Collisionless and resistive ballooning stability

Abstract

It has been suggested [Kleva and Guzdar, Phys. Plasmas 6, 116 (1999)] that reconnecting ballooning modes in which electron inertia replaces resistivity in a nonideal magnetohydrodynamic Ohm’s law can have substantial growth rates in the low collisionality regime. Numerical calculation, albeit necessarily at unrealistically large values of the collisionless skin depth, showed that strongly growing ballooning modes exist at beta values which are below the ideal beta limit. In order to investigate stability at more realistic values of the skin depth we exploit an analytic approach. As in the case of resistive ballooning modes, we find that inertial ballooning modes are stabilized by favorable average curvature effects at moderate values of ΔB′, the stability index for resistive ballooning. Instability only becomes possible close to the ideal stability boundary (ΔB′→∞) or at unrealistically large values of the toroidal mode number n (e.g., n≳102). Another ballooning mode, the collisionless analogue of the Carreras–Diamond mode [Carreras, Diamond, Murakami, Dunlap et al., Phys. Rev. Lett. 50, 503 (1983)] can also be excited at larger values of the collisionless skin depth, but this mode is not valid for realistic parameters in a hot plasma.