An adjoint method for neoclassical stellarator optimization
Abstract
Stellarators remain an enticing route to steadystate fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating highdimensional spaces, often necessitating the use of gradientbased methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring$O(N)$$flux computations, where$$N$$is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finitecollisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ($$O(10^{2})$), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjointbased optimization of the field strength to obtain minimal bootstrap current on a surface. With adjointbased derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Moreover, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.
 Authors:

 Univ. of Maryland, College Park, MD (United States). Inst. for Research in Electronics and Applied Physics
 Univ. of Maryland, College Park, MD (United States). Inst. for Research in Electronics and Applied Physics; Chalmers Univ. of Technology, Göteborg (Sweden)
 Publication Date:
 Research Org.:
 Univ. of Maryland, College Park, MD (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES)
 Contributing Org.:
 National Energy Research Scientiﬁc Computing Center (NERSC)
 OSTI Identifier:
 1597696
 Grant/Contract Number:
 FG0293ER54197; FC0208ER54964
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Plasma Physics
 Additional Journal Information:
 Journal Volume: 85; Journal Issue: 5; Journal ID: ISSN 00223778
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma confinement; plasma simulation
Citation Formats
Paul, Elizabeth J., Abel, Ian G., Landreman, Matt, and Dorland, William. An adjoint method for neoclassical stellarator optimization. United States: N. p., 2019.
Web. doi:10.1017/S0022377819000527.
Paul, Elizabeth J., Abel, Ian G., Landreman, Matt, & Dorland, William. An adjoint method for neoclassical stellarator optimization. United States. https://doi.org/10.1017/S0022377819000527
Paul, Elizabeth J., Abel, Ian G., Landreman, Matt, and Dorland, William. Fri .
"An adjoint method for neoclassical stellarator optimization". United States. https://doi.org/10.1017/S0022377819000527. https://www.osti.gov/servlets/purl/1597696.
@article{osti_1597696,
title = {An adjoint method for neoclassical stellarator optimization},
author = {Paul, Elizabeth J. and Abel, Ian G. and Landreman, Matt and Dorland, William},
abstractNote = {Stellarators remain an enticing route to steadystate fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating highdimensional spaces, often necessitating the use of gradientbased methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring$O(N)$flux computations, where$N$is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finitecollisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ($O(10^{2})$), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjointbased optimization of the field strength to obtain minimal bootstrap current on a surface. With adjointbased derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Moreover, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.},
doi = {10.1017/S0022377819000527},
journal = {Journal of Plasma Physics},
number = 5,
volume = 85,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
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