Hybrid magnetohydrodynamic-kinetic model of standing shear Alfvén waves

We have developed a hybrid magnetohydrodynamics (MHD) kinetic box model valid for standing shear Alfvén waves using the cold plasma MHD equations coupled to a system of kinetic electrons. The guiding centre equations are used for the motion of the electrons and the system is closed via an expression for the field-aligned electric field in terms of the perpendicular electric field and moments of the electron distribution function. The perpendicular electric fields are derived from the ideal MHD approximation. We outline the basic model equations and method of solution. Simulations are then presented comparing the hybrid model results with a cold plasma MHD model. Landau damping is shown to heavily damp the standing shear Alfvén wave in the hybrid simulations when v_{th} ≥ V_{A}. The damping rate is shown to be in good agreement with the theoretical rate calculated for the model parameters.