Negative specific heat of a magnetically self-confined plasma torus

Abstract

It is shown that the thermodynamic maximum-entropy principle predicts negative specific heat for a stationary, magnetically selfconfined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.T he goal of the controlled thermonuclear fusion program is to make the energy source that powers our sun available to human society. Deep in our sun's interior, favorable conditions for the quasistationary nuclear burning of the solar plasma prevail as a result of the immense gravitational self-forces that keep this huge accumulation of matter together. Because gravitational self-confinement is not operative at the reactor and laboratory scale, alternate means of confinement have to be used to achieve sufficiently high plasma densities and temperatures in a reactor. In the perhaps most prominent stationary fusion-reactor scheme, the tokamak, strong electric ring currents are induced in an electrically neutral plasma to achieve axisymmetric magnetic self-confinement in a rotationally invariant toroidal vessel T. In a torus with a sufficiently large major axis, such a magnetic self-confinement mimics gravitational self-confinement on account of the Biot-Savart law, according to which in a system of parallel current filaments all filaments attract each other magnetically with the same force law as would be the case gravitationally in a system of parallel mass filaments. What makes the magnetic forces more attractive (in the double sense of this phrase) than gravity for laboratory purposes is their very much bigger coupling constant [Ϸ10 40 v 2 ͞c 2 for two electrons moving on parallel trajectories with speed v as measured in the laboratory; note that the even stronger (v 2 ͞c 2 is replaced by 1) electrostatic repulsive forces between the same two electrons are very effectively screened in a neutral plasma and are traditionally neglected to a good approximation]. Of course, the analogy does not extend to all aspects of plasma selfconfinement. In particular, the solenoidal-vectorial character of stationary current densities necessitates the toroidal topology of magnetic self-confinement, whereas gravity not only allows but manifestly prefers spherical confinement over toroidal. Unfortunately, axisymmetric toroidal magnetic selfconfinement is not known for its stability either. Although major efforts are devoted to the stabilization of the plasma configuration, a vast reservoir of instabilities capable of destroying the confinement has dramatically slowed down the development of an operating tokamak fusion reactor.Matters are not exactly helped by the fact that our theoretical understanding of the physics on the various space-time scales that govern magnetic plasma confinement is still quite incomplete. In particular, although the solenoidal character of the magnetic induction together with the axisymmetry and stationarity of the law of momentum balance tell us that the poloidal magnetic f lux function ⌿ and the toroidal current density j must satisfy some local functional r...

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