The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, consequently, the general two-dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function , in which four profile functionals of appear. Apart from a singularity occurring when the modulus of Mach number associated with the Alfvén velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equilibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having (i) a flat current density and (ii) a peaked current density are obtained and studied.
Separation of p and ℓi in tokamaks of non-circular cross-section