Transcript Profile reconstruction techniques for the JET neutron and gamma-ray cameras

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)
e-mail: [email protected]
5th EURATOM-MEdC Association Days Meeting, Bucharest, 26-27 November, 2009
Premises
Limited Data Set Tomography
A set of reconstruction methods
proved to provide good results in
the tomographic reconstruction
from limited data sets in a number
of physical problems:
Fission products distribution
in the cross-section of the
irradiated nuclear fuel rods
Reconstruction of time-resolved
energy spectrum of
short-pulsed neutron sources
3.00
2.75
(M
eV 2.50
)En
2.25
100
125
150
175
200
t (ns)
1.00
0.75
/d
Ed 0.50
n
tdY
Aim
0.25
Reconstruction
methods
customisation/development
for the JET neutron and
gamma profile monitor
Fast enough to allow intershot analysis
100
3.00
2.75
t (ns)
150
2.50
2.25
200
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
(MeV)
En
I.
Tiseanu,
T.
Craciunescu,
“The
reconstruction of time dependent energy
spectrum of short neutron pulses“, Nuclear
Science and Engineering, Vol. 122, p. 384394, 1996
JET-KN3 tomography
Np
pk   wik  f i
pk
i 1
- highly ill posed problem 
19 equations

35 X 20
unknown
(90 mm pixel size)
fi
- 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)
Aditional
Smoothing
Main
median filtering using a circulating window
along the magnetic contour lines
fi 
j  wmed
m
j  wmed
wmedLk
ji
hj
Takes into account the magnetic
information in order to supply the lack
of information
Projection resampling (x4) - cubic interpolation
projection resampling == virtual lines of sight
Improved coverage of the recontruction domain
Maximum likelihood
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 socalled likelihood function:
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
solution
and
Lange-Carson
iterative
w
ik
fi
i
pk
 1 



LP / F    
  wik f i   exp    wik f i 
k 

 i

 pk !  i
w
ik
k
f i (iter1)  f ij( iter)
w
w
jl
l
ik
k
enables the manipulation of the
reconstructed image at each iteration, for
inserting a priori knowledge
pk
f j( iter)
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).
This algorithm starts from an empty image
fi  0
  , f     S    MAX
1
2
Monte Carlo backprojection algorithm
2
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:
Tikhonov regularization
Seeking for a solution defined as the minimizer of the
weighted combination of:
- residual norm
- a discrete approximation of the derivative operator

  f   W  f  p 2     L f  f 0 
2
i

2
2
 MIN
pk   f i  do wik  0
The restored object is built up by such
successive successful allocations.
Testing the method - phantoms
 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
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
 ML method is the only one able to
encompass the reconstruction, with a
good quality, of all structures of the
emissive distribution.
Projections
calculated using
the phantom and
the
reconstruction,
respectively
Horizontal and
vertical line
profiles
profiles along
magnetic
contour lines
 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.
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 DTneutron 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
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
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.
Information about the temporal evolution of the neutron emissivity
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).
ML reconstruction robust enough to work with low statistic data – good reconstructions
for time step ~ 75 ms
Diagnostics support
Software
User friendly MATLAB implementation. The
computation time allows the use of the
method for inter-shot analysis
provided in JET experimental campaigns for
fast ion studies
#69432
56.55 s
The implementation allow fast reconstruction
suitable for inter-shot analysis
METHOD
RECONSTRUCTION
TIME (min)
ML
2.5
ME
8-12
TR
0.8
MCBP
6
#73213
50.50 s
#79168
53.26 s
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.
Conclusion:

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.
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).