Estimation of the thermal diffusion coefficient in fusion plasmas taking frequency measurement uncertainties into account

Abstract

In this paper, the estimation of the thermal diusivity from perturbative experiments in fusion plasmas is discussed. The measurements used to estimate the thermal diusivity suer from stochastic noise. Accurate estimation of the thermal diusivity should take this into account. It will be shown that formulas found in the literature often result in a thermal diusivity that has a bias (a dierence between the estimated value and the actual value that remains even if more measurements are added) or have an unnecessarily large uncertainty. This will be shown by modeling a plasma using only diusion as heat transport mechanism and measurement noise based on ASDEX Upgrade measurements. The Fourier coecients of a temperature perturbation will exhibit noise from the Circular Complex Normal Distribution (CCND). Based on Fourier coecients with a CCND, it is shown that the resulting Probability Density Function (PDF) of the thermal diusivity is an inverse non-central chi-squared distribution. The thermal diusivity that is found by sampling this distribution will always be biased and averaging of multiple estimated diusivities will not necessarily improve the estimation. Condence bounds are constructed to illustrate the uncertainty in diusivity using several formulas that are equivalent in the noiseless case. Finally, a dierent method of averaging, that reduces the uncertainty signicantly, is suggested. The methodology is also extended to the case where damping is included and it is explained how to include the cylindrical geometry.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

“…In the noiseless slab-geometry case, it does not matter if ω 1 or ω 2 is used for ω in A A and φ . However, in practice generally the best choice is to use a weighted average as described in [37]. Easier to implement, but less accurate is to use ω 1 as it has generally the best Signal-to-Noise ratio (SNR).…”

“…In the special case that τ invs is considered to be zero a single harmonic suces to estimate both χ and V s . This can be derived from (36) and (37), which results in…”

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

“…The first necessary step is the inclusion of an uncertainty analysis with errors in the frequency domain. In this experiment only two periods were used these should be increased to at least three and preferably to 7 to retain important statistical properties under Gaussian noise assumptions [53]. Note that here some noise statistics is done based on the intermediate frequency and under the assumption of white noise, but this can be significantly improved.…”

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

“…As such this calculation simultaneously checks if the assumption of stationary white-noise is valid. The definitions can be found in [17]. This method is abbreviated with caf (from conditional average in the frequency domain).…”