Effects of a poloidal divertor separatrix on resistive magnetohydrodynamic instabilities in a tokamak

A computer code package has been developed to simulate the linear and nonlinear evolution of long-wavelength resistive magnetohydrodynamic (MHD) instabilities in a four-node poloidal divertor tokamak (e.g., Wisconsin Tokapole II [Nucl. Fusion 19, 1509 (1979)]). Distinguishing features of this package include the use of a full set of three-dimensional (3-D) nonlinear resistive MHD equations and the inclusion of the divertor separatrix and the plasma outside the divertor separatrix in the computational domain. The present numerical results suggest that the plasma current outside the divertor separatrix tends to linearly stabilize the resistive MHD instability dominated by the m=2, n=1 mode, and, to a lesser extent, that dominated by the m=1, n=1 mode. (Here, m and n are poloidal and toroidal mode numbers, respectively.) However, the nonlinear evolution of the m=1, n=1 dominant instability is not significantly affected by the divertor configuration; the m=1, n=1 island is shown to reconnect totally by developing a large region of magnetic stochasticity. Hence, the cause of the partial reconnection observed in Tokapole II seems to lie beyond the scope of the classical resistive MHD model.