Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

Blommaert, Maarten; Heumann, Holger; Baelmans, Martine; Gauger, Nicolas R.; Reiter, D.

doi:10.1051/proc/201653004

Cited by 7 publications

(10 citation statements)

References 30 publications

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“…But there are many more applications in fusion science that can benefit from an MEM approach. The control of the location of the plasma boundary defining point for heat load minimization of divertor design [6,7] or the computation of plasma equilibria with so-called snowflake configuration [52] are two of such very relevant applications. Figure 5.…”

Section: Discussionmentioning

confidence: 99%

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Heumann

Rapetti

2017

Journal of Computational Physics

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International audienceExisting finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping

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Section: Discussionmentioning

confidence: 99%

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Heumann

Rapetti

2017

Journal of Computational Physics

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“…To this end, we summarize the magnetic optimization approach as outlined in Refs. [ ], focussing on the impact of discretization errors on the calculation of gradients of the so‐called “cost functional”. Finally, the accuracy of the PA gradients is assessed as a function of grids of varying coarseness by calculating the gradient with both finite differences (FDs) and the adjoint model.…”

Section: Optimizationmentioning

confidence: 99%

Towards numerical optimization of snowflake topologies

Kerkhof

Blommaert

Heumann

et al. 2018

Contributions to Plasma Physics

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In this paper, the framework for gradient‐based optimization of snowflake magnetic divertor topologies is discussed. A continuous in‐parts adjoint approach is adopted to calculate the gradient. A robust grid generator developed within the in‐house DivOpt code enables different topologies in an automated way. However, a large flux expansion exists near second‐order and closely spaced first‐order X‐points. This might induce significant discretization errors. As accurate gradients are needed for the correct functioning of the numerical optimization algorithm, the importance of the discretization error is assessed by calculating the gradient with both finite differences and the continuous adjoint approach on three systematically refined grids. It is shown that sufficiently fine grids are needed to achieve accurate gradient calculation and a corresponding good functioning of the optimization algorithm.

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“…To efficiently calculate the sensitivities of the objective functional (37) with respect to the control variables ϕ, an in parts adjoint approach is employed [9]. In this section we briefly explain this approach.…”

Section: An In Parts Adjoint Strategy To Sensitivity Calculationmentioning

confidence: 99%

“…Nested optimization methods were also successfully applied to design the magnetic divertor configuration [7]. Since a full adjoint procedure, including sensitivities of a specific field-aligned grid generator, appeared cumbersome, an in parts adjoint procedure was developed that focuses on the expensive plasma edge transport simulation [8,9]. This paper considers the application of one-shot optimization to magnetic divertor design.…”

Section: Introductionmentioning

confidence: 99%

A practical globalization of one-shot optimization for optimal design of tokamak divertors

Blommaert

Dekeyser

Baelmans

et al. 2017

Journal of Computational Physics

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In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust ranktwo Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

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Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

Cited by 7 publications

References 30 publications

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Towards numerical optimization of snowflake topologies

A practical globalization of one-shot optimization for optimal design of tokamak divertors

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