Magnetohydrodynamic Stability of a Sharp Boundary Toroidal Plasma

For a toroidally symmetric sharp boundary plasma, the magnetohydrodynamic stability analysis of Lüst, Suydam, Richtmyer, Rotenberg, and Levy is extended to equilibria with a small ratio of azimuthal to longitudinal magnetic fields and a large aspect ratio (α). These equilbria exist only when β<α(field ratio)2/2. In the limit of small β, the stability criteria are identical to those of a straight cylindrical plasma with length 2πα. This is true to leading order in 1/α in spite of mathematical complications arising from toroidal effects. However, as β is increased to its maximum value for field ratios of order 1/α, toroidal effects help stabilize long-wavelength kink modes. The limits considered apply to tokamaks.