Gn. Throumoulopoulos et G. Pantis, MAGNETOHYDRODYNAMIC EQUILIBRIA OF A CYLINDRICAL PLASMA WITH POLOIDAL MASS-FLOW AND ARBITRARY CROSS-SECTIONAL SHAPE, Plasma physics and controlled fusion, 38(10), 1996, pp. 1817-1823
The equilibrium of a cylindrical plasma with purely poloidal mass Bow
and cross section of arbitrary shape is investigated within the framew
ork of the ideal MHD theory. For the system under consideration it is
shown that only incompressible Bows are possible and, consequently, th
e general two-dimensional flow equilibrium equations reduce to a singl
e second-order quasilinear partial differential equation for the poloi
dal magnetic flux function psi, in which four profile functionals of p
si appear. Apart from a singularity occurring when the modulus of Mach
number associated with the Alfven velocity for the poloidal magnetic
field is unity, this equation is always elliptic and permits the const
ruction of several classes of analytic solutions. Specific exact equil
ibria for a plasma confined within a perfectly conducting circular cyl
indrical boundary and having (i) a flat current density and (ii) a pea
ked current density are obtained and studied.