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International Conference on Nuclear Data for Science and Technology 2010
2.3 Evaluation Sensitivity Coefficients for Integral
Experiments
In order to evaluate the sensitivity coefficients of the
nuclear parameters to the integral parameters measured in a
reactor physics experiment, a folding procedure is applied,
where the sensitivity calculated by EMPIRE, are folded
with those calculated by ERANOS (i.e multigroup cross
section sensitivity coefficient to integral parameters).
Following this procedure, the sensitivities of integral
experiments to nuclear parameters pk are defined as:
AR ARI (1)
k k d(j '
where R is an integral reactor physics parameter (e. g. Keff
reaction rates, reactivity coefficient, etc.), and aj a
multigroup cross section (the j index accounts for isotope,
cross section type and energy group).
In general to compute aj one can use a) EMPIRE with
an appropriate set of parameters pk to generate first b) an
ENDF/B file for that specific isotope and successively, c) to
use NJOY, to obtain multi-group cross sections.
As specified in the previous section, one can compute
the variation of the cross sections Asj resulting from a
variation of each parameter pk variation.
Specifically, the procedure would consist in the
generation of the Asj corresponding to fixed, well chosen
variations of each pk taken separately and therefore
generating the Ajpk . Following each EMPIRE
calculation, an ENDF/B file for the isotope under
consideration is generated and a subsequent run of NJOY on
this file generates multigroup cross sections in the same
energy structure used for the computation of the reactor
physics integral parameters. The multigroup cross section
variations associated to the individual fundamental
parameter that has been varied in the corresponding
EMPIRE calculation are readily computed by difference
with the reference NJOY calculation for the isotope under
consideration.
In parallel, the cross section sensitivity coefficients to
integral parameter R:
are provided, using the standard Generalized Perturbation
Theory in the ERANOS code system.
Folding the two contributions (from EMPIRE and
ERANOS) one obtains the sensitivity coefficients of the
nuclear physics parameters to the integral measured
parameters, see Eq. (1).
2.4 Data Assimilation
Finally as far as data adjustment (or data
"assimilation") the methodology makes use of:
- quantified uncertainties and associated
variance-covariance data;
- well documented, high accuracy and "representative"
integral experiments;
- sensitivity coefficients for a variety of integral
parameters.
A statistical adjustment is performed using these quantities.
Formulation is given in reference [1].
3. INTEGRAL EXPERIMENT ANALYSIS
As a practical example we have considered the case of
the 23Na isotope. For this case we have used propagation
experiments of neutrons in a medium dominated by this
specific isotope. These kinds of experiments were
specifically intended for improving the data used in the
shielding design of fast reactors. Two experimental
campaigns taken from the SINBAD database [10] have
been used in this practical application: the EURACOS
campaign, and the JANUS-8 campaign.
3.1 EURACOS Sodium Neutron Propagation
Experiment
The Ispra sodium benchmark project was performed
under the EURACOS (Enriched URAnium COnverter
Source) irradiation facility. The main purpose of this
experiment was to study the neutron deep penetration in
homogeneous materials found in the construction of
advanced reactors (i.e., Na and Fe). Thus, the analysis of
this experiment can be effectively utilized for the sodium
cross section improvement. The neutron source of this
system is made by the Al-U plate, having 80 cm in diameter
and 1.8 cm in thickness. This source is driven by TRIGA
Mark II reactor located right next to this irradiation facility.
Measurements with activation detectors were carried out at
distances from the source 18.35, 66.4, 125.2, 184.5, 243.2,
302.4, 362.2 cm for 32S(n,p) and '97Au (n,y) in order to
analyze fast and epithermal neutron attenuations.
1 0E+00-
1 0E-01 -
1 0E-02 -
1 0E-03 -
1 0E-04 -
1 OE-E -
1 OE-6 -
1 0E-07 -
1 OE-OS
o so 100 1so 200 250
Distance [cm]
300 350 400
Fig.1. Neutron attenuation of EURACOS sodium experiment for
32S and [ Au detectors. (Error bars = lG)
Analysis was performed by the Monte Carlo code
'' - - s
- - - - - - - - - - - - -"- - - - - - - - - - - - t - -
- - - - - - - - - - - - - - - - - - - - - - -
_ - n p97n,gamma)Au198
a
0
0
