Free Boundary Magnetohydrodynamic Equilibria with Flow

Equilibria with flow are known to exhibit characteristics different from static equilibria. In particular, plasma rotation often reduces turbulent transport, as exhibited by H-mode confinement state observed in tokamaks. The equations that govern MHD equilibrium with flow are the generalized Grad-Shafranov equation and the magnetic Bernoulli equation. The finite element, free boundary equilibrium solver in the M3D code has been modified to included arbitrary toroidal and poloidal flows. The M3D+FLOW code differs from other codes in that, being a free boundary code, it includes the separatrix and the region outside the separatrix. Results for M3D+FLOW are presented for both subsonic and transonic flows. Application to data from the XGC gyrokinetic code is also presented.