In low-density high-temperature astrophysical plasmas, e.g., intracluster gas, protogalaxies, the ion Larmor radius is much smaller than the mean free path already for very weak magnetic fields. In this regime, while the magnetic field may not yet be dynamically important, plasma is magnetised and the adiabatic invariant is approximately coserved. This leads to the anisotropisation of the pressure (viscous stress) tensor, so the the viscous dissipation along and across the field is different. When pressure is anisotropic, there appear very fast plasma instabilities. Their growth rates are proportional to the parallel wavenumber of the perturbation, so small-scale fluctuations grow at very small scales and with growth rates that far exceed the rate of strain of the turbulent eddies. The instabilities are not fully suppressed by either Braginskii viscosity or, in the collisionless regime, by the magnetic Landau damping. The stabilisation only occurs at scales somewhat above the ion cyclotron radius, where plasma is no longer perfectly magnetised. I will present a theoretical description of these instabilities both for collisional MHD with Braginskii viscosity and in the collisionless regime. Estimates are made for the effective magnetic cutoff scale. I will also discuss the feasibility of numerical simulations of MHD with Braginskii viscosity and report on some preliminary numerical studies.
- http://www.damtp.cam.ac.uk/user/as629/ - preprints etc.