Sherwood 2015

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approvedcerfon_sherwood.pdf2015-03-18 13:16:15Antoine Cerfon
approvedsherwood_2015_abstract.pdf2015-01-17 11:18:50Antoine Cerfon

Accurately calculating equilibrium quantities with any Grad-Shafranov solver

Author: Antoine Cerfon
Requested Type: Poster Only
Submitted: 2015-01-17 11:17:53

Co-authors: L.F. Ricketson, M. Rachh, J.P. Freidberg

Contact Info:
Courant Institute NYU
251 Mercer St
New York, NY   10012

Abstract Text:
Static MHD equilibria in toroidally axisymmetric devices are computed by solving the Grad-Shafranov equation. While the output of any numerical Grad-Shafranov solver is the poloidal flux function psi, many physically important equilibrium quantities are functions of the derivatives of psi instead of psi itself. For example, the magnetic field and the safety factor are functions of the first derivatives of psi, and some quantities that play a critical role in MHD stability and transport calculations, such as the parallel current density and the magnetic curvature, depend on the second derivatives of psi.
The direct methods finite difference and finite element Grad-Shafranov solvers use to evaluate derivatives of psi lead to the loss of at least one order of convergence of the numerical error per derivative calculated numerically. In contrast, we present a new, general method that allows the evaluation of any derivative of psi with a numerical error that converges as fast as the error on psi itself. Our method is based on two main ingredients: 1) we first analytically differentiate the Grad-Shafranov equation to obtain linear elliptic partial differential equations for the partial derivatives of psi we want to evaluate; 2) we then use an integral equation formulation to compute with high accuracy the values of the derivatives of psi on the plasma boundary, which allow us to solve the linear PDEs numerically.
Our method can be applied to any direct Grad-Shafranov solver (as opposed to inverse solvers). We demonstrate its effectiveness for the particular case of bicubic Hermite finite element solvers, which are very popular in the fusion community.


March 16-18, 2015
The Courant Institute, New York University