Landau fluid models of collisionless magnetohydrodynamics

A closed set of fluid moment equations including models of kinetic Landau damping is developed which describes the evolution of collisionless plasmas in the magnetohydrodynamic parameter regime. The model is fully electromagnetic and describes the dynamics of both compressional and shear Alfvén waves, as well as ion acoustic waves. The model allows for separate parallel and perpendicular pressures p_∥ and p_⊥, and, unlike previous models such as the Chew-Goldberger-Low theory, correctly predicts the instability threshold for the mirror instability. Both a simple 3 +1 moment model and a more accurate 4 + 2 moment model are developed, and both could be useful for numerical simulations of astrophysical and fusion plasmas.