1
|
Moser K, Bock A, David P, Bernert M, Fischer R, ASDEX Upgrade Team. Gaussian Process Tomography at ASDEX Upgrade with Magnetic Equilibrium Information and Nonstationary Kernels. FUSION SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1080/15361055.2022.2072659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Affiliation(s)
- Korbinian Moser
- Max Planck Institute for Plasmaphysics, Garching, Germany
- Ludwig-Maximilians-Universität, Munich, Germany
| | - Alexander Bock
- Max Planck Institute for Plasmaphysics, Garching, Germany
| | - Pierre David
- Max Planck Institute for Plasmaphysics, Garching, Germany
| | | | - Rainer Fischer
- Max Planck Institute for Plasmaphysics, Garching, Germany
| | | |
Collapse
|
2
|
VanMeter PD, Delgado-Aparicio LF, Reusch LM, Den Hartog DJ. Robust analysis of space-, time-, and energy-resolved soft x-ray measurements of magnetically confined fusion plasmas (invited). THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:053549. [PMID: 34243280 DOI: 10.1063/5.0043787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 04/03/2021] [Indexed: 06/13/2023]
Abstract
A novel compact multi-energy soft x-ray (ME-SXR) diagnostic based on the PILATUS3 100K x-ray detector has been developed in collaboration between the Princeton Plasma Physics Laboratory and the University of Wisconsin-Madison and tested on the Madison Symmetric Torus (MST) reversed-field pinch. This solid-state photon-counting detector consists of a two-dimensional array of ∼100 000 pixels for which the lower photon absorption cutoff energy can be independently set, allowing it to be configured for a unique combination of simultaneous spatial, spectral, and temporal resolution of ∼1 cm, 100 eV, and 500 Hz, respectively. The diagnostic is highly versatile and can be readily adapted to diverse plasma operating conditions and scientific needs without any required downtime. New results from improved-confinement and quasi-single helicity plasmas in the MST demonstrate how the detector can be applied to study multiple aspects of the evolution of magnetically confined fusion-grade plasmas. These include observing the evolution of thermal emissivity, characterizing the energy of mid-Z excitation lines, extracting the Te profile, and observing the evolution of non-thermal populations. A technique for integrating the ME-SXR diagnostic into an integrated data analysis framework based on Bayesian inference is also presented. This allows ME-SXR measurements to be combined with data for complementary diagnostics in order to simultaneously infer Te and nZ from all available information.
Collapse
Affiliation(s)
- P D VanMeter
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - L M Reusch
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - D J Den Hartog
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| |
Collapse
|
3
|
Kwak S, Hergenhahn U, Höfel U, Krychowiak M, Pavone A, Svensson J, Ford O, König R, Bozhenkov S, Fuchert G, Pasch E, Brunner KJ, Knauer J, Kornejew P, Trimiño Mora H, Pedersen TS. Bayesian inference of spatially resolved Z eff profiles from line integrated bremsstrahlung spectra. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:043505. [PMID: 34243367 DOI: 10.1063/5.0043777] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 03/12/2021] [Indexed: 06/13/2023]
Abstract
In nuclear fusion research, the effective ion charge Zeff, which characterizes the overall content of impurities, can be experimentally derived from the plasma electron-ion bremsstrahlung, given the electron density ne and temperature Te. At Wendelstein 7-X, a multichannel near-infrared spectrometer is installed to collect the plasma bremsstrahlung along 27 lines of sight covering more than half the plasma cross section, which provides information on Zeff over the entire plasma radius. To infer spatially resolved Zeff profiles, a Bayesian model is developed in the Minerva framework. Zeff, ne, and Te profiles are modeled as Gaussian processes, whose smoothness is determined by hyperparameters. These profiles are transformed to fields in Cartesian coordinates, given the poloidal magnetic flux surfaces calculated by the variational moments equilibrium code. Given all these physical quantities, the model predicts line-of-sight integrals of near-infrared bremsstrahlung spectra. The model includes the predictive (forward) models of the interferometer, Thomson scattering system, and visible and near-infrared spectrometers. Given the observations of all these diagnostics, the posterior probability distribution of Zeff profiles is calculated and shown as an inference solution. The smoothness (gradient) of the profiles is optimally chosen by Bayesian Occam's razor. Furthermore, wall reflections can significantly pollute the measurements of the plasma bremsstrahlung, which leads to over-estimation of Zeff values in the edge region. In the first results presented in this work, this problem does not appear, and the posterior samples of Zeff profiles are overall plausible and consistent with Zeff values inferred, given the data from the single-channel visible spectrometer.
Collapse
Affiliation(s)
- Sehyun Kwak
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - U Hergenhahn
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | - U Höfel
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - M Krychowiak
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - A Pavone
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - J Svensson
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - O Ford
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - R König
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - S Bozhenkov
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - G Fuchert
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - E Pasch
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - K J Brunner
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - J Knauer
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - P Kornejew
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | | | - T S Pedersen
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| |
Collapse
|
4
|
Matos F, Svensson J, Pavone A, Odstrčil T, Jenko F. Deep learning for Gaussian process soft x-ray tomography model selection in the ASDEX Upgrade tokamak. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2020; 91:103501. [PMID: 33138591 DOI: 10.1063/5.0020680] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 09/29/2020] [Indexed: 06/11/2023]
Abstract
Gaussian process tomography (GPT) is a method used for obtaining real-time tomographic reconstructions of the plasma emissivity profile in tokamaks, given some model for the underlying physical processes involved. GPT can also be used, thanks to Bayesian formalism, to perform model selection, i.e., comparing different models and choosing the one with maximum evidence. However, the computations involved in this particular step may become slow for data with high dimensionality, especially when comparing the evidence for many different models. Using measurements collected by the Soft X-Ray (SXR) diagnostic in the ASDEX Upgrade tokamak, we train a convolutional neural network to map SXR tomographic projections to the corresponding GPT model whose evidence is highest. We then compare the network's results, and the time required to calculate them, with those obtained through analytical Bayesian formalism. In addition, we use the network's classifications to produce tomographic reconstructions of the plasma emissivity profile.
Collapse
Affiliation(s)
- F Matos
- Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
| | - J Svensson
- Max Planck Institute for Plasma Physics, Wendelsteinstr. 1, 17491 Greifswald, Germany
| | - A Pavone
- Max Planck Institute for Plasma Physics, Wendelsteinstr. 1, 17491 Greifswald, Germany
| | - T Odstrčil
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - F Jenko
- Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
| |
Collapse
|
5
|
Langenberg A, Svensson J, Marchuk O, Fuchert G, Bozhenkov S, Damm H, Pasch E, Pavone A, Thomsen H, Pablant NA, Burhenn R, Wolf RC. Inference of temperature and density profiles via forward modeling of an x-ray imaging crystal spectrometer within the Minerva Bayesian analysis framework. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:063505. [PMID: 31255024 DOI: 10.1063/1.5086283] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Accepted: 06/06/2019] [Indexed: 06/09/2023]
Abstract
At the Wendelstein 7-X stellarator, the X-ray imaging crystal spectrometer provides line integrated measurements of ion and electron temperatures, plasma flows, as well as impurity densities from a spectroscopic analysis of tracer impurity radiation. In order to infer the actual profiles from line integrated data, a forward modeling approach has been developed within the Minerva Bayesian analysis framework. In this framework, the inversion is realized on the basis of a complete forward model of the diagnostic, including error propagation and utilizing Gaussian processes for generation and inference of arbitrary shaped plasma parameter profiles. For modeling of line integrated data as measured by the detector, the installation geometry of the spectrometer, imaging properties of the crystal, and Gaussian detection noise are considered. The inversion of line integrated data is achieved using the maximum posterior method for plasma parameter profile inference and a Markov chain Monte Carlo sampling of the posterior distribution for calculating uncertainties of the inference process. The inversion method shows a correct and reliable inference of temperature and impurity density profiles from synthesized data within the estimated uncertainties along the whole plasma radius. The application to measured data yields a good match of derived electron temperature profiles to data of the Thomson scattering diagnostic for central electron temperatures between 2 and 5 keV using argon impurities.
Collapse
Affiliation(s)
- A Langenberg
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - J Svensson
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - O Marchuk
- Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung-Plasmaphysik, 52425 Jülich, Germany
| | - G Fuchert
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - S Bozhenkov
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - H Damm
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - E Pasch
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - A Pavone
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - H Thomsen
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - N A Pablant
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
| | - R Burhenn
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - R C Wolf
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| |
Collapse
|
6
|
Kobayashi T, Kobayashi M, Iwama N, Kuzmin A, Goto M, Kawamura G. Single field-of-view tomographic imaging of 3D impurity emission distribution in magnetized edge plasma of LHD. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:123502. [PMID: 30599606 DOI: 10.1063/1.5048218] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Accepted: 11/12/2018] [Indexed: 06/09/2023]
Abstract
A new tomographic scheme is proposed for reconstructing three dimensional (3D) impurity emission distributions from two dimensional (2D) measurements with a single field-of-view in the magnetized edge plasma in a Large Helical Device (LHD). The 2D image is obtained with a multi-channel fiber array spectrometer, which views the entire region of the edge stochastic magnetic layer of LHD, including divertor plates, divertor legs, the stochastic layer, and the last closed flux surface. The scheme introduces new regularization terms in the Lagrangian function, based on the transport feature in magnetized plasma that the transport parallel to the magnetic field lines is much faster than the transport across the magnetic field, thus assuming smooth distribution in the parallel direction. The scheme is benchmarked with the test data of 3D distribution in the measurement volume, where the effectiveness of the various regularization terms is surveyed and feasibility of the scheme is confirmed. The new scheme is applied to the experimental data in LHD for carbon impurity emissions of C1+ and C3+, where the obtained distributions are discussed taking into account the plasma wall interaction and charge dependence of ionization potentials.
Collapse
Affiliation(s)
- Taisuke Kobayashi
- SOKENDAI (The Graduate University for Advanced Studies), 322-6 Oroshi-cho, Toki 509-5292, Japan
| | - Masahiro Kobayashi
- SOKENDAI (The Graduate University for Advanced Studies), 322-6 Oroshi-cho, Toki 509-5292, Japan
| | - Naofumi Iwama
- National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki 509-5292, Japan
| | - Arseniy Kuzmin
- National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki 509-5292, Japan
| | - Motoshi Goto
- SOKENDAI (The Graduate University for Advanced Studies), 322-6 Oroshi-cho, Toki 509-5292, Japan
| | - Gakushi Kawamura
- SOKENDAI (The Graduate University for Advanced Studies), 322-6 Oroshi-cho, Toki 509-5292, Japan
| |
Collapse
|
7
|
Yang X, Xu T, Xiao C, Chen Y, Wang T, Lin C, Xu M, Yu Y, Wang L, Wang X. A reconstruction method based on evolution of partial differential equation for the Laser-driven Ion-beam Trace Probe (LITP). THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:10I130. [PMID: 30399900 DOI: 10.1063/1.5039426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 07/03/2018] [Indexed: 06/08/2023]
Abstract
The Laser-driven Ion-beam Trace Probe (LITP) is a new poloidal magnetic field (Bp) diagnostic method in tokamak devices. It measures the ion displacements which are linear integrations of Bp along the ion beam traces, and a proper tomography method is necessary for the Bp reconstruction. A tomography method based on the solution of partial differential equation is used. The diffusion term and perturbation term are used to avoid the divergence and smooth the reconstructed results. Numerical results show that both the diffusion term and the perturbation term obviously improved the reconstruction results of Bp for LITP.
Collapse
Affiliation(s)
- X Yang
- State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
| | - T Xu
- State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
| | - C Xiao
- State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
| | - Y Chen
- State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
| | - T Wang
- Center for Fusion Science of Southwestern Institute of Physics, P.O. Box 432, Chengdu 610041, China
| | - C Lin
- State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
| | - M Xu
- Center for Fusion Science of Southwestern Institute of Physics, P.O. Box 432, Chengdu 610041, China
| | - Y Yu
- School of Physics, University of Science and Technology of China, Hefei 230026, China
| | - L Wang
- Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
| | - X Wang
- Laboratory for Space Environment and Physical Sciences, Harbin Institute of Technology, Harbin 150001, China
| |
Collapse
|
8
|
Joung S, Kim J, Kwak S, Park KR, Hahn SH, Han HS, Kim HS, Bak JG, Lee SG, Ghim YC. Imputation of faulty magnetic sensors with coupled Bayesian and Gaussian processes to reconstruct the magnetic equilibrium in real time. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:10K106. [PMID: 30399691 DOI: 10.1063/1.5038938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Accepted: 06/25/2018] [Indexed: 06/08/2023]
Abstract
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 Maxwell's equations, specifically Gauss's law for magnetism and Ampère's 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.
Collapse
Affiliation(s)
- Semin Joung
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| | - Jaewook Kim
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| | - Sehyun Kwak
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| | - Kyeo-Reh Park
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| | - S H Hahn
- National Fusion Research Institute, Daejeon 34133, South Korea
| | - H S Han
- National Fusion Research Institute, Daejeon 34133, South Korea
| | - H S Kim
- National Fusion Research Institute, Daejeon 34133, South Korea
| | - J G Bak
- National Fusion Research Institute, Daejeon 34133, South Korea
| | - S G Lee
- National Fusion Research Institute, Daejeon 34133, South Korea
| | - Y-C Ghim
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| |
Collapse
|
9
|
Wang T, Mazon D, Svensson J, Li D, Jardin A, Verdoolaege G. Incorporating magnetic equilibrium information in Gaussian process tomography for soft X-ray spectroscopy at WEST. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:10F103. [PMID: 30399849 DOI: 10.1063/1.5039152] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Accepted: 07/14/2018] [Indexed: 06/08/2023]
Abstract
Gaussian process tomography (GPT) [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and D. Li, J. Svensson, H. Thomsen, F. Medina, A. Werner, and R. Wolf, Rev. Sci. Instrum. 84, 083506 (2013)] is a recently developed tomography method applied earlier to soft X-ray (SXR) spectroscopy on WEST-Tungsten (W) Environment in Steady-state Tokamak. The short execution time of the algorithm makes GPT an important candidate for providing real-time information on impurity transport and for fast MHD control. In earlier work, GPT has shown its flexibility by providing good reconstruction results without background information about the magnetic equilibrium. On the other hand, information about the magnetic flux surface geometry can in general be useful for additional regularization of the solution. In this paper, we develop a way to take into account the equilibrium information, by constructing a covariance matrix of the prior Gaussian process depending on the flux surface geometry. The GPT method is validated using synthetic SXR emissivity profiles relevant to WEST plasmas and compares favorably with the classical algorithm based on minimization of the Fisher information.
Collapse
Affiliation(s)
- T Wang
- Southwestern Institute for Physics, CNNC, C-610200 Chengdu, China
| | - D Mazon
- Institute for Magnetic Fusion Research, CEA, F-13115 Saint-Paul-lez-Durance, France
| | - J Svensson
- Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald, Germany
| | - D Li
- Southwestern Institute for Physics, CNNC, C-610200 Chengdu, China
| | - A Jardin
- Institute for Magnetic Fusion Research, CEA, F-13115 Saint-Paul-lez-Durance, France
| | - G Verdoolaege
- Department of Applied Physics, Ghent University, B-9000 Ghent, Belgium
| |
Collapse
|
10
|
Reusch LM, Nornberg MD, Goetz JA, Den Hartog DJ. Using integrated data analysis to extend measurement capability (invited). THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:10K103. [PMID: 30399657 DOI: 10.1063/1.5039349] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Accepted: 07/12/2018] [Indexed: 06/08/2023]
Abstract
The analysis approach called integrated data analysis (IDA) provides a means to exploit all information present in multiple streams of raw data to produce the best inference of a plasma parameter. This contrasts with the typical approach in which information (data) from a single diagnostic is used to measure a given parameter, e.g., visible bremsstrahlung → Z eff. Data from a given diagnostic usually contain information on many parameters. For example, a Thomson scattering diagnostic is sensitive to bremsstrahlung and line emission in addition to electron temperature. This background light is typically subtracted off and discarded but could be used to improve knowledge of Z eff. IDA encourages explicit awareness of such information and provides the quantitative framework to exploit it. This gives IDA the ability to increase spatial and temporal resolution, increase precision and accuracy of inferences, and measure plasma parameters that are difficult or impossible to measure using single diagnostic techniques. One example is the measurement of Z eff on Madison symmetric torus using IDA since no single diagnostic can provide a robust measurement. As we enter the burning plasma era, application of IDA will be critical to the measurement of certain parameters, as diagnostic access in the harsh fusion environment will be extremely limited.
Collapse
Affiliation(s)
- L M Reusch
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - M D Nornberg
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - J A Goetz
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - D J Den Hartog
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| |
Collapse
|
11
|
Wang T, Mazon D, Svensson J, Li D, Jardin A, Verdoolaege G. Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:063505. [PMID: 29960552 DOI: 10.1063/1.5023162] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Gaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information.
Collapse
Affiliation(s)
- T Wang
- Southwestern Institute for Physics, CNNC, C-610200 Chengdu, China
| | - D Mazon
- Institute for Magnetic Fusion Research, CEA, F-13115 Saint-Paul-lez-Durance, France
| | - J Svensson
- Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald, Germany
| | - D Li
- Southwestern Institute for Physics, CNNC, C-610200 Chengdu, China
| | - A Jardin
- Institute for Magnetic Fusion Research, CEA, F-13115 Saint-Paul-lez-Durance, France
| | - G Verdoolaege
- Department of Applied Physics, Ghent University, B-9000 Ghent, Belgium
| |
Collapse
|
12
|
Li D, Dong YB, Deng W, Shi ZB, Fu BZ, Gao JM, Wang TB, Zhou Y, Liu Y, Yang QW, Duan XR. Bayesian tomography and integrated data analysis in fusion diagnostics. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2016; 87:11E319. [PMID: 27910627 DOI: 10.1063/1.4960542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this article, a Bayesian tomography method using non-stationary Gaussian process for a prior has been introduced. The Bayesian formalism allows quantities which bear uncertainty to be expressed in the probabilistic form so that the uncertainty of a final solution can be fully resolved from the confidence interval of a posterior probability. Moreover, a consistency check of that solution can be performed by checking whether the misfits between predicted and measured data are reasonably within an assumed data error. In particular, the accuracy of reconstructions is significantly improved by using the non-stationary Gaussian process that can adapt to the varying smoothness of emission distribution. The implementation of this method to a soft X-ray diagnostics on HL-2A has been used to explore relevant physics in equilibrium and MHD instability modes. This project is carried out within a large size inference framework, aiming at an integrated analysis of heterogeneous diagnostics.
Collapse
Affiliation(s)
- Dong Li
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Y B Dong
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Wei Deng
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Z B Shi
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - B Z Fu
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - J M Gao
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - T B Wang
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Yan Zhou
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Yi Liu
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - Q W Yang
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| | - X R Duan
- Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China
| |
Collapse
|
13
|
Kwak S, Svensson J, Brix M, Ghim YC. Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2016; 87:023501. [PMID: 26931843 DOI: 10.1063/1.4940925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
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.
Collapse
Affiliation(s)
- Sehyun Kwak
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| | - J Svensson
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - M Brix
- Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - Y-C Ghim
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, South Korea
| |
Collapse
|