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Bayesian soft X-ray tomography using non-stationary Gaussian Processes
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10.1063/1.4817591
/content/aip/journal/rsi/84/8/10.1063/1.4817591
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/8/10.1063/1.4817591

Figures

Image of FIG. 1.
FIG. 1.

A schematic view of the miniature soft X-ray system (MiniSoX diagnostic system) in Wendelstein 7-AS shows the eight compact detector arrays with a total of 256 sight lines in one poloidal cross-section, achieving a substantial coverage. The dashed black lines indicate the magnetic flux surfaces of a typical plasma in Wendelstein 7-AS.

Image of FIG. 2.
FIG. 2.

Experimental data from W7-AS: time trace of signals from two different detectors during discharge #56316 shows the variance of data increase abruptly once the discharge starts.

Image of FIG. 3.
FIG. 3.

Scatter plot showing the linear relation between the most likely standard deviation of one data set and the average of this data set. The possible values of the standard deviation are chosen to be within a certain maximum percentage level (from 2.5% to 25%) of the average of one data set. The most likely standard deviations of many data sets appear around the 12.5% of the average of data.

Image of FIG. 4.
FIG. 4.

A 2D emissivity distribution in the poloidal plane, where the MiniSoX-Tomography system was located, was simulated based on a typical magnetic configuration in W7-AS.

Image of FIG. 5.
FIG. 5.

To compare the different inversion methods, the artificial line integral data calculated from a simulated emissivity distribution is taken as input data of the different methods. Red dots: Artificial data without errors; green diamonds: artificial data with independently normally distributed random noise, used as input data.

Image of FIG. 6.
FIG. 6.

Distribution of the reciprocal of local length scales inferred by a stationary Gaussian Process regression. The black line indicates the boundary of the vacuum vessel.

Image of FIG. 7.
FIG. 7.

Reconstructions by (a) non-stationary GP and (b) MaxEnt methods using the artificially noisy data, and the errors in both methods are exactly described as how they are added. The black contours show the simulated emissivity distribution for a clear comparison.

Image of FIG. 8.
FIG. 8.

The 1D plots about the profiles intercepted at (a) = 2.0 and (b) = 1.9 from the reconstructions by two methods. Red asterisks: simulated emissivity profiles; green dots: the non-stationary GP reconstruction with 95% confidence intervals; blue circles: the MaxEnt reconstruction.

Image of FIG. 9.
FIG. 9.

Fit between the data predicted from reconstruction by non-stationary GP and the artificially noisy data. Green diamonds: artificially noisy data used for the inversion of reconstruction; red dots: predicted data with their 95% confidence intervals.

Image of FIG. 10.
FIG. 10.

Comparison of the reconstructions from shot number 56316 by (a) non-stationary GP and (b) MaxEnt using the experimental data from W7-AS. The black contours show the flux surface derived from the equilibrium calculation of the vacuum configuration.

Image of FIG. 11.
FIG. 11.

The 1D plots about profiles intercepted at (a) = 2.0 and (b) = 1.9 from the reconstructions by two methods using the experimental data. The green dots show the reconstructed profile with 95% confidence intervals given.

Image of FIG. 12.
FIG. 12.

Hundred samples of possible reconstructions, drawn from the multivariate normal posterior distribution to visualize the uncertainties of reconstruction.

Image of FIG. 13.
FIG. 13.

Fit between the predicted data from the reconstruction by non-stationary GP and the used experimental data. Red dots show the predicted data with error bars

Image of FIG. 14.
FIG. 14.

Comparison of the reconstructions by two methods using the experimental data from shot number 53962 at time point 0.3741 s. For comparison, black contours show the flux surface derived from the equilibrium calculation of the vacuum configuration.

Image of FIG. 15.
FIG. 15.

Reconstructions at two different time points with high β in center from shot number 51755 in W7-AS, calculated by the non-stationary GP, shows a large horizontal shift, which also coincide with the equilibrium flux surfaces (black contours) calculated by free boundary VMEC calculations and also a large indentation frequently occurring in the inboard side. The green and red lines indicate the locations of the magnetic axis of the vacuum and finite β configurations, respectively. Specifically, a strongly inward axis of vacuum configuration is achieved by low magnetic fields and comparably higher vertical fields for high β experiments.

Image of FIG. 16.
FIG. 16.

(a) Schematic diagram of the setup of a soft X-ray diagnostic system in TJII, which consists of five detector arrays with each array having 16 detectors. (b) Experimental data from a typical discharge.

Image of FIG. 17.
FIG. 17.

Comparison of the reconstructions by the non-stationary GP and EBITA methods using the experimental data from shot number 18272 in TJ-II. They both have similar shape and location. Black contours show the flux surface derived from the equilibrium calculation of the vacuum configuration.

Tables

Generic image for table
Table I.

Notations used in overall processes about the model assumption.

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/content/aip/journal/rsi/84/8/10.1063/1.4817591
2013-08-13
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Bayesian soft X-ray tomography using non-stationary Gaussian Processes
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/8/10.1063/1.4817591
10.1063/1.4817591
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