Nonlinear Evolution of the Resistive MHD Modes in a Toroidal Plasma

The nonlinear stabilities of resistive MHD modes are investigated in a tokamak configuration by a three dimensional MHD simulation based on a rectangular column model under the fixed boundary condition. The m =1 internal resistive kink mode is excited for the central safety factor, q 0 < 1, resulting in a sawtooth oscillation of temperature. Only the m =2 mode is excited for q 0 < 2 and a small resistivity. On the other hand, the several modes of (- m : n )=(2:1), (1:1) and (3:2) appear for q 0 < 2 and a little large resistivity depending on the q -configuration through the variation of toroidal current. The (3:2) mode plays an important role on the mode coupling between the (1:1) and (2:1) modes. As the result, the (2:1) mode finally determines the stability and stable configurations of plasma are formed with the condition of \(q 2\).