Some properties of a thermodynamic model for the equilibrium of a current-carrying quasineutral plasma

Aly, J. J.
February 1993
Physics of Fluids B: Plasma Physics;Feb93, Vol. 5 Issue 2, p281
Academic Journal
This paper establishes some general properties of a two-dimensional (z-invariant) model describing smooth equilibria of a magnetized quasineutral plasma enclosed in a finite cylindrical box of arbitrary cross section Ω and submitted to the following constraints: (i) the normal component of the magnetic field is fixed on the box boundary; (ii) the plasma is in contact with a heatbath at temperature T; (iii) the plasma carries in the z direction a current whose total intensity I is externally imposed. It is shown in particular that: (i) the free energy of the system is bounded from below if and only if the dimensionless control parameter λ≤1 (λ∝IT-1/2); (ii) a minimum free energy state (thus thermodynamically absolutely stable) exists for λ≤1 and is actually the unique equilibrium that can be achieved if λ is small enough; (iii) this state is absolutely stable with respect to all ideal magnetohydrodynamic perturbations; (iv) no equilibrium can exist if λ exceeds a critical value λc≥1 (at least in the case where Ω is ‘‘star shaped’’). The nonexistence of a minimum free energy state and even of any available regular equilibria with high current may have some consequences for understanding eruptive processes in plasmas, which are briefly discussed.


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