Axisymmetric equilibria with anisotropic resistivity and toroidal flow

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and toroidal flow is investigated within the framework of magnetohydrodynamics (MHD). The stationary states are determined by an elliptic differential equation for the poloidal magnetic flux function ψ, a Bernoulli equation for the pressure and two relations for the resistivity components η_∥ and η_⊥ parallel and perpendicular to the magnetic field, respectively. The flow can affect the equilibrium properties solely in the presence of toroidicity because in the limit of infinite aspect ratio, the axial velocity does not appear in the equilibrium equations. The equilibrium characteristics of a tokamak with rectangular cross-section are studied by means of eigenfunctions in connection with exact solutions for the cases of "compressible" flows with constant temperature, T(ψ), but varying density on magnetic surfaces and incompressible ones with constant density, ρ(ψ), but varying temperature thereon. Those eigenfunctions can describe either single or multiple toroidal configurations. In the former case the equilibrium has the following characteristics: (i) the η_∥- and η_⊥-profiles on the poloidal cross-section having a minimum close to the magnetic axis, taking large values on the boundary and satisfying the relation η_⊥ > η_∥ are roughly collisional; (ii) the electric field perpendicular to the magnetic surfaces possesses two local extrema within the plasma and vanishes on the boundary; and (iii) the toroidal current density is peaked close to the magnetic axis and vanishes on the boundary. The impact of the flow and the aspect ratio on the aforementioned quantities is evaluated for both "compressible" and incompressible flows.