On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch–Schlüter diffusion

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function psi along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities eta(parallel to) and eta(perpendicular to) parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G.N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either eta(parallel to)(psi) or eta(perpendicular to)(psi) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with 771, and y, profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that eta(perpendicular to)>eta(parallel to). For equilibria with vanishing flows satisfying the relation (dP/dpsi)(dI(2)/dpsi)>0, where P and I are the pressure and the poloidal current functions, the difference eta(perpendicular to)-eta(parallel to) for the reversed-field pinch scaling, B(p)approximate toB(t), is nearly two times larger than that for the tokamak scaling, B(p)approximate to0.1B(t) (B-p and B-t are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of-but not inconsistent with-Pfirsch-Schluter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas. (C) 2003 American Institute of Physics. Physics of Plasmas