Numerical computation of MHD spectrum of non-circular, small-aspect-ratio Tokamaks

A spectral code has been developed to compute the ideal MHD spectrum of axisymmetric toroidal plasmas of arbitrary cross-section; it is applied to the Soloviev equilibrium. The aspect ratio is kept fixed to 3. The corresponding ratio between the safety factors at the edge and on the axis q sub s/q(0) is equal to 1.74. Two different shapes are considered: an almost circular cross-section and a D-shaped elongated cross-section with a half-axis ratio of 2. The two extreme cases of no conducting shell round the plasma and of the shell tight against the plasma surface are treated. The growth rate of the most unstable mode is plotted versus q(0). In the rigid boundary limit the low n modes are found to be stable above a value of q sub 0, which is below the Mercier limit. The structure of the modes shows the combined effects of shear and toricity. The calculation is repeated for the free boundary case. The growth rate of the kink plotted versus q(0) has the same general behavior as in the straight case, but the modes show a complicated structure which can be construed as a coupling between an internal mode and a kink of different m through the toricity.