Technical note on the linearity and power dependence of the diffusion coefficient in W7-AS

Berkel, M. van; Zwart, Hans; Hogeweij, G. M. D.; Baar, M.R. de

doi:10.1088/1361-6587/aa6a2b

Cited by 3 publications

(6 citation statements)

References 11 publications

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“…(ii) In LHD under similar conditions as the observations in [9], the two-tone linearity test showed only a weak nonlinearity, which was 1-2 orders smaller than the main perturbation component [10]. (iii) Step responses at W7-AS show that at some distance to the deposition profile the temperature responses are linear and close to the deposition profile the temperature responses are non-linear [23]. As such at some distance to the source the linearity condition is satisfied.…”

Section: Perturbative Experiments Generally Results In Linear Perturb...mentioning

confidence: 62%

“…Hence, at spatial locations where there is no deposition and at sufficient distance to the boundary for which (22) Figure 14. (a) The spatial dependency of the diffusion coefficient based on the temperature perturbations amplitude at different frequencies for a narrow deposition profile (lines) and wide redistributed profile (dashed-lines), which has been calculated using (23). (b) The spatial dependency of the diffusion coefficient based on the phase of temperature at different frequencies for a narrow deposition profile (lines) and wide redistributed profile (dashed-lines), which has been calculated using (23).…”

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

confidence: 99%

“…If one calculates the diffusion coefficient based on the harmonic components of (24) using the assumption that no deposition is present on the domain, i.e. using (23), then with increasing frequency the diffusion coefficient becomes larger. This is because with increasing frequency the slope should become larger in the pure diffusive case, but because there is no change in slope, the diffusion coefficient will need to compensate for this effect.…”

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

confidence: 99%

“…It is also possible to express the error directly in the diffusion coefficient. Therefore, the relationships in (23) are used, which can be accurately applied as there is no measurement noise and the discretization is very dense. The estimated profiles of χ e in terms of χ A and χ φ are shown in figure 14.…”

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

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: Perturbative Experiments Generally Results In Linear Perturb...mentioning

confidence: 62%

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

confidence: 99%

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

confidence: 99%

Section: Frequency Domain: Effect On the Estimated Transport Coeffici...mentioning

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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“…Note that fast transport components and errors in the deposition profile cannot be seen here as they contribute to the difference in power levels and not in the slopes. On the other hand, the power dependence of the diffusion coefficient can be studied due to the separation of slopes for the corresponding power levels as is discussed in, e.g., [25,26]. The corresponding effective diffusion coefficient in steadystate is given by the diffusion coefficient that has been estimated using the slope for the corresponding power level.…”

Section: Effective Diffusion Calculation From Projectionmentioning

confidence: 99%

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

et al. 2018

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The heat flux is one of the key theoretical concepts used to quantify and understand transport in fusion devices. In this paper, a new method is introduced to calculate the heat flux including its confidence with high accuracy based on perturbed measurements such as the electron temperature. The new method is based on ideal filtering to optimally reduce the noise contributions on the measurements and piece-wise polynomial approximations to calculate the time derivative. Both methods are necessary to arrive at a heat flux and effective diffusion coefficient with high accuracy. The new methodology is applied to a measurement example using electron cyclotron resonance heating block-wave modulation at the Large Helical Device showing the merit of the newly developed methodology.

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Quantifying electron cyclotron power deposition broadening in DIII-D and the potential consequences for the ITER EC system

et al. 2023

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The injection of electron cyclotron (EC) waves fulfills a number of important tasks in nuclear fusion devices for which detailed knowledge of the spatial power deposition profile is critical. This deposition profile is commonly determined using forward models such as beam or ray tracing. Recent numerical and experimental studies have shown that small-angle scattering of the EC beam as it passes through the turbulent plasma edge can cause significant broadening of the effective deposition profile, leading to considerable underestimation of the deposition width by forward methods. However, traditional inverse methods to determine the deposition profile from measurements overestimate the deposition profile width due to transport broadening. In this work, we implement three novel methods to resolve the EC power deposition profile from measurements that counteract transport broadening by simultaneously resolving transport and power deposition. We validate their assumptions and compare the results from these methods to the traditional break-in-slope method as well as to the TORAY ray-tracing code in a set of DIII-D discharges spanning five different confinement modes. We show that the four different inverse methods, novel and established, paint a consistent picture of deposition broadening. Specifically, we show that the measured power deposition profile is between 1.6 and 3.6 times wider than the TORAY profiles. Moreover, we show the considerable consequences that this level of broadening can have for ITER.

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Technical note on the linearity and power dependence of the diffusion coefficient in W7-AS

Cited by 3 publications

References 11 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)

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

Quantifying electron cyclotron power deposition broadening in DIII-D and the potential consequences for the ITER EC system

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