Extended Solov'ev type equilibria for rotating plasmas with positive and negative triangularity

The Solov'ev ansatz is employed to solve the equilibrium equation for plasmas rotating in the toroidal direction. The plasma shape can be controlled by fixing the values of the aspect ratio, elongation, triangularity, and curvature at the equatorial points. In addition, it is possible to set the values of the plasma current, total β, and Mach number. Analytic expressions for the shape coefficients and examples of equilibria with positive and negative triangularity are presented.