Thermodynamics of the magnetic equilibria of a semi-collisionless plasma

Abstract

A statistical model of the collisionless or semi-collisionless equilibria of a magnetically confined plasma is presented which allows the calculation of the entropy and of the thermodynamic potentials as functionals of the collective equilibrium quantities. The entropy principle enables the identification of the magnetic equilibria which are preferentially chosen by the plasma. Stability criteria are derived by declaring unstable an equilibrium which admits in its neighbourhood an accessible equilibrium with higher entropy. The requirement of thermodynamic stability imposes considerable restrictions on the magnetic configuration, on the pressure distribution and on the velocity distribution function. New conditions for magnetic stability are derived and known results reinterpreted. The theory points towards the force-free configurations, in the case of a current carrying plasma subject to certain physical constraints, or towards the minimum-B configurations, in the general case of arbitrary ², as the most stable states from the thermodynamic point of view. The formalism is applied to identify the most promising lines to be pursued experimentally in order to achieve magnetic stability in a thermonuclear device.