Internal (m=1, n=1) and (m=2, n=1) resistive modes in the toroidal tokamak with circular cross-section

A linear analysis is presented of the toroidal coupling between the internal resistive modes (m=1, n=1) and (m=2, n=1) in the tokamak with circular cross-section. The resistive and diamagnetic effects are included in the singular layers where the safety factor q takes respectively the values one and two. By expanding the MHD equations in powers of epsilon, the local inverse of the aspect ratio, a system of two coupled equations is obtained for the harmonic amplitudes. When the shear is finite on q=1 the toroidal coupling is negligible. In the opposite limit, one can explain (a) the experimental behaviour of the (m=1, n=1) mode before the internal disruption, and (b) the simultaneous observation of the modes (m=1, n=1) and (m=2, n=1) before the main disruption. (author)