A non-linear theory of tearing modes in a magnetized plasma which retains the effect of cross-field diffusion on the ion polarization current is presented. This ion polarization current is predicted to influence the tearing mode evolution when its amplitude is small, corresponding to a magnetic island with a width that is comparable to the ion Larmor radius. It is therefore likely to be most relevant for understanding whether tearing modes can drive magnetic turbulence, and for understanding the threshold physics of neoclassical tearing modes, of particular relevance to tokamaks. There are two opposing contributions to the ion polarization current: one from a narrow layer in the vicinity of the island separatrix and one in the opposite direction from outside this layer. These contributions are comparable, so the net effect of the ion polarization current on tearing mode stability requires a quantitative prediction of both. The region outside the layer is relatively well understood. The separatrix layer, on the other hand, must treat a range of complex physics mechanisms, including finite Larmor radius effects and the influence of cross-field diffusion. This paper treats both together for the first time. The cross-field diffusion is found to have the following influences on the separatrix region: (i) the density distribution is smoothed across the separatrix; (ii) density is no longer a flux surface function and (iii) the distribution function is not entirely Maxwellian. The net effect of including cross-field diffusion is a substantial reduction of the contribution of the ion polarization current from the separatrix layer region.
Analysis of turbulence diffusion and H-mode transition in conjunction with gyrocentre shift at the boundary of fusion devices