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A length-scale formula for confined quasi-two-dimensional plasmas

Published online by Cambridge University Press:  01 August 2009

TIMOTHY D. ANDERSEN  and
CHJAN C. LIM
TIMOTHY D. ANDERSEN
Affiliation:
Mathematical Sciences, RPI, 110 8th Street, Troy, NY 12180, USA (andert@alum.rpi.edu)
CHJAN C. LIM
Affiliation:
Mathematical Sciences, RPI, 110 8th Street, Troy, NY 12180, USA (andert@alum.rpi.edu)
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Abstract

Typically a magnetohydrodynamical model for neutral plasmas must take into account both the ionic and the electron fluids and their interaction. However, at short time scales, the ionic fluid appears to be stationary compared to the electron fluid. On these scales, we need consider only the electron motion and associated field dynamics, and a single fluid model called the electron magnetohydrodynamical model which treats the ionic fluid as a uniform neutralizing background applies. Using Maxwell's equations, the vorticity of the electron fluid and the magnetic field can be combined to give a generalized vorticity field, and one can show that Euler's equations govern its behavior. When the vorticity is concentrated into slender, periodic, and nearly parallel (but slightly three-dimensional) filaments, one can also show that Euler's equations simplify into a Hamiltonian system and treat the system in statistical equilibrium, where the filaments act as interacting particles. In this paper, we show that, under a mean-field approximation, as the number of filaments becomes infinite (with appropriate scaling to keep the vorticity constant) and given that angular momentum is conserved, the statistical length scale, R, of this system in the Gibbs canonical ensemble follows an explicit formula, which we derive. This formula shows how the most critical statistic of an electron plasma of this type, its size, varies with angular momentum, kinetic energy, and filament elasticity (a measure of the interior structure of each filament) and in particular it shows how three-dimensional effects cause significant increases in the system size from a perfectly parallel, two-dimensional, one-component Coulomb gas.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 4 , August 2009 , pp. 437 - 454
Copyright
Copyright © Cambridge University Press 2009

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