Alfven wave heating in the ideal MHD and Guiding Center Plasma models

Plasma heating through resonant absorption of Alfven waves is studied within the framework of the ideal MHD and Guiding Center Plasma models. The heating procedure is applied to a plasma in a steady state equilibrium in a one-dimensional slab surrounded by vacuum regions on both sides. First, the well-established ideal MHD model is reviewed. In the presence of an external excitation, the equation for the displacement of the plasma from its equilibrium position is presented along with the appropriate boundary conditions and corresponding energy absorption rate. Later, the similar calculations are done in the Guiding-Center Plasma model, where the controversial assumptions of adiabaticity and implicit large collisionality of ideal MHD are dropped and the stress tensor is allowed to be anisotropic. A one dimensional gyrokinetic equation is utilized to find the gyrokinetic distribution function. Moments of this distribution function are calculated to find the stress tensor which is then inserted into MHD equations to obtain an ordinary differential equation for the displacement of the plasma. It is found that the cusp resonance of ideal MHD has disappeared and that another resonance continuum depending on the plasma dispersion relation has appeared in this model. Finally, a numerical code is developed for both models and results are compared