Tokamak MHD instabilities: allowance methods for toroidicity in the theory of internal kink modes

This chapter presents the so-called covariant form of linearized ideal MHD equations. The correspondence of these equations are discussed with the potential-energy functional. The perturbations and metric coefficients are expanded in the Fourier series in azimuthal harmonics to perform simplifications related to the assumption of a large aspect ratio of the tokamak. As a result the author arrives at the desired set of equations necessary for subsequent analysis of the ideal internal kink mode stability