Beschreibung:
The theory by Bussac et al. [Phys. Rev. Lett. 35, 1638 (1975)] on the stability of the ideal, internal kink mode in a toroidal plasma with circular cross section is extended to finite values of the inverse aspect ratio εa. The aspect ratio dependence comes from the term following the Bussac term in a large aspect ratio expansion of the potential energy δW of the mode. Although formally of higher order in the inverse aspect ratio, this term is of the same order of magnitude as the Bussac term when the safety factor q is close to (but below) unity at the plasma center and εa is finite. The new term is always stabilizing, but affects δW only marginally when the poloidal beta value βp is small and/or εa is small. For values of εa relevant for most tokamaks and βp larger than 0.3–0.5, however, the new term strongly modifies δW and leads to a second stability regime of the ideal, internal kink mode, in agreement with earlier numerical calculations.