Nonlinear gyrokinetic theory for steady-state mirror mode magnetic structures

Abstract

The analytic study of the saturated state of the mirror instability is presented. The perpendicular ion momentum is described by the hydrodynamic equations, with the finite Larmor radius corrections found from the collisionless stress tensor, while the ion density, the parallel flow, and the pressure are calculated using the gyrokinetic description, accounting for the nonlinear convection by the grad-B drift. Within such a model and using a generalized Schamel's distribution function for the trapped ions, it is possible to study fully nonlinear wave-particle interactions, including the contributions of the finite ion Larmor radius correction and of the trapped ions. The numerical solution reveals the bistability in the stationary regime. Two different nonlinear solutions are found under the same physical conditions, in the form of magnetic humps and magnetic holes, resulting from the wave-wave and wave-particle couplings, respectively. The trapped particles are found to be heated in the parallel direction and their temperature is almost isotropic. The solution is in a good agreement with the magnetic structures observed in the magnetosheath within the solar system and in computer simulations. It provides an explanation for the transformation of humps into holes, as observed in recent computer simulations.