Nonlinear modeling of kinetic plasma instabilities

Many kinetic plasma instabilities, in quite different physical systems, share a genuinely similar mathematical structure near isolated phase-space islands. For this reason, dynamical features such as faster-than-exponential growth of the instability, as well as nonlinear frequency sweeping, are found to be universal. Numerical delta f methods, which follow the evolution of the (nonlinear) perturbed distribution function along single-particle orbits, have been applied to analytic models, which include a continuous particle source, resonant particle collisions, and wave damping. The result is a series of codes that can reliably model the nonlinear evolution of kinetic instabilities, including some specific to tokamak plasmas, over experimentally relevant time scales. New results include (i) nonlinear simulations of two-species, one-degree-of-freedom plasmas; (ii) simulations of fishbone bursts in tokamak plasmas; (iii) nonlinear modeling of beam-driven toroidal Alfven eigenmode activity in tokamaks. (C) 1999 American Institute of Physics. [S1070-664X(99)96905-7].