Stability of elongated cross-section tokamaks to axisymmetric even poloidal mode number deformations

In a recent paper, Nakayama, Sato, and Matsuoka [Phys. Fluids 31, 630 (1988)] suggested that elliptical cross-section tokamaks with aspect ratio R /a = 3.2 and with elongation κ = 2.6 are unstable to a splitting (m = 2, n = 0) instability for plasma β> 5%, and that κ≥4.0 plasmas are unstable to a splitting for β≥1%. The magnetohydrodynamic evolution code TSC [J. Comput. Phys. 66, 481 (1986)] indicates, however, that such plasmas are robustly stable with respect to this splitting. In fact, a κ = 3.7 plasma with β = 23.0% shows no tendency to split. However, the addition of pinching coils at the waist will cause the plasma to split if the current in these coils exceeds a critical value I_c, which decreases with increasing beta.