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Bayesian Inference for Microwave Diagnostics at Joint European Torus

Time: Thu 2022-06-02 09.00

Location: F3, Lindstedtsvägen 26 & 28, Stockholm

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Language: English

Subject area: Electrical Engineering

Doctoral student: Stefan Schmuck , Fusionsplasmafysik, ISTP-CNR (Milan, Italy)

Opponent: Doctor Laurie Porte, École polytechnique fédérale de Lausanne (EPFL)

Supervisor: Professor Per Brunsell, Fusionsplasmafysik; Associate Professor Thomas Jonsson, Fusionsplasmafysik; Doctor Jakob Svensson, Max-Planck-Institut für Plasmaphysik Teilinstitut Greifswald, Wendelsteinstraße 1, D-17491 Greifswald, Germany

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QC 20220509


The major goal of this thesis is to perform Bayesian inference jointly for electron kinetic profiles, a toroidal magnetic field correction, diagnostic sensitivities, and wall reflection properties given noisy measurements of four microwave diagnostics at the tokamak JET. Besides the measurements, this kind of inference considers prior knowledge, like profile length-scales, to update objectively the information about the physics parameters. Such a probabilistic update, i.e. a posterior probability distribution or posterior, states the plausibility of parameter combinations and captures parameter uncertainties and correlations. The already existing Bayesian framework Minerva was used to carry out the inference.Contrary to standard approaches, plasma physics and diagnostic models and physics parameters are used to make predictions which are compared objectively with the data provided by one reflectometer and three electron cyclotron emission (ECE) diagnostics; two broadband Martin-Puplett interferometers and one heterodyne radiometer. In addition, these models represent reality more closely, for instance: (i) the smoothnesses of temperature and density profiles are modelled and estimated by length-scale parameters, (ii) the models SPECE and ECEPT, predicting each broadband ECE spectra, take into account relativistic and density effects like the finite optical thickness, (iii) the working principle and measurement uncertainty of each diagnostic are considered. As an example for the latter point, the two interferometers supply convoluted ECE spectra over several harmonic ranges up to 500 GHz and in mainly ordinary and extra-ordinary wave mode polarisations. The uncertainties on these spectra originate mostly from absolute calibrations for which a dedicated, robust and reliable procedure had to be established during this thesis.Further intermediate achievements of this thesis are for example: (i) the analytical derivation of the generalised square-exponential covariance function, enabling the estimation of multiple length-scales for electron temperature and density profiles in the plasma core and edge domains, (ii) the already existing ray-tracer SPECE, which predicts accurately but slowly ECE spectra, was parallelised successfully by a client-server approach, (iii) the derivation of the model ECEPT to predict quickly and sufficiently accurately broadband ECE spectra for an Ohmically heated plasma, and (iv) the extension of the multi-reflection model to allow different properties for the high-field and low-field side walls of a fusion device, affecting substantially the predictions of ECE spectra at frequencies for which the plasma has a low optical thickness.For a low temperature and low density plasma, the joint inference of more than 200 parameters was carried out for a given flux surface geometry, using either SPECE or ECEPT as predictor for the measured ECE spectra from 50 GHz to 280 GHz (first three harmonic ranges at least) with contributions from the ordinary and extra-ordinary wave-modes. For the ECEPT case, the shape of the joint posterior could be explored numerically. Related findings are, for example, smooth electron temperature and density profiles with values at the centre of 1.5 keV and 1.75x1e19 m^-3 and at the separatrix of 80 eV and 2x1e18 m^-3 with uncertainties of the order of 10 eV and few 1e17 m^-3. Furthermore, the smoothness of each core and edge profile originates in the inferred length-scale. These results were confirmed by the most likely parameter combination of the posterior when the more accurate predictor SPECE is used. The only exceptions are the correction to the magnetic field, which increased from 1.4% to 2%, and the reflectivity of the ITER-like wall, which elevated from 0.72 to 0.92.With ECEPT in use, multiple posterior correlation features could be revealed of which many could be explained. For instance, each profile smoothness, due to the estimated length-scale, implies considerable correlationsbetween nearby locations. In addition, a global correlation feature is evidentfor edge and core density profiles, likely caused by the measurement principle of the reflectometer.

The second part of this thesis focusses on Bayesian inference about spectra in the field of Fourier transform spectroscopy. An example application has been carried out for the calibration data measured with one of the Martin-Puplett interferometers at JET. Compared to standard analysis techniques, more information could be extracted about the spectra from the so-called double-, single- and zero-sided data domains. The spectra have been modelled as Brownian bridge processes a priori, by which the global trend of the data located in double- and single-sided domains is modelled. This enables the estimation of the posterior uncertainties of the spectra due to non-probed data domains, especially the zero-sided domain. Such consideration is not made in any form by conventional techniques, because no method has been developed to estimate the seemingly lost information contained in the zero-sided domain. The lower and upper limits of the spectra have been estimated by (33+/-1.7) GHz and (913+/-2.9) GHz. These limits are rated to be more likely by a factor of 1e277 than the limits at 0 GHz and 3747 GHz (Nyquist frequency) assumed by conventional analysis approaches but never checked for plausibility.