Magnetohydrodynamics equilibria with toroidal and poloidal flow

In the present work, the effects of flow on tokamak equilibria are investigated, focusing in particular on the effects of poloidal flows. It is shown that discountinuous transonic equilibria with a pedestal structure can be obtained for relatively low values of the poloidal velocity. Equilibria with poloidal flow of the order of the poloidal Alfvén speed are shown to develop inverted Shafranov shift. Since the rotation is damped by the neoclassical poloidal viscosity, a quasi-omnigenous solution for equilibria with large rotation is also derived in order to minimize the flow damping. In this solution, the magnetic field is construed to be a function of the poloidal magnetic flux Ψ up to a small correction by an appropriate choice of the flow profiles. All numerical results are obtained with the code FLOW [L. Guazzotto, R. Betti, J. Manickam, and S. Kaye, Phys. Plasmas 11, 604 (2004)].