New developments in JET gamma emission tomography
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1 New developments in JET gamma emission tomography T. CRACIUNESCU, A. MURARI, V. KIPTILY, I. LUPELLI, A. FERNANDES, S. SHARAPOV, I. TISEANU, V. ZOITA and JET Contributors
2 Acknowledgements T. Craciunescu 1, A. Murari 2, V. Kiptily 3, I. Lupelli 3,4, A. Fernandes 5, S. Sharapov 6, I. Tiseanu 1, V. Zoita 1 and JET Contributors* EUROfusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, UK 1 IAP, National Institute for Laser, Plasma and Radiation Physics, Bucharest, Romania 2 Consorzio RFX, Padova, Italy 3 CCFE, Culham Science Centre, Abingdon, Oxon, UK 4 University of Rome Tor Vergata, Roma, Italy 5 Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Portugal * See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia Logos of Labs
3 Geometry of JET g-ray and neutron tomography JET profile monitor, composed by 3 different detectors in each LOS, includes the following diagnostics: - NE213 liquid organic scintillator for simultaneous measurements of the 2.5MeV D-D neutrons, 14MeV D-T neutrons and g-rays [E > 1.8 MeV] - CsI detectors for measuring the hard X-rays and g-ray emission [E= MeV] - connected to digital DAQ (KH6 system) - BC418 plastic scintillator, insensitive to g-rays with Ego10MeV for the measurements of 14MeV D-T neutrons 2-D slice located in the plane defined by the major torus radius (R) and the major torus axis (Z). Thickness of the plasma slice along the toroidal direction ~ 75mm (determined by the collimation system). g m = g = N p H mnf n, m = 1,, N d n=1 g + n g f = f + n f T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 3
4 JET reconstruction methods 20 x 35 reconstruction grid (90 x 90 mm 2 pixel size) 700 pixel values to be retrieved from 19 experimental data JET g and neutron JET SXR JET bolometer L.C. Ingesson, et al., Nucl. Fusion 38 (1998) Search for the emissivity distribution by using a priori physical information about the expected emission profile. Methods based on different objective functions including: smoothness on magnetic flux surfaces measurements as constraints principles but with Constrained optimization: reconstruction constant on flux surfaces and gently varying in the radial direction. Grid of pyramid local basis functions for the discretization of the tomographic instead of traditional square pixels Recent approach for neutron tomography: minimization of the RMS between normalized electron and neutron density profiles (J. Bielecki & L. Giacomelli) Used for g-ray and neutron tomographic emissivity reconstruction: V.G. Kiptily, et al., Nucl. Fusion 42 (2002) 999. V.G. Kiptily,, Nucl. Fusion 45 (2005) L21. T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 4
5 JET reconstruction methods J. Mlynar, et al., Plasma Phys. Controlled Fusion 45 (2003) 169. Minimum Fisher regularization T. Craciunescu, et al., NIMA 605 (2009) 373. Maximum likelihood principle Smoothing operator, defined as median/averaging filtering along the magnetic contour lines. Regularization matrix enforcing preferential emissivity smoothness along magnetic flux surfaces M. Odstrcil, et al., NIMA 686 (2012) 156. Used for neutron emissivity reconstruction and 2-D spatial distributions of D-D and D-T neutron emission in JET ELMy H-mode plasmas with Tritium puff. G. Bonheure, et al., Nucl. Fusion 46 (2006) 725. Used for both neutron tomography but mainly for the reconstruction of g-ray emissive profiles related during fast ion physics experiments V. Kiptily, et al., Nuclear Fusion 49-6 (2009) Recently applied to HXR emissivity reconstruction in runaway generation studies C33-34 campaigns E. Ronchi, et al., NIMA 613 (2010) 295. Based on a neutron emissivity parametric model A feed-forward neural network T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 5
6 Evaluation of Reconstruction Errors and Artifacts Estimating the errors associated with the reconstructed emissivity profile still an opened problem qualitative interpretation quantitative analysis Accurate modelling of projection noise propagation Monte Carlo solutions (using a large number of noise realizations) impractical: - High computational burden - Multiple noise realizations are generally unavailable for JET gamma and neutron tomography Analytic solutions, applicable on a routine basis, would be very advantageous - A few number of approaches, for limited data tomography developed Image quality - depends also on: - the constraints imposed by the restrictive measuring geometry (which leads to highly limited data sets) - specific experimental conditions Main sources of artefacts: - use of magnetic equilibrium profiles for compensating the lack of experimental data. - neutron induced gamma-ray background - medical field (PET, SPECT, theranostics) - expectationmaximization class of methods - dedicated to specific algorithms except statistical bootstrapping based methods T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 6
7 Maximum Likelihood method (ML) Assumption: Emission - a Poisson process g = Hf + n g g m - sample from a Poisson distribution g - expected value The probability of obtaining the measurement g = g m m = 1,, N d if the image is f = f n n = 1,, N p is given by the likelihood function: L g f = m 1 g k! g g k exp g f ML = argmax f L g f f n k+1 = f k n g s m n m j H mj f j k H mn Enables the manipulation of the reconstructed image at each iteration, for inserting a priori knowledge T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 7
8 Maximum Likelihood method (ML) Smoothness on magnetic surfaces (given by plasma equilibrium) Implemented as an 1-D average filtering, using a sliding window which moves along the magnetic contour lines Computing time (MATLAB): ~ 1s/iteration when running on JET computers Typically: iterations Better coverage of the reconstruction domain obtained by introducing additional virtual lines of sight Suitable for inter-shot analysis Most time consuming step: smoothing along contour lines Magnetic contour lines are unfolded to straight lines in order to allow averaging using a sliding window Implies projection interpolation T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 8
9 Examples of ML reconstructions ML proved to be able to retrieve the most sophisticated emissive distribution structures T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 9
10 Modelling the projection noise propagation Projection resampling by interpolation - Complex algebra because of the need to keep calculating correlation terms, even when all of the uncertainties in the measured variables are uncorrelated - Optimal choice - Lagrange interpolation: 2 u g x = N d i=1 L 2 i x u 2 gi, where: L m x = N d n=1,n m x x n x m x n Iterative update of the ML reconstructed image - Reformulation of the ML iterative formula: y k = ln f k y k+1 = y k + ln 1 s i j=1 N d H T ij g j H f k j An expectation value of y (k) can be defined: E y (k) f = ln a (k) ε (k) - the deviation of y (k) from the expectation value y (k) = ln a (k) + ε (k) T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 10
11 Modelling the projection noise propagation Approx. #1 Noise in the reconstruction is small compared to the mean reconstruction Approx. #2 The projection of the current estimate is close to the noise-free projection f k = a k exp ε k a k 1 + ε k Separating the noise from the signal: Ha k Hf Works well for well conditioned objective function, with fast convergence f (k+1) = f k diag f k diag s 1 H T diag H f k 1 g H T I f k can be retrieved by running the ML algorithm with noisefree data ε k+1 = B k n + I A k ε k rule for finding the random noise in the current estimate. A k = diag f k diag s 1 H T diag H f k 1 H B k = diag f k diag s 1 H T diag H f k 1 A k = diag f k diag s 1 H T diag H f k 2 diag g H For preconditioners that are explicitly dependent on projection data T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 11
12 Modelling the projection noise propagation Covariance matrix Noise free initial estimate: ε (0) = 0 ε (k) = U (k) n, where: U (k+1) = B (k) + I A (k) U (k) Projection elements g Samples from a Poisson distribution. K ε (k) - covariance matrix for ε (k) : For a reasonable large number of photons/neutrons: their distribution is approximated by a normal law ε (k) will follow also a normal distribution: (k) K ε = U (k) (k) T K U K - covariance matrix for the data: K = diag g p(ε k f = 2πN K ε k exp 2 ε k T k K ε 1 ε k T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 12
13 Monte Carlo validation of the analytical procedure Simulated distributions with shapes characteristic of the JET neutron and gamma tomography Generation of a large number N s of projection samples with different noise realizations Noise properties of reconstructed images - analyzed in terms of the covariance matrix: pixel value K exp i, j = 1 N s f n N s 1 i f i f n j f j n=1 mean pixels value calculated for the whole set of images Simulated superimposed noise has been calculated using the relation: Phantom Monte Carlo variance image σ m = g m 2 + ε m g m uncertainty on the number of raw counts calibration error of the individual detectors (max. 10%) Reconstruction Analytical variance image T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 13
14 HXR emissivity reconstruction HXR emissivity reconstruction for runaway electrons (RE) studies Time, spatial and energy resolved measurements of bremsstrahlung originated in interaction of fast electrons with plasma spceies, gas puff or injected pellet. Allows the observation of RE in flight before their interaction with the plasma facing components Detailed data on temporal evolution and spatial structure of RE beams during disruptions. A. Shevelev, et al., AIP Conf. Proc. 1612, 125 (2014) Monitoring of runaway electrons (RE) is one of the most important issues for the safe tokamak operation. T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 14
15 HXR emissivity reconstruction and statistical errors T = s T = s T = s T = s T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 15
16 HXR emissivity reconstruction and statistical errors T = s T = s T = s T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 16
17 Standard EFIT data (SURF/FLUSH 50 ms) High time resolved EFIT++ data (10 ms) Artefacts influence of the magnetic equilibrium profiles # T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 17
18 Artefacts Influence of the neutron induced g-ray background Experiment: Reconstruction of the gamma-ray image of D-beam ions accelerated with ion cyclotron resonance heating (ICRH) JET pulse #86456 Significantly altered by the neutron induced gamma-ray background Background removal: g-ray measurements for the NBI-only discharge #86372 Measurements: Averaged for the significant part of the discharge (55-59 s) Normalized using: Neutron production ratio between #86456 and #86372 The tomographic projections after background removal differ significantly from the raw data. T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 18
19 Artefacts Influence of the neutron induced g-ray background JET pulse #86456 Before background extraction After background extraction Variance image Significantly different tomographic reconstructions T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 19
20 Conclusions ML reconstruction - suitable for numerical evaluation of the statistical properties of the uncertainties in gamma and neutron emissivity reconstructions. The methodology takes into account the additional techniques introduced in the reconstruction process for tackling with the limited data set: projection resampling smoothness regularization depending on the magnetic field profiles. Analytical uncertainty evaluation can be applied on a routine basis. Computation time - compatible with inter-shot analysis Artefacts related to the experimental conditions for recording the projection data and to the restrictive measuring geometry should be identified and quantified for accurate tomography. T. Craciunescu et al. TM IAEA FDPVA 2015 Nice, France 1-3 June 2015 Page 20
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