arXiv subjects

J. Svensson

Publications and source records attributed to J. Svensson.

7 recordsLinked to original sources

arXiv2022

Bayesian equilibria of axisymmetric plasmas

We present a Bayesian method for inferring axisymmetric plasma equilibria from the magnetic field and plasma pressure measurements. The method calculates all possible solutions for plasma current and pressure distributions consistent with the measurements and magnetohydrodynamic (MHD) force balance. Toroidal plasma current and magnetic field coils are modelled as a set of axisymmetric current-carrying solid beams. The other parameters such as plasma pressure and poloidal current flux are given as a function of poloidal magnetic flux, which is determined given a 2D current distribution. Plasma pressure and poloidal current flux profiles are modelled as Gaussian processes whose smoothness is optimally chosen based on the principle of Occam's razor. To find equilibrium solutions, we introduce an MHD force balance constraint at every plasma current beam as a part of the prior knowledge. Given all these physical quantities, predictions calculated by the predictive (forward) models for diagnostics are compared to the observations. The high dimensional complex posterior probability distribution is explored by a new algorithm based on the Gibbs sampling scheme.

physics.plasm-ph↗

arXiv2021

Bayesian modelling of multiple plasma diagnostics at Wendelstein 7-X

Consistent inference of the electron density and temperature has been carried out with multiple heterogeneous plasma diagnostic data sets at Wendelstein 7-X. The predictive models of the interferometer, Thomson scattering and helium beam emission spectroscopy systems have been developed in the Minerva framework and combined to a single joint model. The electron density and temperature profiles are modelled by Gaussian processes with their hyperparameters. The model parameters such as the calibration factor of the Thomson scattering system and the model predictive uncertainties are regarded as additional unknown parameters. The joint posterior probability distribution of the electron density and temperature profiles, hyperparameters of the Gaussian processes and model parameters is explored by Markov chain Monte Carlo algorithms. The posterior samples drawn from the joint posterior distribution are numerically marginalised over the hyperparameters and model parameters to obtain the marginal posterior distributions of the electron density and temperature profiles. The inference of these profiles is performed with different combinations of the interferometer and Thomson scattering data as well as either the empirical electron density and temperature constraints at the limiter/divertor positions introduced by \textit{virtual observations} or the edge density and temperature from the helium beam emission data. Furthermore, the addition of the X-ray imaging crystal spectrometers to the joint model for the ion temperature profiles is demonstrated. All these profiles presented in this work are inferred with the optimal hyperparameters and model parameters by exploring the full joint posterior distribution which intrinsically embodies Bayesian Occam's razor.

physics.plasm-ph↗

arXiv2016

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 system, measuring Li I line radiation using 26 channels with ~1 cm spatial resolution and 10~20 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 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 line with impurity lines.

physics.plasm-ph↗

arXiv2015

Bayesian modelling of the emission spectrum of the JET Li-BES 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 (Li-BES) 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.

physics.plasm-ph↗

arXiv2013

Optimisation of out-vessel magnetic diagnostics for plasma boundary reconstruction in tokamaks

To improve the low frequency spectrum of magnetic field measurements of future tokamak reactors such as ITER, several steady state magnetic sensor technologies have been considered. For all the studied technologies it is always advantageous to place the sensors outside the vacuum vessel and as far away from the reactor core to minimize radiation damage and temperature effects, but not so far as to compromise the accuracy of the equilibrium reconstruction. We have studied to what extent increasing the distance between out-vessel sensors and plasma can be compensated for sensor accuracy and/or density before the limit imposed by the degeneracy of the problem is reached. The study is particularized for the Swiss TCV tokamak, due to the quality of its magnetic data and its ability to operate with a wide range of plasma shapes and divertor configurations. We have scanned the plasma boundary reconstruction error as function of out-vessel sensor density, accuracy and distance to the plasma. The study is performed for both the transient and steady state phases of the tokamak discharge. We find that, in general, there is a broad region in the parameter space where sensor accuracy, density and proximity to the plasma can be traded for one another to obtain a desired level of accuracy in the reconstructed boundary, up to some limit. Extrapolation of the results to a tokamak reactor suggests that a hybrid configuration with sensors inside and outside the vacuum vessel could be used to obtain a good boundary reconstruction during both the transient and the flat-top of the discharges, if out-vessel magnetic sensors of sufficient density and accuracy can be placed sufficiently far outside the vessel to minimize radiation damage.

physics.ins-det↗

arXiv2012

Evidence Cross-Validation and Bayesian Inference of MAST Plasma Equilibria

In this paper, current profiles for plasma discharges on the Mega-Ampere Spherical Tokamak (MAST) are directly calculated from pickup coil, flux loop and Motional-Stark Effect (MSE) observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the Joint-European Tokamak (JET) [J. Svensson and A. Werner. Current tomography for axisymmetric plasmas. {\em Plasma Physics and Controlled Fusion}, 50(8):085002, 2008]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable good agreement between Bayesian inference of the last closed flux-surface (LCFS) with other corroborating data, such as such as that from force balance considerations using EFIT++ [L. Appel et al., Proc. 33rd EPS Conf., Rome, Italy, 2006]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry, as well as directly predicting the Shafranov shift of the plasma core.

physics.plasm-ph↗

arXiv2010

Model Data Fusion: developing Bayesian inversion to constrain equilibrium and mode structure

Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal forward-models, together with prior knowledge of the state of the plasma, to yield predictions of internal magnetic structure. A feature of the framework, known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion 50, 085022, 2008), is the inference of magnetic flux surfaces without the use of a force balance model. We discuss results from a new project to develop Bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak; and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac.

physics.plasm-ph↗