# Use of Nuclear Data Sensitivity and Uncertainty Analysis for the Design Preparation of the HCLL Breeder Blanket Mockup Experiment for ITER

Authors: I. Kodeli
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

An experiment on a mockup of the test blanket module based on helium-cooled lithium lead (HCLL) concept will be performed in 2008 in the Frascati Neutron Generator (FNG) in order to study neutronics characteristics of the module and the accuracy of the computational tools. With the objective to prepare and optimise the design of the mockup in the sense to provide maximum information on the state-of-the-art of the cross-section data the mockup was pre-analysed using the deterministic codes for the sensitivity/uncertainty analysis. The neutron fluxes and tritium production rate (TPR), their sensitivity to the underlying basic cross-sections, as well as the corresponding uncertainties were calculated using the deterministic transport codes (DOORS package), the sensitivity/uncertainty code package SUSD3D, and the VITAMINJ/ COVA covariance matrix libraries. The cross-section reactions with largest contribution to the uncertainty of the calculated TPR were identified to be (n,2n) and (n,3n) reactions on plumb. The conclusions of this work support the main benchmark design and suggest some modifications and improvements. In particular this study recommends the use, as far as possible, of both natural and enriched lithium pellets for the TRP measurements. The combined use is expected to provide additional and complementary information on the sensitive cross-sections.


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## Body

## 1. Introduction

The
future fusion experimental reactor ITER will be based on the fusion reaction of
deuterium and tritium (D-T reaction). Unlike deuterium which is stable and
readily available in nature (oceans), tritium is a radioactive isotope with a
relatively short half life of about 12.3 years and it will have to be produced
in the fusion reactor plant locally. The tokamak will be therefore surrounded
by lithium blanket and tritium will be produced by bombardment of lithium atoms
with neutrons escaped from the D-T reaction in plasma. For tritium production (breeding),
two blanket concepts are considered within the EU fusion technology programme, the helium-cooled
pebble bed (HCPB) blanket with lithium ceramics pebbles (Li4SiO4 or Li2TiO3) as breeder material and beryllium pebbles as
neutron multiplier, and the helium-cooled lithium-lead (HCLL) blanket with the
Pb-Li eutectic alloy plays the role of breeder and neutron multiplier. Both
blanket designs will use helium as coolant.The
two breeding-blanket modules are candidates for the blanket
module design for a fusion power demonstration reactor (DEMO) to be constructed after ITER. To validate the engineering
designs and the viability of the fusion plant, the
test blanket modules (TBM) of both designs will be installed in ITER.Tritium
self-sufficiency which will be needed for DEMO reactor is still to be
demonstrated, taking into account both the losses of the tritium inventory as
well as the uncertainties in the tritium production. Experimental studies involving irradiation of the two proposed
blanket designs were therefore undertaken at the
Frascati Neutron Generator (FNG) 14 MeV facility [1–3] in cooperation
between the Ente per le Nuove tecnologie, l’Energia e l’Ambiente (ENEA), Frascati;
Forschungszentrum Karlsruhe (FzK); Technische Universität Dresden (TUD); and Institut
Jožef Stefan,
Ljubljana (IJS).  NEA Data Bank also participates in this
study to perform transport and sensitivity studies as well as to
assure the final integration of the experimental results and their
evaluation into the shielding benchmark experiments database
(SINBAD) in order to make these data easily available to the
international community. The objective of
these experiments is to assess the uncertainty on tritium production rate (TPR)
due to the uncertainty in the relevant nuclear data. The
FNG experiments in particular contribute to the validation of the computational
tools and nuclear data needed for the neutronics analysis. The helium-cooled
pebble bed (HCPB) breeder blanket mockup benchmark experiment was performed in 2005 and consists of a metallic
beryllium setup with two double layers of breeder material (Li2CO3 powder). The reaction rate measurements include the Li2CO3 pellets for the tritium breeding monitoring and activation foils, inserted at
several axial and lateral locations in the block. The experiment and the results
of the analysis using the Monte Carlo and deterministic transport,
sensitivity, and uncertainty code system were presented in [4, 5].The
tritium breeding-module helium-cooled lithium-lead benchmark experiment (TBM
HCLL) is under preparation and will
be performed in 2008. The aim of the present work is the preanalysis and the
optimisation of the benchmark experiments design using the deterministic
transport, sensitivity, and uncertainty code system. The analysis includes the
calculation of the tritium production rate (TPR) in LiPb layers and the neutron
reaction rates, which will be measured in the benchmark, their
sensitivity to the underlying cross-sections, as well as the corresponding
uncertainty estimations. The SUSD3D cross-section
sensitivity and uncertainty code package together with the two- and  three-dimensional (2D/3D) deterministic transport codes DORT/TORT are used for the analysis of
the experiment. Based on the sensitivity analyses, the most important nuclear
reactions and energy ranges in the particular reaction rate measurements can be
identified. This information will be used to anticipate the
benefits obtained from the experiment and thus guide and optimise its design and
to assess the nuclear data needs.


## 2. TBM-HCLL Experimental Mockup

The experimental geometry which will be irradiated in the FNG facility
consists of a block of45cm×47.4cm side view and 34.6 cm long, placed 5.3 cm in front of the 14 MeV FNG neutron source (Figure 1). The block is composed of 12 stainless steel layers, 0.65 cm thick each, and 3.6 cm high layers (11 in
total) composed of LiPb bricks, between them. Seven detector positions are
planned between 3.7 cm and 27.7 cm in the block to measure the tritium production
rate (TPR) using Li2CO3 pellets.Figure 1
Schematic diagram of the TBM-HCLL mockup showing steel (dark red) and LiPb (orange) layers. The detectors are placed on the central axis.The modelling of the TBM HCLL mockup geometry requires full 3D
description; a 2D approximate model often used in the previous studies is not
applicable. Like in the previous HCPB tritium breeder module mockup benchmark
experiment, the 3D calculational procedure was used based on the following
codes:(i)
TORT [6] discrete ordinates transport code for 3D geometries,(ii)
GRTUNCL-3D [7] code to prepare uncollided and 1st collision neutron source for TORT,(iii)
SUSD3D [8] code for the cross-section sensitivity and uncertainty analysis.SUSD3D
code performs the sensitivity/uncertainty analysis and assessment of uncertainties
in calculations using discrete ordinate approach based on the first-order
perturbation theory where sensitivity coefficients are derived from the direct
and adjoint flux moments calculated by the discrete ordinates codes.On the other hand, the 3D calculations are much more time consuming than the 2D analyses which
were used in the past,  for simpler benchmarks, such as the FNG-ITER Blanket
Bulk Shield, Neutron Streaming, SiC and W benchmarks
modelled in 2-dimensional geometry using the codes
DORT and TWODANT. TORT calculations required
several days of CPU on a Linux computer, comparing to a few minutes for 2D DORT analysis. For testing and studies of different
effects and computational approximations, a simpler and approximate
2-dimensional model was therefore prepared. In the case of the HCPB tritium
breeder module mockup benchmark [5] the comparison of the results obtained
using the 3D code system with the results of the standard well-established 2D
system based on GRTUNCL/DORT/DUSD3D codes already revealed few problems and
inconsistencies in the TORT/GRTUNCL-3D code system requiring some modifications
in our SUSD3D sensitivity code. Consistent use of both methods contributes in
this way to better confidence in the results.The preparation of cross-section for deterministic codes is case
dependent, in particular due to the self-shielding phenomena, which are of
course different than those in the previous
experiments and require explicit treatment. Among the available multigroup
cross-section libraries for deterministic codes, the FENDL-2 and -2.1 libraries
[9] are dedicated to the fusion applications and were found the most suitable.
The latest version, FENDL-2.1, was used in these analyses.The response functions from IRDF-90 to the recent
IRDF-2002 [10] data were processed.The covariance matrices of
lead were needed for the uncertainty analyses in addition to those already
processed for the previous experiments. The most recent data were found to be
available in the ENDF/B-VI.8 evaluation and were processed using the NJOY-99
code [11].


## 3. Results of Transport Calculation

The 3D transport calculations
using the TORT code required up to several days of CPU. Both direct and adjoint
calculations were performed, adjoint ones being even more time consuming (~2 days runs). The calculated TPR from theLi6(n,t) and Li7(n,nt) reactions at the 7 planned detector positions are shown in Table 1 and Figure 2. The results are consistent with
those reported in [1], obtained using the MCNP Monte Carlo code. Likewise the
recommendation given in [1] to use enriched Li instead of the natural one is
confirmed, leading to smaller gradients between the front and back detector
positions and in this way assuring that the TPR is above the detector limit for
the deep detector positions.Table 1
Calculated Tritium production rates. (TORT/FENDL-2.1: S-16,P-5)
Li6+7(n,t) reaction rateY (cm)Natural Li90% enriched3.7 (P1)6.70⋅10−61.61⋅10−57.7 (P2)3.46⋅10−61.36⋅10−511.7 (P3)1.81⋅10−61.06⋅10−515.7 (P4)1.08⋅10−68.06⋅10−619.7 (P5)7.70⋅10−76.43⋅10−623.7 (P6)4.93⋅10−74.54⋅10−627.7 (P7)3.43⋅10−73.30⋅10−6Ratio (P7/P1)19.54.9Figure 2
Tritium production rate for the natural and enriched Li pellets.Table2 shows, furthermore,
the fraction of the TPR produced by the direct source neutrons (uncollided
flux). It is shown that the uncollided flux contribution to the TPR is
important in the first detector positions in case of using natural Li. This is
due to the TPR from the high energy Li7(n,nt)
reaction, as demonstrated in Table 3 presenting the ratio between the TPR from
the reactions on Li6 and Li7. In the case of enriched Li most of tritium is as expected produced
by the Li6(n,t) reactions sensitive to
thermal neutrons.Table 2
Contribution of the uncollided flux. (TORT/FENDL-2.1: S-16,P5)
Uncollided and 1st collision contributionY (cm)Li6+7(n,t)-naturalLi6+7(n,t)-90%3.756%6%7.737%2%11.721%0.8%15.712%0.4%19.78%0.2%23.75%0.1%27.74%0.1%Table 3
Contribution ofLi6(n,t) and Li7(n,nt).
Li6(n,t)/Li6+7(n,t)Y (cm)Natural90% enriched3.719%96%7.732%98%11.748%99%15.762%99%19.769%100%23.777%100%27.780%100%


## 4. Results of Cross-Section Sensitivity/Uncertainty Analysis

The cross-section sensitivity
and uncertainty calculations were performed using the SUSD3D code, which
requires as input quantities the direct and adjoint angular moment fluxes
calculated by the discrete ordinates codes (DORT or TORT), as well as the
transport cross-sections, and
covariance matrices for the relevant materials and reactions. Both 3D and 2D sensitivity and
uncertainty analyses were performed, using,
respectively, fluxes calculated by the TORT code and from DORT simplified geometry calculations. Good consistency between the 2D and 3D
calculations can be observed, demonstrating again that the sensitivity analyses do not require
extremely precise models, which can be explained by the fact that the
sensitivities are derivatives and as such relative quantities.The sensitivities and uncertainties in the calculated TPR for two
detector positions are presented in Tables4 and 5, calculated, respectively,
using 2D and 3D computational model. The sensitivities at the D2 position correspond
to the use of natural and 90% enriched Li, and those at the D7 position are
relevant both for case of natural or enriched Li.Table 4
Sensitivity of the TPR to cross-sections for the detector position D7 (SUSD3D results based on the TORT 3D neutron fluxes).
Li6(n,t) D7(∼27cm)Sensitivity (%/%)ReactionPb206Pb207Pb208Li6Li7Total0.270.250.420.960.07Elastic0.160.160.370.0040.06Inelastic0.080.060.002−5⋅10−4(n,2n)0.030.020.06(n,3n)7⋅10−54⋅10−56⋅10−4(n,t)0.960.01(n,γ)−0.004−0.003−0.001Uncertainty2.1%2.0%6.4%0.2%0.1%Table 5
Sensitivity of the TPR to cross-sections for two detector positions. Both natural and 90% enriched Li were considered (SUSD3D results based on the DORT 2D neutron fluxes).
(a)Li6+7(n,t) Li-natural D2 (~7 cm)Sensitivity (%/%)ReactionPb206Pb207Pb208Li6Li7Total0.020.020.010.310.69Elastic0.040.040.091E−30.01Inelastic0.010.01−0.003−3E−4−1E−3(n,2n)−0.03−0.03−0.08(n,3n)2⋅10−51⋅10−52⋅10−4(n,t)0.310.68Uncertainty0.9%0.8%3.0%0.9%0.1%(b)Li6+7(n,t) Li-90% enr. D2 (~7 cm)Sensitivity (%/%)ReactionPb206Pb207Pb208Li6Li7Total0.290.250.500.970.06Elastic0.130.130.283⋅10−30.04Inelastic0.070.050.037⋅10−50.01(n,2n)0.100.080.19(n,3n)1⋅10−46⋅10−51⋅10−3(n,t)0.970.02Uncertainty2.0%1.8%9.7%0.3%0.1%(c)Li6(n,t) D7(∼7cm)Sensitivity (%/%)ReactionPb206Pb207Pb208Li6Li7Total0.310.270.480.960.07Elastic0.170.170.370.0040.06Inelastic0.090.070.01−3⋅10−4(n,2n)0.050.040.10(n,3n)7⋅10−54⋅10−56⋅10−4(n,t)0.960.01(n,γ)−0.004−0.003−0.001Uncertainty1.9%1.8%6.5%0.2%0.1%Comparison of results in Tables4 and 5 proves good consistency between
the 2D and 3D calculations, as already mentioned above.We can furthermore observe that the sensitivities to the Pb cross-sections
are relatively low, below 1% of change in TPR per 1% of change in cross-section.
The most sensitive reaction was found to the elastic scattering on Pb.
Controversially, this is not the reaction causing the largest uncertainty,
since the corresponding cross-section uncertainty is relatively low. On the
other hand, the precision in the (n,2n) and (n,3n) reactions on Pb isotopes
is rather low, consequently most of the overall uncertainty in the calculated
TPR is caused by the uncertainty in these cross-section reactions.Comparison of the sensitivities at the front detector positions (D2) for
the natural and 90% enriched Li in Table5 indicates rather large differences
in the sensitivities. In particular, in case of using natural Li in the front
positions the sensitivity to the (n,2n) reaction on Pb is negative, and
positive in case of using enriched as well as for deep positions (both for
natural or enriched Li). This has an important and very beneficial consequence
for the cross-section validation studies. Use of both enriched and natural Li
would provide different (and complementary) information on the cross-sections and
would contribute to validate the data at different energy ranges and for
different nuclear reactions.


## 5. Conclusions

DORT and TORT/GRTUNCL-3D/SUSD3D
computational schemes were used in the preanalysis of FNG-HCLL benchmark
mock-up. The following conclusions and
recommendation concerning the experimental setup can be summarised from this study.(i) Using the ENDF/B-VI.8 covariance
matrices, the uncertainties in TPR due to cross-section uncertainties
were estimated to be between 5–10%. According to
these covariance data the reactions (n,2n) and (n,3n) on lead
were found to cause the highest uncertainty, although the corresponding
sensitivities are not particularly high. The TPRs are most sensitive to the Pb
elastic scattering cross-sections which are on the other hand known with much
higher accuracy. Inelastic cross-sections were also found to be important for
some isotopes of lead.(ii) Large and potentially advantages differences in the sensitivities of
TPR to the Pb cross-sections between natural and enriched Li pellets in the
front detector positions were observed. This is due to
the strong spectral-dependence of tritium production in different Li isotopes.
The tritium production cross-section fromLi6 is high at low
energies, while tritium production in Li7 is a threshold reaction. In particular, in the front
positions the sensitivity to the (n,2n) reaction on Pb is negative in case of
using natural Li, and positive in case of using enriched Li. For deep positions
the sensitivity is positive both for natural or enriched Li. This has an
important and very beneficial consequence for the cross-section validation
studies. Use of both enriched and natural Li would provide complementary
information on the cross-sections and would permit to validate the data at
different energy ranges and for different nuclear reactions. Combined use of natural and enriched Li pellets is therefore strongly
recommended for the TPR measurements
at the front detector positions, as far as the neutron flux level (and the experimental setup) permits it.(iii) In addition to measurements
on the axis of the experimental setup, off-axis measurements would provide
additional information on the angular distributions, as well as on TPR generated
at different energy spectra. The feasibility of placing the detectors at
off-axis positions in the experimental setup should be investigated.



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*Source: 659861-2008-10-28.xml*