Nonlinear modeling of kinetic plasma instabilities

Many kinetic plasma instabilities, in quite different physical systems, sha re a genuinely similar mathematical structure near isolated phase-space isl ands. For this reason, dynamical features such as faster-than-exponential g rowth of the instability, as well as nonlinear frequency sweeping, are foun d to be universal. Numerical delta f methods, which follow the evolution of the (nonlinear) perturbed distribution function along single-particle orbi ts, have been applied to analytic models, which include a continuous partic le 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 experimenta lly relevant time scales. New results include (i) nonlinear simulations of two-species, one-degree-of-freedom plasmas; (ii) simulations of fishbone bu rsts in tokamak plasmas; (iii) nonlinear modeling of beam-driven toroidal A lfven eigenmode activity in tokamaks. (C) 1999 American Institute of Physic s. [S1070-664X(99)96905-7].