Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape

摘要

The equilibrium of a cylindrical plasma with purely poloidal mass flow andcross section of arbitrary shape is investigated within the framework of theideal MHD theory. For the system under consideration it is shown that onlyincompressible flows are possible and, conscequently, the general twodimensional flow equilibrium equations reduce to a single second-orderquasilinear partial differential equation for the poloidal magnetic fluxfunction $\psi$, in which four profile functionals of $\psi$ appear. Apart froma singularity occuring when the modulus of Mach number associated with theAlfv\'en velocity for the poloidal magnetic field is unity, this equation isalways elliptic and permits the construction of several classes of analyticsolutions. Specific exact equlibria for a plasma confined within a perfectlyconducting circular cylindrical boundary and having i) a flat current densityand ii) a peaked current density are obtained and studied.