THE THERMODYNAMIC HIERARCHY OF THE MAGNETIC EQUILIBRIA - FORCE-FREE CONFIGURATIONS VS THE TOKAMAK
In this paper we have searched for the equilibria of maximum entropy in the case of an axially symmetric toroidal geometry. We have found an approximate solution in the limit of a large aspect ratio and a large toroidal field, which corresponds to a Tokamak and a rigorous solution which corresponds to a force free equilibrium. We have not proven that these are the only solutions of maximum entropy in the axially symmetric toroidal geometry. The best Tokamak from the thermodynamic point of view has a large aspect ratio, a circular cross section and a poloidal beta near to 3, but is only a relative (and approximate) maximum of the entropy. The force free equilibrium with a minimum alpha**2 (where j = alphaB) is associated with an absolute maximum of the entropy in the class of the magnetic Vlasov equilibria. The entropy of a force free configuration is also maximum with respect to the dissipative decay of the plasma magnetic energy, provided that K = integral of A x BdV is conserved up to first order. The present investigation is an example of application of the thermodynamic method to the global stability of Vlasov (in general not Maxwellian) magnetic equilibria.
Bibliographic Reference: COURSE ON MIRROR-BASED AND FIELD-REVERSED APPROACHES TO MAGNETIC FUSION, HELD AT VARENNA (ITALY), SEPT. 7-17, 1983 VOL. 2, PP. 41-70 VOL. 1: 388 P., VOL. 2: 324 P., 1984 WRITE TO MONTYPIA FRANCHI, ST. LUCIA - VIALE UMBRIA NO. 28, 06012 CITTA DI CASTELLO,
Record Number: 1989124010400 / Last updated on: 1987-01-01
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