### 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 language | English (US) |
---|---|

Pages (from-to) | 28-45 |

Number of pages | 18 |

Journal | Journal of Computational Physics |

Volume | 243 |

DOIs | |

State | Published - Jun 5 2013 |

### Fingerprint

### 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

*Journal of Computational Physics*,

*243*, 28-45. https://doi.org/10.1016/j.jcp.2013.02.045

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

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 243, pp. 28-45. https://doi.org/10.1016/j.jcp.2013.02.045

}

TY - JOUR

T1 - A fast, high-order solver for the Grad-Shafranov equation

AU - Pataki, Andras

AU - Cerfon, Antoine J.

AU - Freidberg, Jeffrey P.

AU - Greengard, Leslie

AU - O'Neil, Michael

PY - 2013/6/5

Y1 - 2013/6/5

N2 - 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.

AB - 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.

KW - Conformal mapping

KW - Grad-Shafranov

KW - High-order

KW - Kerzman-Stein

KW - Plasma physics

KW - Poisson solver

KW - Spectrally-accurate

UR - http://www.scopus.com/inward/record.url?scp=84876325094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876325094&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2013.02.045

DO - 10.1016/j.jcp.2013.02.045

M3 - Article

AN - SCOPUS:84876325094

VL - 243

SP - 28

EP - 45

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -