Non-linear mirror instability

Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early non-linear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasi-linearly at a steady, low-amplitude level. Instead, the trapping of particles in small-scale mirrors leads to non-linear secular growth of magnetic perturbations, delta B/B proportional to t(2/3). Our theory explains recent collisionless simulation results, provides a prediction of the mirror evolution in weakly collisional plasmas and establishes a foundation for a theory of non-linear mirror dynamics with trapping, valid up to delta B/B = O(1).