Vortices in Plasma Hydrodynamics

Abstract

As we have seen, the point vortices play an important role in the two-dimensional hydrodynamics. Therefore, it is natural to want to generalize the concept of point vortices on the plasma hydrodynamics that would allow us to apply a number of ideas and methods from the fluid hydrodynamics to the plasma hydrodynamics. A lot of works deals with the approximation of point vortices for Charney–Hasegawa–Mima equation for the electrostatic drift waves in an inhomogeneous plasma or the large scale vortex motion in planetary atmospheres (e.g. [1–3]). The exact solutions which describe a point vortex model for the modon solution of the Charney–Hasegawa–Mima equation are found in [4]. The exact solutions in the form of point vortices for the current vortex filamentation of the nonlinear Alfven perturbations in high temperature magnetized plasma are found in [5–7]. This chapter describes the theory of point vortices in two-fluid plasma hydrodynamics very similar to the theory of point vortices in the ordinary hydrodynamics. These vortices form two classes: pure plasma vortices and vortices with a hydrodynamic envelope and plasma core. Such solutions are typical of the two-dimensional plasma hydrodynamics. In the case of the three-dimensional plasma hydrodynamics the nontrivial topological configurations of electron and ion fluids, so-called topological solitons, are possible. Such localized structures have the increased stability and can live a long time in the plasma.