implementation of an analytical model accounting for sample inhomogeneities in refit k. kauwenberghs...
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Implementation of an analytical model accounting for sample
inhomogeneities in REFIT
K. Kauwenberghs
EC – JRC – IRMM
Standards for Nuclear Safety, Security and Safeguards (SN3S)
Introduction (EC - JRC- IRMM)
Neutron Resonance Transmission and Capture Analysis
Motivation
Initial model validation
Experimental model validation
Summary
Outline
JRC-IRMM major provider in Europe of ND for nuclear energy applications
GELINA
VdG
EC - JRC – IRMMneutron facilities
GELINA Van de Graaff
White neutron source+
Time-of-flight (TOF)
99Tc(n,) cross section
Mono-energetic neutrons(cp,n) reactions
10-2 100 102 104 10610-4
10-2
100
102
104
(n,)
(n,)
/ bar
n
Neutron Energy / eV
99Tc + n
EC - JRC – IRMMneutron facilities
Pulsed white neutron source
(10 meV < En < 20 MeV)
High resolution TOF measurements
Multi-user facility: 10 flight paths
Flight path lengths: 10 m – 400m
Measurement stations with special equipment to perform:
• Total cross section measurements• Partial cross section measurements
FLIGHT PATHS SOUTH
FLIGHT PATHS NORD
ELECTRON LINAC
TARGET HALL
Mondelaers and Schillebeeckx, Notizario 11 (2006) 19
EC - JRC – IRMMGELINA
NEUTRONMODERATOR
ELECTRONBEAMLINE EXIT
NEUTRONTARGET
NEUTRONFLIGHT PATHS
e- accelerated to Ee-,max ≈ 140 MeV
Bremsstrahlung in U-target
(rotating & cooled with liquid Hg)
( , n) , ( , f ) in U-target
Low energy neutrons by moderation
(water moderator in Be-canning)
EC - JRC – IRMMGELINA
Neutron Resonance Transmissionand Capture Analysis
CaptureTransmission
totn
tot
Y (1 e )
totneT
T : transmissionFraction of the neutron beam traversing the sample without any interaction
Y : capture yieldFraction of the neutron beam creating a (n,) reaction in the sample
out
inexp C
CT
,exp
CY
totn
tot
Y (1 e )
totneT
CaptureTransmission
Schillebeeckx et al., Nuclear Data Sheets 113 (2012) 3054 - 3100
Neutron Resonance Transmissionand Capture Analysis
,exp
CY
totn
tot
Y (1 e )
totneT
CaptureTransmission
Schillebeeckx et al., Nuclear Data Sheets 113 (2012) 3054 - 3100
out
inexp C
CT
Neutron Resonance Transmissionand Capture Analysis
104 105 106 10710-2
10-1
100
101
102
103
W
Bi
Co
Ag
C'
out
B'
out
Re
spo
nse
/ (1
/ns)
Time Of Flight / ns
Na
104 105 106 10710-2
10-1
100
101
102
103
WAg
Bi
Co
Na
C'
in
B'
in
Re
spo
nse
/ (1
/ns)
Time Of Flight / ns
104 105 106 1070.0
0.2
0.4
0.6
0.8
1.0
1.2
Tra
nsm
issi
on
Time Of Flight / ns
Sample out Sample in
'out
'out
'in
'in
expBC
BCT
Schillebeeckx et al., Nuclear Data Sheets 113 (2012) 3054 - 3100
Neutron Resonance Transmissionand Capture Analysis
Motivationgood geometry + homogeneous sample
out
inexp C
CT
dEe)E,t(R)t(T )E(nmmM
tot 0.1 1 10
0.2
0.4
0.6
0.8
1.0
Texp
TM
Tra
nsm
issi
on
Neutron energy / eVR(tm,E) response of TOF-spectrometer
REFIT, M. Moxon
241Am
inC
outC
Schillebeeckx et al., Nuclear Data Sheets 113 (2012) 3054 - 3100
2.5 2.6 2.7 2.8
-4-3-2-101234
resi
dual
s
energy [eV]
300 K Pu-242 Simultaneuos Fit
0.5
0.6
0.7
0.8
0.9
1.0
Literature= 25 meV
n= 2.00 meV
FIT = 36.5 meV
n= 1.46 meVT
rans
mis
sion
Ignoring sample inhomogeneities:
• Underestimation of speak
• Overestimation of GG
Motivationheterogeneous sample
Transmission + Capture data
sample properties
resonance parameters
Motivationgood geometry + homogeneous sample
Expected transmission
• Homogeneous sample:
• Heterogeneous sample:
totneT
tottot
tot
)'dn)'n(p'n(n
'n
ee)n(T
'dn)'n(pe'dn)'n(p)'n(TT
p(n') : distribution of areal density1cm
From H. Uetsuka, et al., “Gamma Spectrometry of TMI-2 Debris” (written in Japanese), JAERI-Research 95-084.
Motivationheterogeneous sample
Analytical models to account for inhomogeneities of a powder sample:• Kopecky et al. (ND2007)
• LP Model (Levermore, Pomraning et al., J. Math. Phys. 27, 2526, 1986)
• …
Comparison with transmission spectra produced by stochastic calculations (MC simulations)
LP model performs the best
35th ESARDA 2013Becker et al., "Particle size inhomogeneity effect on NRD"
Initial model validation
35th ESARDA 2013Becker et al., "Particle size inhomogeneity effect on NRD"
Initial model validation
Kopecky et al.:• Macroscopic model to describe the variation of the thickness
Kopecky et al., ND2007 , Nice , pp. 623 – 626; Schillebeeckx et al., NDS 113 (2012) 3054 - 3100
LP Model:• Microscopic model
Levermore, Pomraning et al., J. Math. Phys. 27, 2526, 1986
2
22
2 2
)2/(lnexp
2
1)(
s
sx
sxxp
h
k'k f1
nn
hh
En
ffdxxpeT kktotk
)1()()(,
'
𝑇=¿~Σ=𝑝 𝛽 𝜆𝛼+𝑝𝛼 𝜆𝛽+𝜆𝛼
−1+𝜆𝛽−1
2𝑟±=Σ+~Σ±√ (Σ−~Σ )2+4θ
θ=(Σ𝛼−Σ𝛽 )2𝑝𝛼𝑝𝛽
Experimental validation of the model
= based on capture and transmission measurements at GELINA:
• Cu powder samples with known grain size distribution• W powder samples with known grain size distribution
35th ESARDA 2013Becker et al., "Particle size inhomogeneity effect on NRD"
Experimental model validation
54th INMM 2013Schillebeeckx et al., "Contribution of the JRC to the development of NRD"
1 10 100 100010-5
10-4
10-3
10-2
10-1
Cin
Bin
Cou
nts
/ (1/s
)
TOF / s
natW-metal disc (80 cm diameter, 14 g natW)
natW-powder mixed with natS-powder(80 cm diameter, 14 g natW, 3.5 g natS)
1 10 100 100010-5
10-4
10-3
10-2
10-1
Cin
Bin
Cou
nts
/ (1/
s)
TOF / s
Experimental model validation
0.0
0.4
0.8
Texp
TM (hom.)
Tra
nsm
issi
on
10 20 30 40 50-10
-5
0
5
10
Res
idua
l
Neutron energy / eV
natW-metal disc (80 cm diameter, 14 g natW)
54th INMM 2013Schillebeeckx et al., "Contribution of the JRC to the development of NRD"
Experimental model validation
0.0
0.4
0.8
Texp
TM (hom.)
TM (in-hom.)
Tra
nsm
issi
on
10 20 30 40 50-10
-5
0
5
10
Res
idua
l
Neutron energy / eV
natW-powder mixed with natS-powder(80 cm diameter, 14 g natW, 3.5 g natS)
54th INMM 2013Schillebeeckx et al., "Contribution of the JRC to the development of NRD"
0.0
0.4
0.8
Texp
TM (hom.)
Tra
nsm
issi
on
10 20 30 40 50-10
-5
0
5
10
Res
idua
l
Neutron energy / eV
Experimental model validation
Model accounting for inhomogeneities of a powder sample is implemented in REFIT
Initial validation of possible models with MC simulations
LP Model performs the best
Experimental validation of the model with capture and transmission measurements at GELINA
W powder samples with known grain size distribution
Summary
Contributors:
B. Becker, F. Emiliani, S. Kopecky, P. SchillebeeckxEC – JRC – IRMM, Geel (B)
H. Harada F. Kitatani, M. Koizumi, H. TsuchiyaJAEA, Tokai-mura (Japan)
Acknowledgement:
This work was supported by the European Commission within the Seventh Framework Programme through ERINDA (FP7 – 269499).