Theory of resistive modes in the ballooning representation

The linear theory of current-driven resistive modes is presented in terms of the ballooning formalism, which employs the extended poloidal angle as the independent variable. This variable is proportional to the radial wave number. In the vicinity of the singular boundary layer, this formalism is applied to modes with high as well as with low poloidal mode numbers. The MHD solutions in the external region impose singular boundary conditions on the inner solutions, which must be satisfied near the origin of the extended variable. This is in contrast with coordinate space where they are expressed in integral form. These conditions are characterized by a single parameter which is assumed to be known. The collisional tearing and Alfven modes and the m=1 internal kink mode are obtained from a common dispersion relation. This is also the case for the semi-collisional tearing and Alfven modes. The structure of the modes in kr-space as well as in coordinate space is discussed.