Computation of two-fluid, flowing equilibria

Equilibria of flowing two-fluid plasmas are computed for realistic compact-toroid and spherical-tokamak parameters. In these examples the two-fluid parameter \textit{$\varepsilon $} (ratio of ion inertial length to overall plasma size) is small, \textit{$\varepsilon $ }$\sim $ 0.03 -- 0.2, but hardly negligible. The algorithm is based on the nearby-fluids model [1] which avoids a singularity that otherwise occurs for small \textit{$\varepsilon $}. These representative equilibria exhibit significant flows, both toroidal and poloidal. Further, the flow patterns display notable flow shear. The importance of two-fluid effects is demonstrated by comparing with analogous equilibria (e.g. fixed toroidal and poloidal current) for a static plasma (Grad-Shafranov solution) and a flowing single-fluid plasma. Differences between the two-fluid, single-fluid, and static equilibria are highlighted: in particular with respect to safety factor profile, flow patterns, and electrical potential. These equilibria are computed using an iterative algorithm: it employs a successive-over-relaxation procedure for updating the magnetic flux function and a Newton-Raphson procedure for updating the density. The algorithm is coded in Visual Basic in an Excel platform on a personal computer. The computational time is essentially instantaneous (seconds). [1] L.C. Steinhauer and A. Ishida, Phys. Plasmas \textbf{13}, 052513 (2006).