On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

It is shown that the magnetohydrodynamic (MHD) equilibrium states of an axi symmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second order partial differential equatio n for the poloidal magnetic flux function psi coupled with a Bernoulli-type equation for the plasma density (which are identical in form to the corres ponding ideal MHD equilibrium equations) along with the relation Delta*psi = V(c)sigma (here Delta* is the Grad-Schluter-Shafranov operator, sigma is the conductivity and V-c is the constant, toroidal-loop voltage divided by 2 pi). In particular, for incompressible flows, the above-mentioned partial differential equation becomes elliptic and decouples from the Bernoulli eq uation [H. Tasso and G. N. Throumoulopoulos, Phys. Plasma 5, 2378 (1998)]. For a conductivity of the form sigma = sigma (R, psi) (where R is the dista nce from the axis of symmetry), several classes of analytic equilibria with incompressible flows can be constructed having qualitatively plausible cr profiles, i.e. profiles with sigma taking a maximum value close to the magn etic axis and a minimum value on the plasma surface. For sigma = sigma(psi) , consideration of the relation Delta*psi = V(c)sigma(psi) in the vicinity of the magnetic axis leads then to a proof of the non-existence of either c ompressible or incompressible equilibria. This result can be extended to th e more general case of non-parallel flows lying within the magnetic surface s.