Author: C. R. Sovinec
Requested Type: Poster
Submitted: 2016-02-15 21:34:23
Co-authors: J. R. King, E. C. Howell
University of Wisconsin-Madison
1500 Engineering Drive
Madison, WI 53706-1
Analyzing the linear and nonlinear macroscopic stability of a realistic axisymmetric confinement configuration typically begins with solving the Grad-Shafranov equation numerically. To minimize truncation errors and to avoid interpolation errors in NIMROD computations, the NIMEQ equilibrium solver [Howell and Sovinec, CPC 185, 1415 (2014)] uses NIMROD's spectral-element representation. Recent extensions of NIMEQ broaden its applicability. Methods are described for identifying the separatrix to distinguish the closed- and private-flux regions when solving diverted equilibria. They also allow NIMEQ to refine diverted equilibria that are read from previously computed profiles, such as equilibria fitted to experimental data. The profiles can now be smoothed over the separatrix, yielding force-free parallel current on open field lines. In addition, grid refinement has been incorporated to produce accurate solutions on a mesh that is well aligned with magnetic flux surfaces.
Another development generalizes NIMEQ to solve free-boundary equilibria. The chosen approach solves an expansion for toroidal current density simultaneously with an expansion for the poloidal flux function so that surface-flux values are part of the linear algebraic system of each nonlinear step. This improves convergence properties relative to updating surface-flux values through an outer iteration. Convergence is further improved by using numerical differences of the nonlinear terms, apart from the separatrix location dependence, in the linear algebraic system to permit Newton-like iteration.