Stability of force-free plasma–vacuum equilibria

Abstract

The magnetohydrodynamic stability of force-free plasma–vacuum systems (curl B=μB in the plasma, with constant μ) is studied in circular cylinders with identified ends (topological torus). A necessary stability criterion is derived by considering large poloidal mode numbers. This takes a simple form (the magnetic rotation numbers at the axis and plasma–vacuum interface must have opposite signs) if the magnetic field lines in the interface are not closed. If they are closed, then violation of this simple condition does not imply instability unless the aspect ratio exceeds some value which depends on both the numerator and denominator of the rational magnetic rotation number at the interface. For aspect ratios greater than unity, combination with the criterion for stability to internal kinks implies that the inhomogeneity parameter ‖μ‖ must be above the threshold for reversal of the toroidal current density, but below that for reversal of the poloidal one. This condition is independent of the wall radius, in contrast to the well-known necessary and sufficient stability criterion in the limit of infinite aspect ratio, which remains sufficient for arbitrary aspect ratios, and which requires that ‖μ‖ be in a smaller interval that does depend on the wall radius.