Generalized relaxation theory and vortices in plasmas

Abstract

We present a generalization of the relaxation theory based on the canonical momentum of each species fluid in a multicomponent plasma. The generalized helicity, as a topological quantity, has a lifetime larger than the lifetime of the energy. We then propose a simple variational principle that suggests the existence of vortex structures. We study localized solutions, assuming the existence of a separatrix. Two-dimensional and three-dimensional solutions are studied for an electron-positron-proton plasma. Ideal magnetohydrodynamic three-dimensional localized vortices are studied as well. Possible cosmological implications are discussed.