ON THE SELF-CONSISTENT SHAFRANOVS PROBLEM

A paper by one of us has recently been published concerning the possib ility of self-consistently computing the MagnetoFluidDynamic (MFD) sta tionary states (i.e. the generally non-static equilibria) of a cylindr ical plasma column with simply connected cross-section, contained in a given (cylindrical, co-axial, perfectly conductive in its normal plan e) shell, and with a vacuum (or gas) region, having annular cross-sect ion, in between. Self-consistence refers to the full set of fluid equa tions which have been used, in some convenient approximation, to model the physical system considered: i.e. the mass, momentum and energy co nservation equations, Maxwell system, linear constitutive relations (O hms's and Fourier's generalized laws), and laws of state. The aim of t he present study is to extend the above free-interface problem to the toroidal symmetry, limitedly to the case of a tol-ic shell, and to sol ve it by a standard Ist-order asymptotic expansion w.r.t. the (small) inverse aspect ratio. This classical problem in plasma equilibrium the ory, whose non-self-consistent version was solved in the 60's by Shafr anov, is faced here from the self-consistence standpoint in a systemat ic way.