Rapid calculation of tokamak equilibria with toroidal rotation via minimization of a functional

摘要

The fixed surface tokamak plasma equilibria are analyzed by a variational steepest descent method employing global functions for the shift, ellipticity, and triangularity of the flux surfaces. The stationary and toroidally rotating axisymmetric tokamak equilibria have specific functionals from which the Grad-Shafranov equations can be derived as the equation for the ψ (poloidal flux) variation. These functionals are minimized numerically to obtain the solutions. The global functions characterizing the plasma flux surface shift, ellipticity, and triangularity are conveniently given by a limited set of variational parameters which are obtained iteratively by the aforementioned minimization of the functional. In the case of the stationary equilibrium, the results obtained by the minimization of the functional are compared with those given by the pest code.