A kinetic theory for the evolution of magnetic islands is considered in a tokamak plasma, in both the low (νi ≪ ω) and high (νi ≫ ω) collision frequency limits (νi is the ion collision frequency, is the inverse aspect ratio and ω is the island propagation frequency in the E × B rest frame). The calculation of the bootstrap current perturbation in the presence of a magnetic island is reviewed, and is confirmed to be independent of ω and the collision frequency regime. The neoclassical polarization current perturbation is calculated in the two collision frequency limits (within the banana regime). The result in the collisional limit is in agreement with a fluid theory. The effect of collisions in the 'dissipation layer' at the trapped/passing boundary is also considered, for νi ≪ ω. It is found that the dissipation layer provides an additional contribution to the neoclassical polarization current perturbation. Consequently, if the polarization current is stabilizing, it provides a critical island width for instability, which is found to scale as , where r is a weak logarithmic function of .
Localized drift dissipative modes in Tokamaks