Profile reconstruction techniques for the JET

neutron and gamma-ray cameras

Teddy Craciunescu, Ion Tiseanu, Vasile-Liviu Zoita, Sorin Soare(Euratom-MEdC)

Georges Bonheure(“Euratom-Belgian state”)

Vasily Kiptily(Euratom-UKAEA)

Andrea Murari(Euratom-ENEA)

5th EURATOM-MEdC Association Days Meeting, Bucharest, 26-27 November, 2009

e-mail: teddy@infim.ro

Limited Data Set Tomography

Aim

Reconstruction methods customisation/development for the JET neutron and gamma profile monitor

Fast enough to allow inter-shot analysis

Reconstruction of time-resolved energy spectrum ofshort-pulsed neutron sources

I. Tiseanu, T. Craciunescu, “The reconstruction of time dependent energy spectrum of short neutron pulses“, Nuclear Science and Engineering, Vol. 122, p. 384-394, 1996

T. Craciunescu, C. Niculae, Gh. Mateescu, C. Turcanu, “A comparison of four tomographic methods for nuclear fuel pins analysis”, J. Nucl. Mater. Vol. 224, p.199-206, 1995

Fission products distribution in the cross-section of the irradiated nuclear fuel rods

Premises

A set of reconstruction methods

proved to provide good results in the tomographic reconstruction from limited data sets in a number of physical problems:

JET-KN3 tomography

pN

iiikk fwp

1

fi

pk

19 equations

35 X 20 unknown

(90 mm pixel size)

- scarcity of the data -

non-uniformity of the domain coverage by the lines of sight

persists even after taking into account the beam width

Reconstruction domain coverage by the lines of sight (weight matrix)

- highly ill posed problem -

Projection resampling (x4) - cubic interpolation

projection resampling == virtual lines of sight

Improved coverage of the recontruction domain

Smoothing

median filtering using a circulating window along the magnetic contour lines

med

kmed

med

wj

Lwwj

jjii hmf

Takes into account the magnetic information in order to supply the lack of information

Main

Aditional

The emission is assumed to be a Poisson process, and Pkm is a sample from a Poisson distribution whose expected value is:

Then, the probability of obtaining the measurement p if the image is f is the so-called likelihood function:

Maximum likelihood

i

iik fw

k iiik

p

iiik

k

fwfwp

FPLk

exp!

1/

The ML method solves the problem of evaluating f, if p is known, by selecting the particular f that maximizes L(P|F).

Shepp-Vardi and Lange-Carson iterative solution

kik

k

l

iterjjl

kik

iterij

iteri w

fw

pw

ff

)(

)()1(

enables the manipulation of the reconstructed image at each iteration, for inserting a priori knowledge

MAXSf 212,

Maximum entropy method

A supplementary criterion:

maximization of the informational entropy of the system of N x N pixels, taking into account the experimental data via Lagrange multipliers (Eq. 1).

Tikhonov regularization

Seeking for a solution defined as the minimizer of the weighted combination of:

- residual norm - a discrete approximation of the derivative operator

MINffLpfWfi

2

2

02

2

Monte Carlo backprojection algorithm

0if

This algorithm starts from an empty image

Then, mathematically "grains" of fixed intensities do are randomly allocated. The grain is accepted in a pixel if it lead o an image compatible with all existing projection:

0 ikik wdofp

The restored object is built up by such successive successful allocations.

Testing the method - phantoms

Phantom Reconstruction method

ML ME TR MCBP

peak 0.993 0.990 0.989 0.996

hollow 0.961 0.949 0.951 0.870

“banana” 0.935 0.931 0.908 0.857

symmetrically reversed

“banana”

0.875 0.861 0.836 0.832

peak plus “banana” 0.874 0.667 0.837 0.844

numerically simulated emissive distributions characteristic for JET neutron and gamma tomography

cover most of the range of possible distributions for this kind of tomography

simple but frequent shapes are considered together with the retrieval of sophisticated structure in the emissive distribution

The correlation coefficient

Horizontal and vertical line profiles

profiles along magnetic contour lines

Projections calculated using the phantom and the reconstruction, respectively

ML method is the only one able to encompass the reconstruction, with a good quality, of all structures of the emissive distribution.

ML provides the finest results in terms of shapes reconstruction and resolution and produces artefact free images.

T. Craciunescu, G. Bonheure, V. Kiptily, A. Murari, S. Soare, I. Tiseanu, V. Zoita. The Maximum Likelihood Reconstruction Method for JET Neutron Tomography. Nuclear Inst. and Methods in Physics Research, A, 595, p. 623–630, 2008.

T. Craciunescu, G. Bonheure, V. Kiptily, A. Murari, I. Tiseanu, V. Zoita. A comparison of four reconstruction methods for JET neutron and gamma tomography . Nuclear Inst. and Methods in Physics Research, A, 605, pp. 373-384, 2009.

peak plus “banana” profile distribution recorded just after the T-puff, when tritons partly penetrated into the plasma core from the periphery – shot 61132 at 62.67 s

Comparison of DT-neutron emissivity profile reconstructions, using TOMO-5*

and ML methods

experiment with T-puff in the deuterium plasma: peak profile distribution, typical for plasma with tritium which has penetrated to the plasma core in full - shot: 61132 at 62.92 s

“banana” profile distribution corresponding to an experiment where the DT-neutron emission was measured in the ohmic deuterium discharge during the off-axis injection of the T neutral beam – shot 61237 at 46.22 – 46.27s

* L.C. Ingesson, B. Alper, H. Chen, A.W. Edwards, G.C. Fehmers, J.C. Fuchs, R. Giannella, R.D. Gill, L. Lauro-Taroni, M. Romanelli, Nucl. Fusion 38 (1998) 1675.

Temporal evolution of the D-T 14 MeV neutron emissivity in a trace tritium experiment showing the relaxation of the high density plasma, which is heated by D neutral beams after the T-puff - shot 61141 (from 60.87 s to 61.32 s).

Information about the temporal evolution of the neutron emissivity

ML reconstruction robust enough to work with low statistic data – good reconstructions for time step ~ 75 ms

Software

User friendly MATLAB implementation. The computation time allows the use of the method for inter-shot analysis

#69432 56.55 s

#79168 53.26 s

#73213 50.50 s

Diagnostics support

provided in JET experimental campaigns for fast ion studies

METHOD RECONSTRUCTION

TIME (min)

ML 2.5

ME 8-12

TR 0.8

MCBP 6

The implementation allow fast reconstruction suitable for inter-shot analysis

V. G. Kiptily, C. P. Perez von Thun, S. D. Pinches, S. E. Sharapov, D. Borba, F. E. Cecil, D. Darrow, V. Goloborod’ko, T. Craciunescu, T. Johnson, F. Nabais, M. Reich, A. Salmi, V. Yavorskij, M. Cecconello, G. Gorini, P. Lomas, A. Murari, V. Parail , S. Popovichev, G. Saibene, R. Sartori, D.B. Syme, M. Tardocchi, P. de Vries, V.L. Zoita. Recent progress in fast ion studies on JET. Nuclear Fusion, 49, p. 065030, 2009.

V.G. Kiptily, G. Gorini, I. Proverbio, M. Tardocchi, I.N. Chugunov, D. Gin, M. Nocente, S.D. Pinches, S.E. Sharapov, A.E. Shevelev, T. Craciunescu, F.E. Cecil, M. Gatu Johnson, V. Goloborod’ko, C. Hellesen, T. Johnson, K. Kneupner, A. Murari, P.G. Sanchez, D.B. Syme, P. de Vries, V. Yavorskij, V.L. Zoita. Doppler Broadening of Gamma Ray Lines and Fast Ion Distribution in JET plasmas, submitted to Nuclear Fusion.

ML reconstruction method provides good reconstructions in terms of shapes and resolution.

The strategy used for smoothing implementation allows fast reconstructions.

Consequently qualifies the method for inter-shot analysis.

Conclusion:

Future work: Implementation of parallel computing techniques to further reduce the computation time

Migration of several numerical techniques to a new application:

image processing of data provided by the JET fast visible camera in order to retrieve the velocity field of moving object inside the plasma – may lead to a diagnostic method providing information for the study of pellet injection and ablation

(first preliminary results already reported in a TF-D seminar).