Nonlinear toroidal plasma dynamics by reduced fluid models

Fluid models are presented which generalize reduced MHD by allowing for compressibility, Finite Larmor Radius, and long mean free path in toroidal geometry. The Hamiltonian structure of the models leads to a generalized energy principle for determining linear and nonlinear MHD stability of equilibria with flows and Finite Larmor Radius effects. Neoclassical effects from the long mean free path lead to new dissipative terms giving rotation damping, bootstrap currents and the Ware pinch. Rotation damping from non-ambipolar transport in stellarators can lead to self-consistent plasma currents which strongly reduce or ''heal'' steady-state magnetic stochasticity (e.g., from coil errors or Pfirsch-Schlueter currents). The bootstrap current in tokamaks causes the growth of nonlinear magnetic islands in the Rutherford regime. Thus, otherwise stable moderate mode number islands can potentially overlap, with serious detriment to confinement. (author)