Application of the two-dimensional Newcomb problem to compute the stability matrix of external MHD modes in a tokamak

The theory of the Newcomb equation has been applied to low-n external modes in a tokamak and a method has been developed for computing the stability matrix that gives the change of plasma potential energy due to external modes in terms of the surface values of the perturbations. By using this method, the spectral properties of the ideal external modes have been elucidated, such as the coupling between external modes and internal modes, and the difference in the stability properties between a normal shear tokamak and a reversed shear tokamak. These results will also be useful in the stability analysis of resistive wall modes.