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

被引:13
|
作者
van Berkel, M. [1 ,2 ,3 ]
Zwart, H. J. [4 ]
Hogeweij, G. M. D. [1 ]
Vandersteen, G. [5 ]
van den Brand, H. [1 ,2 ]
de Baar, M. R. [1 ,2 ]
机构
[1] EURATOM, DIFFER Dutch Inst Fundamental Energy Res, FOM Inst, Trilateral Euregio Cluster, NL-3430 BE Nieuwegein, Netherlands
[2] Eindhoven Univ Technol, Dept Mech Engn, Control Syst Technol Grp, NL-5600 MB Eindhoven, Netherlands
[3] Natl Inst Nat Sci, Natl Inst Fus Sci, Toki, Gifu 5095292, Japan
[4] Eindhoven Univ Technol, Dept Mech Engn, Dynam & Control Grp, NL-5600 MB Eindhoven, Netherlands
[5] Vrije Univ Brussel, Dept Fundamental Elect & Instrumentat, B-1050 Brussels, Belgium
关键词
perturbative transport; electron diffusivity; estimation; statistics; confidence bounds; diffusion coefficient; HEAT PULSE-PROPAGATION; MODULATION EXPERIMENTS; DIII-D; TRANSPORT; TOKAMAK; INTERFEROMETRY; DEPENDENCE; PROFILE;
D O I
10.1088/0741-3335/56/10/105004
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
In this paper, the estimation of the thermal diffusivity from perturbative experiments in fusion plasmas is discussed. The measurements used to estimate the thermal diffusivity suffer from stochastic noise. Accurate estimation of the thermal diffusivity should take this into account. It will be shown that formulas found in the literature often result in a thermal diffusivity that has a bias (a difference 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 diffusion as heat transport mechanism and measurement noise based on ASDEX Upgrade measurements. The Fourier coefficients of a temperature perturbation will exhibit noise from the circular complex normal distribution (CCND). Based on Fourier coefficients distributed according to a CCND, it is shown that the resulting probability density function of the thermal diffusivity is an inverse non-central chi-squared distribution. The thermal diffusivity that is found by sampling this distribution will always be biased, and averaging of multiple estimated diffusivities will not necessarily improve the estimation. Confidence bounds are constructed to illustrate the uncertainty in the diffusivity using several formulas that are equivalent in the noiseless case. Finally, a different method of averaging, that reduces the uncertainty significantly, is suggested. The methodology is also extended to the case where damping is included, and it is explained how to include the cylindrical geometry.
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页数:18
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