Ideal and resistive MHD stability of one-dimensional tokamak equilibria

The MHD equilibrium and stability of a vertically elongated tokamak configuration are analyzed in the one-dimensional limit corresponding to infinite elongation. Stability against all ideal MHD modes can be obtained for beta-values arbitrarily close to unity. In the finite-resistivity stability analysis, axisymmetric (m = 0) tearing modes, centered on the null trace of the poloidal field, can be stabilized by a loosely fitting conducting shell. The presence of the toroidal field component, however, introduces the possibility of nonsymmetric tearing modes (m not equal to 0), centered away from the null trace. These modes can be stabilized only by a more tightly-fitting shell, plus reliance on finite-pressure effects on the small-major-radius side of the plasma profile. Under these conditions, stable configurations with peak beta values approaching unity are readily found.