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Simple semi-analytic toroidally axisymmetric equilibria with natural D-shape separatrix

Very simple semi-analytic solutions of the Grad–Shafranov equation for toroidally axisymmetric plasma equilibria are presented. These solutions can be used to construct model configurations with their cross-sections having finite aspect ratio, large elongation and triangularity, suitable for modeling the standard tokamak and spherical torus (ST) equilibia. Besides, the model configuration thus obtained has a special merit that it can model the divertor plasma configuration by a single solution both in the plasma region and outside. The method is basically an extension of the original fixed boundary solution. The new model configuration is a combination of two semi-analytic one-dimensional functions in the R-direction and a cosine function in the z-direction. As examples, D-shape tokamak-like divertor plasmas are presented in detail. These solutions provide a convenient tool for investigating the stability, transport and other related physics both for tokamaks and STs.