Trapped-particle effects in the nonlinear evolution of magnetic islands

It has been demonstrated within the framework of neoclassical MHD theory, that the fluctuating bootstrap current can nonlinearly sustain magnetic islands in tokamaks in situations when the tearing-mode stability index Δ' is negative. In that theory it was assumed that the plasma pressure equilibrates along the perturbed magnetic surfaces, so that it is a function of a generalized poloidal flux, p = p(ψ), where ψ = -x2B0/2Ls + ψcosα. On the other hand, in high temperature plasmas such as modern tokamak experiments, the deviation of particle orbits from the flux surface due to the finite banana width might be sufficient to violate the condition p = p(ψ). In a toroidal magnetic field, such oscillations yield an additional contribution to the current closure equation ∇parallelJ+=0 where means everaging along the bounce trajectory and (hor-ellipsis) corresponds to bounce oscillations of corresponding quantities. Resonant magnetic perturbations that create the magnetic islands also produce perturbations of the electrostatic potential. In a stationary state the electrostatic potential can be considered to be approximately constant on magnetic surfaces. Because of the finite deviations of the particle orbits from the magnetic surface, the effective E x B drift experienced by the ions will be different from that for electrons. This difference creates a direct mechanism of charge separation, which, via charge neutrality, induces a longitudinal current. This mechanism is physically similar to that considered by Rebut and Hugon for islands whose width is comparable to the ion Larmor radius. The longitudinal current induced by the combination of the above trapped particle effects may substantially modify the island dynamics when the ion banana width is comparable to the island width