Preliminary results of eigenvalue and eigenvector treatment for kink instabilities in tokamaks

A mathematical method is presented for the treatment of MHD instabilities in a simplified model, but illustrative of the plasmas in a tokamak. First order perturbation treatment of MHD equilibrium equations has been performed, leading to a set of differential equations and associated dispersion relations characteristic of kink modes. Using appropriate boundary conditions these equations are solved and the frequency eigenvalues are found in the stable region. The unstable growth rates have been also found with more accuracy than in the usual functional treatment using the energy integral.