Hall effect upon small wavelength kink instabilities near an elliptic magnetic stagnation line

To explore the question whether the Hall effect removes the unphysical feature of ideal magnetohydrodynamics of predicting unstable small wavelenght kinks near any elliptic magnetic stagnation line, a spectral analysis is performed of the motion of an incompressible plasma about cylindrical Z-pinch equilibria with circular sections. The eigenvalue loci in the complex frequency plane are derived for the equilibrium with constant current density. These show that every particular mode becomes stable as the Hall parameter exceeds a critical value. However, this critical value is a decreasing function of the ideal growth rate and has a pole at the origin, implying that there always remains an infinite reservoir of slowly growing instabilities. Correspondingly, for equilibiria with arbitrary current distributions, the stability criterion is unaffected by the Hall term. (author)