Effect of combined triangularity and ellipticity on the stability limit of the ideal internal kink mode in a tokamak

The effect of combined triangular and elliptical shaping of the plasma cross section on the stability limit of the ideal, internal kink mode in a tokamak is analyzed by means of a computer algebra expansion of the magnetohydrodynamic equations. The work extends the result of a previous investigation of the effect of ellipticity alone on this mode in toroidal plasmas [Wahlberg, Phys. Plasmas 5, 1387 (1998)]. It is shown that, in contrast to the strongly destabilizing effect of (positive) ellipticity alone, the effect of combined positive ellipticity and positive triangularity is stabilizing. The effect is of the same importance as the effect of ellipticity alone if the triangularity of the q=1 surface is of the same order of magnitude as the inverse aspect ratio. When the safety factor at the magnetic axis is close to (but below) unity, the geometrical factor governing the stability of the ideal, internal kink mode is found to be the same as the corresponding factor in the Mercier criterion for shaped tokamaks