Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

Dekeyser, Wouter; Reiter, D.; Baelmans, Martine

doi:10.1016/j.jcp.2014.08.023

Cited by 13 publications

(28 citation statements)

References 20 publications

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“…(For this problem, D generally has full rank, so all the diagonal entries of R are nonzero.) If ∂f /∂p is in the column space of D, the solution to (22) is then given by S = R −1…”

Section: B Surfacesmentioning

confidence: 99%

Computing local sensitivity and tolerances for stellarator physics properties using shape gradients

Landreman

Paul

2018

Nucl. Fusion

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Tight tolerances have been a leading driver of cost in recent stellarator experiments, so improved definition and control of tolerances can have significant impact on progress in the field. Here we relate tolerances to the shape gradient representation that has been useful for shape optimization in industry, used for example to determine which regions of a car or aerofoil most affect drag, and we demonstrate how the shape gradient can be computed for physics properties of toroidal plasmas. The shape gradient gives the local differential contribution to some scalar figure of merit (shape functional) caused by normal displacement of the shape. In contrast to derivatives with respect to quantities parameterizing a shape (e.g. Fourier amplitudes), which have been used previously for optimizing plasma and coil shapes, the shape gradient gives spatially local information and so is more easily related to engineering constraints. We present a method to determine the shape gradient for any figure of merit using the parameter derivatives that are already routinely computed for stellarator optimization, by solving a small linear system relating shape parameter changes to normal displacement. Examples of shape gradients for plasma and electromagnetic coil shapes are given. We also derive and present examples of an analogous representation of the local sensitivity to magnetic field errors; this magnetic sensitivity can be rapidly computed from the shape gradient. The shape gradient and magnetic sensitivity can both be converted into local tolerances, which inform how accurately the coils should be built and positioned, where trim coils and structural supports for coils should be placed, and where magnetic material and current leads can best be located. Both sensitivity measures provide insight into shape optimization, enable systematic calculation of tolerances, and connect physics optimization to engineering criteria that are more easily specified in real space than in Fourier space.

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“…(For this problem, D generally has full rank, so all the diagonal entries of R are nonzero.) If ∂f /∂p is in the column space of D, the solution to (22) is then given by S = R −1…”

Section: B Surfacesmentioning

confidence: 99%

Computing local sensitivity and tolerances for stellarator physics properties using shape gradients

Landreman

Paul

2018

Nucl. Fusion

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“…This simulation effort has played a key role in defining guidelines for the divertor design. Recent effort has been made towards design optimization [5] and determination of reliable transport coefficients [6]. However, stepping towards high performance experiments near the operational limits, taking into account the aging of the components and experimental feedback, will require improved reliability of the numerical tools.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent cross-field transport model for core and edge plasma transport

Baschetti

Bufferand²,

Ciraolo³

et al. 2021

Nucl. Fusion

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The 2D mean-field plasma edge transport description of plasma wall interaction is completed by a κ-ε model as in Reynolds Average Navier Stokes simulations for neutral fluids. The local evolution of the turbulent kinetic energy κ and its dissipation rate ε are revisited and slightly modified. It is shown that the κ-ε extends the quasilinear approach by self-consistently determining κ and the relevant time κ/ε leading to the diffusion coefficient κ 2 /ε. The κ-ε evolution is also shown to be equivalent to both coupled Ginzburg-Landau amplitude equations and predator-prey systems where κ is the prey and ε the predator. The dissipation process ε we enforce describes the small scale dissipation of Kolmogorov cascades. It depends on a free parameter akin to a velocity V . The chosen closure relates V to the the parallel connection time and the normalized Scrape-Off layer width qρ * , q is the safety factor and ρ * the ratio of the characteristic Larmor radius and plasma minor radius. A 1D model with κ-ε self-organized transport is used for comparison to empirical scaling laws of SOL width and energy confinement time in L-mode plasmas. Shortfalls of the scaling laws are analyzed. Possible changes of the closure for V are discussed. The 1D model is also used to test the transport response to a dependence of V to large scale velocity shear. Spontaneous confinement improvement when increasing the heating power 1 is observed with the development of an interface barrier at the separatrix. Plasma-wall interaction simulations for TCV and WEST are analyzed. A single scalar free parameter tunes the cross field transport. Experimental midplane and divertor profiles are compared to the simulations. Remarkable agreement is observed. The SOL width determined by the simulation for WEST is close to the experimental value with less than 20 % difference, while the scaling law for L-mode is off my more than a factor 3. The turbulent transport described by the κ-ε is not homogeneous, but ballooned as experimentally observed together with cross-field transport in the divertor SOL on the low field side, and nearly none in the private flux region.

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“…Numerical derivatives also introduce additional noise, and the finite difference step size must be chosen carefully. To avoid these difficulties, it is advantageous to compute shape gradients using adjoint methods (Pironneau 1974; Glowinski & Pironneau 1975; Dekeyser, Reiter & Baelmans 2012, 2014 a , b ). Adjoint methods allow the analytic derivative with respect to all parameters to be computed with only two solutions to the system of equations.…”

Section: Introductionmentioning

confidence: 99%

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

2019

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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 3D 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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Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

Cited by 13 publications

References 20 publications

Computing local sensitivity and tolerances for stellarator physics properties using shape gradients

Computing local sensitivity and tolerances for stellarator physics properties using shape gradients

Self-consistent cross-field transport model for core and edge plasma transport

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

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