Ideal- and resistive-MHD stability of one-dimensional tokamak equilibria

The MHD equilibrium and stability of a vertically elongated tokamak configuration are analysed 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, centred 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 non-symmetric tearing modes (m ≠ 0), centred 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.