Heat flux reconstruction and effective diffusion estimation from perturbative experiments using advanced filtering and confidence analysis

Berkel, M. van; Kobayashi, Tatsuya; Zwart, Hans; Igami, H.; Kubo, S.; Tamura, N.; Takahashi, Hayato; Baar, M.R. de

doi:10.1088/1741-4326/aad13e

Cited by 5 publications

(4 citation statements)

References 25 publications

(74 reference statements)

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“…On the other hand, the LHD observation in [9, figure 5] does not show such a dependence. However, new experimental results show that such a dependence may exist [32]. Hence, the dependence of χ e on P remains an open question to be resolved but for completeness we have included this dependence in the overall non-linear heat flux model q e (ρ, t) = q P (ρ, P (•, t)) − n e χ e (ρ, P (•, t)) ∇ ρ T e , (12) where q e (ρ, t) is a function of the whole power density profile P (•, t) not the local ρ.…”

Section: Extended Heat Flux Modelmentioning

confidence: 99%

“…This is our first key step to understand this 30 year old problem. In case we use a symmetric block-wave (the standard) modulation: (1) the slopes can be used to estimate the diffusion coefficients (described in detail in [32]); (2) the analysis in section 3.2 shows that the height of the Lissajous curve ∆q e /n e can be used to estimate P eff , which can be compared. In case we do not use a block-wave modulation or we have other slow transport components such as a convective velocity, more advanced methodologies are necessary.…”

Section: Discerning Different Transport Componentsmentioning

confidence: 99%

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Separation of transport in slow and fast time-scales using modulated heat pulse experiments (hysteresis in flux explained)

et al. 2018

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Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated ECH experiments both in tokamaks and stellarators. This is most apparent for modulated experiments in the Large Helical Device (LHD) and in Wendelstein 7 advanced stellarator (W7-AS). In this paper we show that: (1) this power dependence can be reproduced by linear models and as such hysteresis (in flux) has no relationship to hysteresis as defined in the literature; (2) observations of ‘hysteresis’ (in flux) and a direct response to power can be perfectly reproduced by introducing an error in the estimated deposition profile as long as the errors redistribute the heat over a large radius; (3) non-local models depending directly on the heating power can also explain the experimentally observed Lissajous curves (hysteresis); (4) how non-locality and deposition errors can be recognized in experiments and how they affect estimates of transport coefficients; (5) from a linear perturbation transport experiment, it is not possible to discern deposition errors from non-local fast transport components (mathematically equivalent). However, when studied over different operating points non-linear-non-local transport models can be derived which should be distinguishable from errors in the deposition profile. To show all this, transport needs to be analyzed by separating the transport in a slow (diffusive) time-scale and a fast (heating/non-local) time-scale, which can only be done in the presence of perturbations.

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Section: Extended Heat Flux Modelmentioning

confidence: 99%

Section: Discerning Different Transport Componentsmentioning

confidence: 99%

Separation of transport in slow and fast time-scales using modulated heat pulse experiments (hysteresis in flux explained)

et al. 2018

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“…In excitation experiments only a finite number of bins are informative, i.e., those bins which are present in the input S(k) and are above the noise level [14]. Hence, in practice only a -few-finite number of bins need to be considered (see [21] for details).…”

Section: A Frequency Domain Approachmentioning

confidence: 99%

A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

Kampen

Das

Weiland

et al. 2021

IEEE Control Syst. Lett.

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This paper presents a closed-form solution to estimate space-dependent transport parameters of a linear one dimensional diffusion-transport-reaction equation. The infinite dimensional problem is approximated by a finite dimensional model by 1) taking a frequency domain approach, 2) linear parameterization of the unknown parameters, and 3) using a semidiscretization. Assuming full state knowledge, the commonly used output error criterion is rewritten as the equation error criterion such that the problem results in linear least squares. The optimum is then given by a closed-form solution, avoiding computational expensive optimization methods. Functioning of the proposed method is illustrated by means of simulation.

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“…Fast transport in response to applied heating power can obscure the width of the power deposition profile 4 . Determining the full deposition profile therefore requires self-consistent treatment of applied power and the resulting transport 5,6 . To this end, Brookman et al developed a method to self-consistently estimate power deposition and transport profiles from temperature measurements in response to a modulated RF heating source, denoted here as the 'flux fit method' 7 .…”

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confidence: 99%

Extension of the flux fit method for estimating power deposition profiles

et al. 2022

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The flux fit method is used to self-consistently estimate the power deposition profile and heat transport profiles from temperature measurements originating from perturbative experiments with a modulated source. This Letter improves on this method by addressing the limitations and assumptions. The most crucial improvement is the additional freedom in the source deposition profile. Allowing for a variable central deposition location and height and including a skewness parameter produces deposition profiles more consistent with the measurement data, but still wider than equilibrium ray tracing in two different DIII-D discharges. Moreover, we show that the quality of the estimated deposition profile is key to the accuracy of diffusivity and convectivity estimates, but inversely, the estimated transport parameters hardly affect the quality of the power deposition estimate. Using this method, we show that the power deposition profile estimate is broadened with respect to ray-tracing by about 1.7–1.8 times in two DIII-D discharges.

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Heat flux reconstruction and effective diffusion estimation from perturbative experiments using advanced filtering and confidence analysis

Cited by 5 publications

References 25 publications

Separation of transport in slow and fast time-scales using modulated heat pulse experiments (hysteresis in flux explained)

Separation of transport in slow and fast time-scales using modulated heat pulse experiments (hysteresis in flux explained)

A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

Extension of the flux fit method for estimating power deposition profiles

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