Hybrid simulations of the effects of energetic particles on low-frequency MHD waves

A hybrid MHD-gyrokinetic simulation model is presented which is suitable for self-consistent study of the interaction of energetic particles with low-frequency MHD waves. Fully electromagnetic gyrokinetic equations are used to describe the energetic particles, while the cold background plasma is treated as a fluid, using nonlinear one-fluid MHD equations. Based on this model a hybrid MHD-gyrokinetic particle code has been developed. A δfalgorithm has been implemented in the code for β ~ 1 electromagnetic perturbations. The gyrokinetic description enables us to remove the restriction on the particle time step dictated by the gyromotion, while the δfalgorithm strongly reduces the simulation numerical noise level. Therefore, considerably larger time steps and a smaller number of particles can be used in the simulations as compared to conventional methods. The conservation properties of the model and corresponding δfscheme have been investigated. Representative two-dimensional simulations of the mirror instability and the temperature gradient driven instability of the compressional mode were performed, and the simulation results are in very good agreement with linear theory.