Towards fluid simulations of dispersive MHD waves in a warm collisionless plasma

A Landau fluid model suited for the description of the weakly nonlinear dynamics of long wavelength dispersive MHD waves in a magnetized collisionless plasma is presented, that should be useful to study the formation and stability of solitary structures such as magnetic holes or shocklets observed for example in the solar wind and the terrestrial magnetosheath. First simulations in a slab geometry are reported, that focus on the evolution of plane fast magnetosonic waves. Accurate comparisons are made with analytic predictions of the Landau damping rate for various plasma parameters and wave characteristics. In a regime where Landau damping dominates, Alfvén modes eventually become prevalent, which results in the arrest of dissipation at a time that is shorter for waves with larger initial amplitude. In contrast, magnetosonic solitary waves in the form of density and magnetic field depressions are found to emerge in a regime where Landau dissipation is initially negligible compared with nonlinear and dispersive effects. Excellent agreement is also found for the growth rate of the mirror instability at long wavelength but modeling the arrest of the instability at small scales within fluid simulations remains a challenging issue.