New axisymmetric equilibria with flow from an expansion about the generalized Solov'ev solution

We construct analytic solutions to the generalized Grad–Shafranov equation, which incorporates both toroidal and poloidal flows. This is achieved by adopting a general linearizing ansatz for the free-function terms of the equation and expanding the generalized Solov'ev solution [Ch. Simintzis, G. N. Throumoulopoulos, G. Pantis and H. Tasso, Phys. Plasmas 8, 2641 (2001)]. On the basis of these solutions, we examine how the genaralized Solov'ev configuration is modified as the values of the free parameters associated with the additional pressure, poloidal current, and electric field terms changed. Thus, a variety of equilibria of tokamak, spherical tokamak, and spheromak pertinence are constructed, including D-shaped configurations with positive and negative triangularity and diverted configurations with either a couple of X-points or a single X-point.