Current-vortex filament model of nonlinear Alfven perturbations in a finite-pressure plasma

A low-beta, two-fluid model is shown to possess solutions in the form of current-vortex filaments. The model can be viewed as that of reduced magnetohydrodynamics, extended with electron inertia, the Hall term and parallel electron pressure. These drift-Alfven filaments are the plasma analogs of point vortices in the two-dimensional Euler and the Charney-Hasegawa-Mima equations. The discrete system has the same global and local invariants as the original, continuous system. In an unbounded plasma, systems of two and three filaments are integrable. When the global linear momenta vanish, the four filament problem is also integrable. Stationary equilibria of a dipole, tripole, and of von Karman streets are presented. The phase-space of two interacting, balanced pairs of filaments is analyzed in detail. New periodic four filament configurations are identified in plasma cases that do not exist in Euler systems. It is also shown that a collapse of the four vortices can occur in a finite time. (C) 1998 American Institute of Physics. [S1070-664X(98)00511-4].