Helical temperature perturbations associated with radially asymmetric magnetic island chains in tokamak plasmas
The simple analysis of Rutherford is generalized in order to incorporate radial magnetic island asymmetry into the nonlinear theory of tearing mode stability in a low- β , large aspect-ratio, quasi-cylindrical, tokamak plasma. The calculation is restricted to cases in which the radial shifts of the island X- and O-points are (almost) equal and opposite. For the sake of simplicity, the calculation concentrates on a particular (but fairly general) class of radially asymmetric island magnetic flux-surfaces that can all be mapped to the same symmetric flux-surfaces by means of a suitable coordinate transform. Finally, the combination of island asymmetry (in which the radial shifts of the X- and O-points are almost equal and opposite) and temperature-induced changes in the inductive current profile in the immediate vicinity of the island is found to have no effect on tearing mode stability.