Extending HELENA to incompressible plasma rotation parallel to the magnetic field

Abstract: Plasma rotation in connection to both zonal and mean (equilibrium) flows can play a role in the transitions to the advanced confinement regimes in tokamaks, as the L-H transition and the formation of Internal Transport Barriers. For incompressible rotation the equilibrium is governed by a generalized Grad-Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the pressure. For parallel flow the GGS equation can be transformed to one identical in form with the usual GS equation. In the present study on the basis of the latter equation we have extended HELENA, an equilibrium fixed boundary solver. The extended code solves the GGS equation for a variety of the two free-surface-function terms involved for arbitrary Alfv\'en Mach and density functions. We have constructed diverted-boundary equilibria pertinent to ITER and examined their characteristics, in particular as concerns the impact of rotation on certain equilibrium quantities. It turns out that the rotation and its shear affect noticeably the pressure and toroidal current density with the impact on the current density being stronger in the parallel direction than in the toroidal one. Also, the linear stability of the equilibria constructed is examined by applying a sufficient condition.