Stabilization of axisymmetric modes in plasma--vacuum equilibria by current reversal

Two-dimensional plasma--vacuum equilibria are constructed by solving a free-boundary problem for small deviations from a circular cross section, and their two-dimensional stability is studied by examining that eigenmode that reduces to the marginal rigid shift in the circular limit (all other two-dimensional modes are stable). The vacuum is assumed to extend to infinity (no wall), N axial external currents are assumed to be symmetrically placed far away from the plasma, and the plasma current density is assumed to be a linear function of the poloidal magnetic flux. It is found that instability always results for N=2 (elliptical corrugation), but that stability may result for N≥3 if the axial plasma current density changes sign across some pressure surface. It is concluded that axially symmetric modes in toroidal equilibria with large aspect ratio can be stabilized by current reversal, even if no conducting wall surrounds the vacuum