conventional particle simulation algorithms are not practical for such study, because of the disparate time scales A hybrid MHD-gyrokinetic simulation model is presented which is suitable for self-consistent study of the interaction of energetic involved. In particular, in a conventional particle code the particles with low-frequency MHD waves. Fully electromagnetic time step is determined by the particle gyration, rather gyrokinetic equations are used to describe the energetic particles, than by the mode frequency, and this can be a severe while the cold background plasma is treated as a fluid, using nonlinrestriction when the time scales of interest are orders of ear one-fluid MHD equations. Based on this model a hybrid MHDmagnitude larger than the cyclotron period. In addition, gyrokinetic particle code has been developed. A อณf algorithm has been implemented in the code for อฑ ศ 1 electromagnetic perturba-excessive numerical noise due to the use of a limited numtions. The gyrokinetic description enables us to remove the restricber of particles in the simulation of a high beta plasma tion on the particle time step dictated by the gyromotion, while the can also be a problem, especially if the physical instability อณf algorithm strongly reduces the simulation numerical noise level.
of interest is a weak resonant type instability with a very Therefore, considerably larger time steps and a smaller number of low saturation amplitude.
particles can be used in the simulations as compared to conventional methods. The conservation properties of the model and cor-A number of hybrid MHD-gyrokinetic and MHD-drift responding อณf scheme have been investigated. Representative kinetic models has been developed for analytical and nutwo-dimensional simulations of the mirror instability and the temmerical study of kinetic effects on MHD modes with appliperature gradient driven instability of the compressional mode were cation to the space environment [3], as well as energetic performed, and the simulation results are in very good agreement particle effects on MHD stability in tokamaks [4][5][6]. In with linear theory. แฎ 1997 Academic Press these models, energetic particles are treated as gyrokinetic particles, while the cold background plasma is treated as