A fast, high-order solver for the Grad-Shafranov equation

Andras Pataki, Antoine J. Cerfon, Jeffrey P. Freidberg, Leslie Greengard, Michael O'Neil

Research output: Contribution to journalArticle

Abstract

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

Original languageEnglish (US)
Pages (from-to)28-45
Number of pages18
JournalJournal of Computational Physics
Volume243
DOIs
StatePublished - Jun 5 2013

Fingerprint

Plasmas
plasma equilibrium
Conformal mapping
equilibrium equations
conformal mapping
Integral equations
integral equations
Fusion reactions
fusion
Derivatives
Geometry
shift
cross sections
profiles
geometry

Keywords

  • Conformal mapping
  • Grad-Shafranov
  • High-order
  • Kerzman-Stein
  • Plasma physics
  • Poisson solver
  • Spectrally-accurate

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

A fast, high-order solver for the Grad-Shafranov equation. / Pataki, Andras; Cerfon, Antoine J.; Freidberg, Jeffrey P.; Greengard, Leslie; O'Neil, Michael.

In: Journal of Computational Physics, Vol. 243, 05.06.2013, p. 28-45.

Research output: Contribution to journalArticle

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