Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma

The non-linear state of a high-beta collisionless plasma is investigated where an imposed shear amplifies or diminishes a uniform mean magnetic field, driving pressure anisotropies and, therefore, firehose or mirror instabilities. To mimic the local behaviour of a macroscopic flow, the shear is switched off or reversed after one shear time, so a new macroscale configuration is superimposed on previous microscale state. A threshold plasma beta is found: when β ≪ Ω/S (ion cyclotron frequency/shear rate), the emergence/disappearance of firehose or mirror fluctuations is quasi-instantaneous compared to the shear time (lending some credence to popular closures that assume this). This follows from the free decay of these fluctuations being constrained by the same marginal-stability conditions as their growth in the unstable regime, giving the decay time ∼β/Ω ≪ S^-1. In contrast, when β ≳ Ω/S, the old microscale state only disappears on the shear time-scale. In this `ultra-high-beta' regime, driven firehose fluctuations grow secularly to order-unity amplitudes, compensating for the decrease of the mean field and thus pinning the pressure anisotropy at marginal stability without scattering particles - unlike what happens at moderate β. After the shear reverses, the shearing away of these fluctuations compensates for the increase of the mean field and thus prevents growth of the pressure anisotropy, so the system stays close to the firehose threshold, does not go mirror-unstable, the total magnetic energy barely changing at all. Implications for various astrophysical situations, especially the origin of cosmic magnetism, are discussed: collisionless effects appear mostly beneficial to fast magnetic-field generation.