Analytic Grad-Shafranov test criteria and checks of a 1-1/2-D BALDUR code

TL;DRAbstract

As discussed by Shafranov, Solov'ev, and others, two special constraints allow the Grad-Shafranov equation to yield simple analytic solutions. From the simplest solution, formulae are derived for properties of the corresponding toroidally symmetric plasma and for the space profile of poloidal magnetic flux density. These formulae constitute test criteria for code performance once the code is made consistent with the two constraints. Obtaining consistency with the first constraint is straightforward, but with the second it is circumstantial. Moreover, the poloidal flux profile of the analytic solution implies a certain artificial form for the resistivity, which is also derived. These criteria have been used to check a composite code which had been assembled by linking a geometrically generalized 1-D BALDUR transport code with a computationally efficient 2-D equilibrium code. A brief description of the composite code is given as well as of its performance with respect to the Grad-Shafran

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