Three-dimensional stability of drift vortices

Abstract

The three-dimensional stability of drift vortices that are two-dimensionally stable in the framework of the Hasegawa–Mima equation is studied. The three-dimensionality is caused by a coupling of the vortex to ion-acoustic waves that propagate along the magnetic field. It is concluded that this coupling does not significantly destabilize the vortex. A general stability criterion is derived that guarantees stability if the ratio between the parallel wave number k and the azimuthal mode number m is large enough. It is also found that no instability exists in the limit k→0 if the potential vorticity is a strictly decreasing function of r. Such profiles are typical for vortices that are two-dimensionally stable. Some particular profiles where the potential vorticity vanishes outside some radius are also examined. In one case an instability with m=1 is found, but a numerical solution of the eigenvalue problem shows that the maximum growth rate is very small, three orders of magnitude smaller than the angular velocity of the vortex flow.