Investigation of tearing modes with toroidal coupling in a tokamak with arbitrary plasma cross-section and aspect ratio

For an axisymmetric toroidal geometry, the individual poloidal harmonics are coupled together, while the toroidal harmonics remain independent; thus, there can be many resonance surfaces for each toroidal mode number and, correspondingly, many Δ'm/n parameters. The effect of the toroidicity on the tearing modes has been examined elsewhere. In the present paper, a system of Euler equations of the potential energy functional for toroidal tearing modes in a tokamak with arbitrary cross-section and aspect ratio, has been drawn. Starting from this equations, a numerical algorithm has been developed in order to calculate the perturbations of the flux function and the Δ'm/n parameter. Writing the general expression of the potential energy W in terms of the perturbation of the flux function instead of the plasma displacement, one obtains the energy functional for the tearing modes. (author) 5 refs., 2 figs