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].

中文翻译：

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使用光谱元素求解具有环形旋转的托卡马克平衡的 Grad-Shafranov 方程

Grad-Shafranov 方程使用光谱元素求解，用于具有环形旋转的托卡马克平衡。Grad-Shafranov 求解器基于并扩展了 NIMEQ 代码 [Howell and Sovinec, Comput. 物理。社区。185 (2014) 1415] 之前为静态托卡马克平衡开发。随着谱元基的多项式次数的增加，几何收敛和代数收敛都可以实现。除了先前获得的一组不同的平衡和旋转轮廓的解析解之外，还获得了存在刚性环面旋转的 Solov'ev 平衡的 Grad-Shafranov 方程的新解析解。扩展 NIMEQ 的数值解以解析解为基准，具有良好的一致性。此外，扩展的 NIMEQ 代码以 FLOW 代码 [L. 瓜佐托，R. Betti, et al., Phys. 等离子 11(2004)604]。