Tokamak equilibria with non field-aligned axisymmetric divergence-free rotational flows

Rotational ideal divergence-free magnetohydrodynamic (MHD) equations are expressed in terms of transformed variables w→*=(μρ)1/2v→ and μp* = (μp + w*2/2), where v→, p, and ρ are plasma velocity, pressure, and mass density, respectively. With divergence-free flows, ∇·v→=0, the plasma density ρ does not appear in the MHD equations written in terms of w→* and μp*. The non field-aligned rotational Grad-Shafranov equation is represented in spherical coordinates. Tokamak-like axisymmetric equilibria with v→ ⊥∇ρ are obtained analytically by solving for torus solutions under only three source functions.