active.