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Title:
Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria
Authors:
Antonsen, Thomas; Paul, Elizabeth J.; Landreman, Matt
Affiliation:
AA(Institute for Research in Electronics and the Applied Physics, University of Maryland, College Park, MD 20742, USA), AB(Institute for Research in Electronics and the Applied Physics, University of Maryland, College Park, MD 20742, USA), AC(Institute for Research in Electronics and the Applied Physics, University of Maryland, College Park, MD 20742, USA)
Publication:
Journal of Plasma Physics, Volume 85, Issue 2, article id. 905850207, 23 pp.
Publication Date:
04/2019
Origin:
CUP
Keywords:
fusion plasma, plasma simulation
Abstract Copyright:
(c) 2019: © Cambridge University Press 2019
DOI:
10.1017/S0022377819000254
Bibliographic Code:
2019JPlPh..85b9007A

Abstract

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of > O(N) >, where > N > is the number of parameters used to describe the outer flux surface or coil shapes.
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