Neutrons propagation in Lead: a feasibility study for experiments in the RSV TAPIRO fast research reactor

. The increasing worldwide interest in Lead-cooled Fast Reactors (LFRs) substantiates the need to validate the analytical codes and methods used to support their design. For neutronic analyses, this is chiefly reflected in assessing the impact of nuclear data uncertainties on the integral and local parameters resulting from such analyses. The aim of refining nuclear data moves continuous efforts for more accurate measurements, be them differential or integral, for which adequate facilities are required. The availability at the ENEA's Casaccia research center of a fast source reactor – RSV TAPIRO – provides a unique opportunity to perform new integral experiments in support of fast reactors, including LFRs, owing to the well-characterized neutron spectrum of the thermal column. A series of experiments has been envisaged, dealing with the use of Lead in a reactor. The experiments concern the propagation of neutrons through blocks of materials representing relevant elements of a reactor core, and ranging from pure Lead to mixtures reproducing portions of the reflector and shield in LFRs. The paper is focused on the feasibility study of some of these experiments in which Lead and mixture blocks are inserted in the so-called thermal column of the RSV TAPIRO reactor and irradiated by the neutron flux emerging from the Copper reflector surrounding the reactor core.


Introduction
The development of Lead-cooled fast reactors (LFRs) is gathering increasing support worldwide. Design activities are complemented by extensive research and development programmes, which -in the past ~20 years -allowed to increase the technology readiness level to the point where demonstration by a full-scope nuclear reactor is possible.
However, almost all such programmes focused on non-nuclear (i.e., "cold") tests, dealing e.g., with thermal-hydraulics, materials compatibility, components and systems performance. In only a few cases, experiments were performed at zero-power reactors, to confirm the ability of neutronic codes to predicting the behavior of an LFR. Despite such experiments, additional measurements are deemed necessary, particularly dealing with the qualification of prototypic components. Due to the limited number of zero power, fast spectrum reactors, the availability of the RSV TAPIRO is seen as an almost unique opportunity to perform propagation experiments in media properly set up to represent pure Lead regions, reflectors/shields, and absorber devices.
In the European context, the advanced LFR European demonstrator (ALFRED) is chosen as reference system, being the first planned in a roadmap towards commercial deployment of LFR systems. With respect to the ALFRED design [1], all the experiments listed above are envisaged, starting with a test of neutrons propagation through pure Lead, chiefly meant for neutron cross-section adjustment.

The RSV TAPIRO reactor
The TAPIRO (TAratura PIla Rapida Potenza ZerO -Fast pile calibration at 0 power nuclear reactor) (see Fig. 1) is a fast neutrons source based on the Argonne Fast Source Reactor -Idaho Falls. TAPIRO was built in the 1960s and its first criticality was achieved on April 1971. The TAPIRO reactor can operate at the maximum power of 5 kW, and the neutron flux at the center of the core at full power is about 4 × 10 12 n cm -2 s -1 .
The reactor core is a cylinder made of highly enriched uranium-molybdenum alloy (weight 98.5% U; 1.5% Mo) enclosed in a stainless steel cladding. The cylindrical core is surrounded by a coaxial cylindrical reflector made of Copper. The reflector is housed in a steel sheath surrounded by a biological shield made of borated concrete.
The reactor is controlled by several rods made of Copper. The reactor control is achieved by varying the neutron leakage level from the reflector.
TAPIRO is used for different areas of application like: validation of calculation codes for GEN IV fast reactors design; fast neutrons damage; nuclear data integral measurement; testing of innovative detectors and hands-on training in nuclear engineering courses.

The ALFRED reactor
ALFRED is a Lead-cooled fast reactor demonstrator, rated 300 MWth and fueled by Uranium-Plutonium mixed oxide (MOX). The core (see Fig. 2) is made of 134 fuel assemblies (FAs) of hexagonal shape arranged in a triangular lattice [2]. According to a general design approach for LFRs, the fuel rods in the ALFRED FAs are relatively spaced apart, leveraging the Lead cross-sections to favor natural circulation (because of the lower pressure drops of a loose bundle) without impairing the neutronic performance of the core.
Among the dummy assemblies, those in the innermost ring, meant as reflectors, largely exploit Lead for the purpose: in one of the considered options, the volume fraction of steel is limited to the minimum amount required to provide the desired stiffness for core restraint.
Because of the relatively large volume fractions of Lead in the FAs and reflector dummy assemblies, the sensitivity of several key integral parameters to the cross-sections of Lead isotopes is high. As reference, three Lead isotopes reactions are among the top-twelve contributors to the uncertainty of the multiplication factor [3], namely the inelastic cross-section of 207 Pb (by 84.4 pcm); the elastic cross-section of 208 Pb (by 77.6 pcm); the inelastic cross-section of 206 Pb (by 72.0 pcm).

Mock-up definition
Being used as coolant, a large amount of Lead is present in and all around the ALFRED core. Immersed in Lead are also the neutron reflectors and shields, as well as the absorber sub-assemblies. Refining the cross-sections of Lead is therefore of paramount importance, with the experiments in TAPIRO adding integral information for their adjustment.
For the proposed first experiment of neutrons propagation in pure Lead, the possibility of removing a sector of the external TAPIRO reflector was exploited. The sector, originally made of Copper, is replaced by an analogous block of nuclear-grade Lead. Since the removable sector is the one facing the thermal column, the possibility is also exploited, of using the thermal column for adding Lead bricks also downstream the reflector, so that any albedo after the propagation means can still be representative of the ALFRED core.
According to the planned experiment, the selected phenomena of interest are the actual propagation/absorption through the Lead block, and the consequent spectrum softening due to the propagation through the block. For these the associated observables are: the fission spectral indexes U238/U235 and Np237/U235 (hereinafter named f28/f25 and f27/f25, respectively) up-and down-stream the Lead block, and their ratio.
These observables will be correlated with the same quantities computed up-and down-stream the first ring of sub-assemblies around the active ALFRED core, which are supposed replaced by pure Lead channels.

Calculation models and codes specifications
The ERANOS 2.3 deterministic code [4] was used to model in a R-Z 2D geometry [5] both the TAPIRO and ALFRED reactors and to perform a sensitivity and representativeness analysis by means of the Generalized Perturbation Theory (GPT).
The ENDF/B-VIII.0 nuclear data library was prepared in a special format readable by the ERANOS code to be used for this work.
The 80 energy group structure previously refined for ALFRED reactor studies [3] was chosen for this analysis in both systems. Then the GPT was applied to analyze at first the sensitivity of the selected observables to nuclear data for both reactors, and then also for the representativeness of the planned experiment in TAPIRO to the reference ALFRED case.
A new homemade covariance matrix was prepared for ERANOS and used to perform the planned analyses. The covariance matrix was also based on the state-ofthe-art ENDF/B-VIII.0 evaluations, and then extended to include Copper by integrating the uncertainty data of the JEFF-3.3 evaluated data library, to properly take into account the importance of the TAPIRO reflector. A Monte Carlo model of the TAPIRO reactor was also developed, in order to perform a neutron energy spectra distribution comparison in the different selected positions. The MCNP 6.2 code on the ENEA CRESCO HPC grid has been used with the same nuclear data library and energy group structure as for ERANOS evaluations.

Results
A preliminary study about the neutron energy spectra in two different positions of both reactors was carried out to better analyze their neutronic behavior.
In the first position of the TAPIRO (upstream the Lead block), the results, in Fig. 3, show, as expected, a substantially good agreement between ERANOS and MCNP codes, while for the ALFRED spectrum a difference in the fast energy range between 1 keV-1 MeV due to the intrinsic characteristics of the systems can be found.   The sensitivity analysis for the chosen spectral indexes, described in paragraph 3.1, was carried out considering both direct and indirect effects by means of the GPT.
Figs. 5-6 show that, for the spectral index f28/f25, the influence of the Lead block is important, whereas downstream of it both systems have a similar sensitivity when the same perturbation occurs.  Moreover, as shown in Fig.7, the behavior of the sensitivity profiles for the f27/f25 spectral index exhibits an important difference in the upstream position; on the contrary, a good agreement between the two systems can be observed in Fig. 8 for the downstream position.  The uncertainty evaluation was carried out for both indexes and both positions and the results for the whole systems are presented in Table 1. At the level of single isotope contributions to the total uncertainty of the two systems, the major ones are related to: 1. the elastic and inelastic cross sections of the Copper and Lead isotopes in the TAPIRO reactor.

the elastic and inelastic cross sections of the
Lead isotopes in the ALFRED reactor.
Then the representativity analysis [6] for these two spectral indexes was carried out in both positions and considering in the covariance matrix the data uncertainties of the Copper isotopes relative to the JEFF 3.3 nuclear data library. The results obtained, in Table  3, show an important difference between these two systems for the spectral index f28/f25 as compared to the f27/f25 spectral index where the representativity seems to be more relevant. In the end, only for the spectral index f27/f25, the representativity was evaluated without considering the Copper isotopes contribution to the covariance matrix and the relative results are shown in Table 4. The results obtained show that the uncertainties on Copper cross-sections can hinder the potential of representativeness of TAPIRO.

Conclusions
The feasibility of an experiment to study neutrons propagation in Lead for the RSV TAPIRO fast research reactor was discussed in this work.
Both the simple geometry and the fast spectrum of the TAPIRO reactor allow to study this type of propagation experiments and demonstrate its usefulness in support to LFRs design, especially for elements located at the periphery of the core (for shielding, reflection or other purposes).
As expected, sensitivity analyses show some differences between the two systems, especially in the position upstream the Lead propagation block, which are mitigated in the downstream position due to the softening of the energy spectrum.
The representativeness studies of the TAPIRO reactor for ALFRED demonstrator is not straightforward.
The objectives of this experiment are the Lead crosssections adjustment and the qualification of the ALFRED reflective structures, since, as shown in the uncertainty evaluations, the cross-sections of Lead isotopes seem to offer further margin for improvement, to the sake of higher accuracy.
The representativity analysis has shown that the importance of the Copper uncertainties is not negligible and a refinement of the Copper cross-sections would allow to further increase the relevance of these type of experiments demonstrating, as further evidence, the already considerable usefulness of TAPIRO.