Sehyun Kwak

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes

A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy (Li-BES) system, measuring Li I (2p-2s) line radiation using 26 channels with ~1 cm spatial resolution and ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li I line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly developed method to infer JET edge electron density profiles has the following advantages in comparison to the conventional method: (i) providing full posterior distributions of edge density profiles, including their associated uncertainties, (ii) the available radial range for density profiles is increased to the full observation range (~26 cm), (iii) an assumption of monotonic electron density profile is not necessary, (iv) the absolute calibration factor of the diagnostic system is automatically estimated overcoming the limitation of the conventional technique and allowing us to infer the electron density profiles for all pulses without preprocessing the data or an additional boundary condition, and (v) since the full spectrum is modelled, the procedure of modulating the beam to measure the background signal is only necessary for the case of overlapping of the Li I line with impurity lines.

Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X

We make use of a Bayesian description of the neural network (NN) training for the calculation of the uncertainties in the NN prediction. Having uncertainties on the NN prediction allows having a quantitative measure for trusting the NN outcome and comparing it with other methods. Within the Bayesian framework, the uncertainties can be calculated under different approximations. The NN has been trained with the purpose of inferring ion and electron temperature profile from measurements of a X-ray imaging diagnostic at W7-X. The NN has been trained in such a way that it constitutes an approximation of a full Bayesian model of the diagnostic, implemented within the Minerva framework. The network has been evaluated using measured data and the uncertainties calculated under different approximations have been compared with each other, finding that neglecting the noise on the NN input can lead to an underestimation of the error bar magnitude in the range of 10%-30%.

Imputation of faulty magnetic sensors with coupled Bayesian and Gaussian processes to reconstruct the magnetic equilibrium in real time

A Bayesian with Gaussian process-based numerical method to impute a few missing magnetic signals caused by impaired magnetic probes during tokamak operations is developed such that the real-time reconstruction of magnetic equilibria, whose performance strongly depends on the measured magnetic signals and their intactness, is affected minimally. Likelihood of the Bayesian model constructed with Maxwells equations, specifically Gausss law for magnetism and Ampères law, results in an infinite number of solutions if two or more magnetic signals are missing. This undesirable characteristic of the Bayesian model is remediated by coupling the model with the Gaussian process. Our proposed numerical method infers nine non-consecutive missing magnetic signals correctly in less than 1 ms suitable for the real-time reconstruction of magnetic equilibria during tokamak operations.

Feasibility study of direct spectra measurements for Thomson scattered signals for KSTAR fusion-grade plasmas

Feasibility study of direct spectra measurements of Thomson scattered photons for fusion-grade plasmas is performed based on a forward model of the KSTAR Thomson scattering system. Expected spectra in the forward model are calculated based on Selden function including the relativistic polarization correction. Noise in the signal is modeled with photon noise and Gaussian electrical noise. Electron temperature and density are inferred using Bayesian probability theory. Based on bias error, full width at half maximum and entropy of posterior distributions, spectral measurements are found to be feasible. Comparisons between spectrometer-based and polychromator-based Thomson scattering systems are performed with varying quantum efficiency and electrical noise levels.