Two-dimensional drift vortices and their stability

Abstract

Drift vortices in plasmas described by the Petviashvili equation in the case of strong temperature inhomogeneities or by the Hasegawa–Mima equation in the case of density gradients are investigated. Both equations allow for two‐dimensional vortex solutions. The models are reviewed and the forms of the vortices are discussed. In the temperature‐gradient case, the stationary solutions are only known numerically, whereas in the density gradient case analytical expressions exist. The latter are called modons; here the ground states are investigated. The result of a stability calculation is that both types of two‐dimensional solutions, for the Petviashvili equation as well as the Hasegawa–Mima equation, are stable. The methods used to prove this result are either direct (constructing Liapunov functionals) or indirect, and then based on variational principles.