Dynamical Model for Nonlinear Mirror Modes near Threshold

Using a reductive perturbative expansion of the Vlasov-Maxwell (VM) equations for magnetized plasmas, a pseudodifferential equation of gradient type is derived for the nonlinear dynamics of mirror modes near the instability threshold. This model, where kinetic effects arise at a linear level only, develops a finite-time singularity, indicating the existence of a subcritical bifurcation. A saturation mechanism based on the local variations of the ion Larmor radius, is then phenomenologically supplemented. In contrast with previous models where saturation is due to the cooling of a population of trapped particles, the resulting equation correctly reproduces results of numerical simulations of VM equations, such as the development of magnetic humps from an initial noise, and the existence of stable large-amplitude magnetic holes both below and slightly above threshold.