The asymptotic quasi-stationary states of the two-dimensional magnetically confined plasma and of the planetary atmosphere

Details The asymptotic quasi-stationary states of the two-dimensional magnetically confined plasma and of the planetary atmosphere The asymptotic quasi-stationary states of the two-dimensional magnetically confined plasma and of the planetary atmosphere

2005-01-06

arxiv.org/abs/physics/0501020v3

Physics

Plasma Physics

Latex 126 pages, 7 eps figures included. Discussion on various forms of the equation

Scientific paper

10.1103/PhysRevLett.94.235003

We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is related to the system consisting of a discrete set of point-like vortices interacting in plane by a short range potential. A field-theoretical formalism is developed for describing the continuous version of this system. The action functional can be written in the Bogomolnyi form (emphasizing the role of Self-Duality of the asymptotic states) but the minimum energy is no more topological and the asymptotic structures appear to be non-stationary, which is a major difference with respect to traditional topological vortex solutions. Versions of this field theory are discussed and we find arguments in favor of a particular form of the equation. We comment upon the significant difference between the CHM fluid/plasma and the Euler fluid and respectively the Abelian-Higgs vortex models.

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