Analytic Theory of Resistive Ballooning Modes

The linearized resistive magnetohydrodynamic (MHD) equations have been solved analytically in a large‐aspect‐ratio toroidal plasma to obtain a dispersion relation for resistive ballooning modes.   The calculation is limited to values of β=8πnT/B² below the threshold for ideal ballooning modes. The dispersion relation yields a universal curve which can be used to determine mode stability as a function of the plasma parameters. Because of the strong stabilizing influence of plasma compressibility, resistive‐ballooning modes are only unstable in tokamaks which are either quite cold or are very close to the ideal threshold.