Stability against axisymmetric modes and free boundary n = 1 kink modes in a nearly circular tokamak with a poloidal divertor is investigated by using the linear ideal MHD code ERATO-J. Perturbations localized near the plasma surface (divertor) are shown to reduce the growth rate of MHD modes. Although the local variation of the n-index is large because of the presence of an X-point, a wide stability window for axisymmetric modes similar to limiter configurations is obtained. The detailed characteristics of the axisymmetric stability depend on the position of the X-point in the poloidal plane and on the structure of the divertor coil system. The large shear near the plasma surface is effective in stabilizing free boundary n = 1 kink modes. This shear stabilization is sensitive to the details of the divertor geometry, such as the location and number of X-points, and to the plasma pressure. The dependence of the critical beta on the current profile is also discussed.
Shape optimization of surface-current-model tokamaks with elongated cross-sections