Kinetic theory of magnetic island stability in tokamaks

Abstract

The nonlinear behavior of low- and large-wave number tearing modes is studied. The emphasis is laid on diamagnetic effects. A kinetic equation, including transport processes associated with a background of microturbulence, is used to describe the electron component. Such transport processes are shown to play a significant rôle in the adjustment of density and temperature profile, and also in the calculation of the island rotation frequency. The fluctuating electric potential is calculated self-consistently, using the differential response of electrons and ions. Four regimes are considered, related to island width (smaller or larger than an ion Larmor radius) and transport regime (electron–ion collisions or electroviscosity dominated). It is shown that diamagnetism does not influence the island stability for small island width in the viscous regime, as long as the constant Ψ constraint is maintained. It turns out that the release of this constraint may strongly modify the previously calculated stability thresholds. Finally, it is found that diamagnetism is destabilizing (stabilizing) for island width smaller (larger) than an ion Larmor radius, in both resistive and viscous regimes. A typical island evolution scenario is studied which shows that even large-scale tearing modes with positive Δ′ could saturate to island width of order of a few ion Larmor radii. Illustrative Δ′ threshold and island saturation size are calculated.