Solving the Grad-Shafranov equation using spectral elements for tokamak equilibrium with toroidal rotation

TL;DR

This paper develops a spectral element method to solve the Grad-Shafranov equation for tokamak equilibrium with toroidal rotation, extending existing codes and providing analytical solutions for validation.

Contribution

It introduces an extended spectral element solver based on NIMEQ for rotating equilibria and derives new analytical solutions for validation.

Findings

Achieves geometric and algebraic convergence with spectral elements.

Provides analytical solutions for rotating Solov'ev equilibria.

Demonstrates good agreement between numerical and analytical solutions.

Abstract

The Grad-Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad-Shafranov solver builds upon and extends the NIMEQ code [Howell and Sovinec, Comput. Phys. Commun. 185 (2014) 1415] previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad-Shafranov equation is obtained for Solov'ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution for a defferent set of equilibrium and rotation profiles. The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions, with good agreements. Besides, the extended NIMEQ code is benchmarked with the FLOW code [L. Guazzotto, R. Betti, et al., Phys. Plasma 11(2004)604].