Abstract Details
Abstracts
Author: Elizabeth J Paul
Requested Type: Pre-Selected Invited
Submitted: 2019-02-21 16:03:08
Co-authors: M. Landreman, I. Abel, T. Antonsen, Jr.
Contact Info:
University of Maryland, College Park
A.V. Williams Building, 8223 P
College Park, Maryland 20742
United States
Abstract Text:
The design of modern stellarators often employs gradient-based optimization to navigate the high-dimensional spaces used to describe their geometry. However, computing the gradient of a target function is typically quite expensive. The adjoint method provides a means to compute gradients of a target function with respect to many design parameters at much lower computational cost and without the noise associated with numerical derivatives. This technique has been employed widely in automotive and aerodynamic engineering, and we present the first applications to stellarator design.
An adjoint method has been implemented in the stellarator coil design code REGCOIL, allowing for optimization of the coil-winding surface with analytic gradients [1]. An adjoint equation has also been implemented in the SFINCS drift kinetic solver to compute gradients of moments of the distribution function, such as the bootstrap current and radial particle flux, with respect to geometric parameters. We present an adjoint method for obtaining the gradients of functions of MHD equilibria with respect to the shape of the outer plasma boundary or coil shapes, providing an order 100-1000 reduction in cost. Examples of adjoint-based optimization with these methods are presented.
The derivatives obtained from the adjoint method can also be used for sensitivity analysis using the shape gradient. The shape gradient provides a means of quantifying the change in a figure of merit associated with a local perturbation, such as the normal displacement of the plasma surface or the deformation of a coil shape, providing insight into engineering tolerances [2]. For example, derivatives from REGCOIL can inform where the normal field error is most sensitive to displacements of coils. Several applications are presented.
[1] E.J. Paul et al., 2018 Nucl. Fusion 58 076015.
[2] M. Landreman and E.J. Paul, 2018 Nucl. Fusion 58 076023.
[3] T. Antonsen, E.J. Paul, and M. Landreman, 2018 arXiv:1812.06154.
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