Self-consistent equilibria in a cylindrical reversed-field pinch

A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma + gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions: a) to the lowest order, the turbulent dynamo electric field E((t)) is expressed as a homogeneous function of degree 1 of the magnetic field B, say E((t)) = alpha . B, with alpha being a 2nd-rank tensor, homogeneous of degree 0 in B, and generally depending on the plasma state; b) E((t)) does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both alpha and the plasma resistivity eta are isotropic and constant, the magnetic field turns out force-free with constant abnormality alpha mu(0)/eta for vanishing axial electric field E(z). This case has also been solved analytically, for whatever E(z), under circular, besides cylindrical, symmetry.