Self-consistent equilibria in cylindrical reversed-field pinch

摘要

The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: (a) to the lowest order, and according to a standard ansatz, the turbulent DEF say (epsilon)(sup t), is expressed as a homogeneous transform of the magnetic field B of degree 1, (epsilon)(sup t)=((alpha)) (B), with (alpha)(identical to)a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; (b) (epsilon)(sup t) does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both (alpha) and the resistivity tensor (eta) are isotropic and constant, the magnetic field is force-free with abnormality equal to (alpha)(eta)(sub 0)/(eta), in the limit of vanishing (beta); that is, the well-known J.B. Taylor'result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall).