Numerical design of thorium and uranium fuel samples irradiation in lead environment

The paper shows capabilities of thorium-lead fuel assembly for design of irradiation experiments on ThO2 and natural UO2 fuel samples using radioisotope neutron source. The main purpose of the current analysis was to determine the irradiation environment in the samples, especially: neutron spectrum, power, activity, reaction rates, production of Pa and Np as well as breeding of U and Pu. An advanced threedimensional numerical model for Monte Carlo radiation transport and burnup simulations was developed using the Monte Carlo Continuous Energy Burnup Code (MCB). The versatility of the assembly gives a perfect opportunity to perform many irradiation experiments for R&D on the thorium and uranium fuel cycle in a different material and geometrical environments.


Introduction
The paper presents the neutronic analysis of the irradiation experiments planned at the AGH University of Science and Technology in Krakow, Poland, using a state-of-the-art thorium-lead (Th-Pb) fuel assembly. The experiments consider the irradiation of ThO 2 and natural UO 2 fuel samples using radioisotope Cf neutron source. The fuel sample is embedded in the fuel rod placed in the array of the remaining 236 rods of either thorium or natural uranium, reflected by lead rods and bricks. The flexibility of the Th-Pb assembly allows to perform many irradiation experiments with different geometrical configurations of the core. The purpose of the current analysis is to determine the irradiation environment in the sample, especially: neutron spectrum, power, activity, production of 233 Pa and 239 Np as well as breeding of 233 U and 239 Pu for further comparison with the results of the irradiation experiments. An advanced threedimensional numerical model for Monte Carlo radiation transport and burnup simulations was developed using the Monte Carlo Continuous Energy Burnup Code (MCB) [1], developed at the AGH University. The code was equipped with ENDF/B-VII.1 [2] and JEFF3.1 [3] nuclear data libraries for comparative study. The analysis was performed for fuel samples containing ThO 2 and natural UO 2 for the comparison of breeding capabilities of 233 U and 239 Pu.
The research mainly focuses on the ThO 2 fuel sample, which was chosen because of an increasing interest in the thorium fuel cycle and a demand for more basic research into thorium fuels [4,5]. In general, thorium seems to be an attractive option for nuclear fuel mainly due to its abundance, reduced need for enrichment in the fuel cycle, high conversion ratios to 233 U in a thermal neutron spectrum, low production of plutonium and minor actinides and high proliferation resistance. Although many investigations have been carried out into thorium-based fuels while thorium-fuelled power reactors have operated in the past, the thorium fuel cycle as a whole has never been fully developed. As yet, there is no commercial fabrication or reprocessing infrastructure for the thorium fuel cycle, unlike the vast available infrastructure for the uranium fuel cycle. Nevertheless, the experience gained on thorium-based fuels in test and power reactors as well as the results of the numerical analysis are very encouraging [6][7][8][9]. Therefore, the implementation of thorium fuels to the power reactor must be further supported by scientific research to allow better understanding of all components of the thorium fuel cycle. In spite of the large amount of available neutronic data for numerical modelling, better neutronic characteristics supported by experimental validation with dedicated infrastructure such as the Th-Pb assembly are needed.
In Section 2, the technical specification of the Th-Pb assembly and the developed numerical model for the Monte Carlo modelling are described. The results of the numerical modelling are shown in Section 3. Section 4 contains a summary of the study and discussion about possible improvements in the applied methodology.
2 Thorium-lead assembly numerical model Figure 1 shows the Th-Pb fuel assembly located in the shielded irradiation bunker in the radiometric laboratory of the AGH University. The thorium core lays on the steel bottom support plate. The upper cylindrical support plate and aluminium grid fasten the core from the top. In addition, four side bars located symmetrically around the core stabilize the assembly. The side reflector surrounding the core was fabricated using lead bricks with dimensions 100 mm Â 100 mm Â 50 mm and hexagonal lead rods with the length of 120 cm. The cylindrical ThO 2 and UO 2 rods have the same length of 120 cm and radius of 5.32 mm. The active high, gap and clad thickness in both cases equals 100, 0.012 and 0.085 cm respectively. The pitch of hexagonal assembly grid is 1.27 cm. The free space of 0.04 cm between rods was designed to facilitate subtraction of the chosen rods without dismantling of the whole assembly. This, in turn, facilitates introduction of the new elements like e.g. radiation detectors, samples or other materials comprising experiments. In general, Th-Pb assembly is characterised by a quite simple construction, which is an advantage in its maintenance during planning, execution and post-processing of irradiation experiments.
The numerical reconstruction of the assembly was based on the performed profilometric measurements as well as specification of the fuel rods provided by the supplier (Bhabha Atomic Research Centre, India) [10]. The active height of the fertile material (1000 mm) was numerically divided into four radial (RZ) and three axial (AZ) zones presented in Figures 2 and 3. The subsequent zone of 25 mm represents the fuel sample, which was additionally divided into five similar axial segments for the estimation of axial distributions of key physical parameters, such as activity, power and production of the investigated isotopes. The height of each segment equals 0.5 cm, which gives the volume of 0.436 cm 3 . The segment mass depends on the fuel type; in the case of ThO 2 , it is 4.06 g and in the case of UO 2 -4.54 g. The isotopic composition of uranium and thorium dioxide is shown in Tables 1 and 2 respectively. For better numerical precision, results of the simulation were scored in six symmetric zones representing the samples around the neutron source, as it is shown in Figure 2. Then, the results were averaged for particular segments. The Th rods are surrounded by the hexagonal matrix of Pb rods and Pb bricks respectively. The production of 233 U and 239 Pu is the most effective in the thermal neutron spectrum due to the high cross-section for neutron capture on 232 Th and 238 U. Therefore, for the planned irradiation experiments, thermalisation zone made of hexagonal polyethylene rods (C 2 H 4 ) was introduced to the assembly. For the current study, the neutron source was surrounded by two layers of  polyethylene rods of 6 and 12 rods respectively. As a result, the total number of ThO 2 /UO 2 rods in the assembly for the planned experiment equals 234, which gives ThO 2 the mass of 192 kg, including 169 kg of Th, and UO 2 -the mass of 214 kg, including 189 kg of U (1.3 kg 235 U, 187.5 kg 238 U and trace amount of 234 U). The materials used for the numerical modelling and their densities are shown in Table 3. For the modelling of the grid, side bars and top bars, which are characterized by the complicated geometry the volumetric homogenisation technique was applied. The neutron source was modelled according to the specification of the manufacturer [11] as a Cf 2 O 3 -Pd cermet wire closed in two stainless steel capsules. Figure 2 shows the location of the source in the middle of the assembly. The chosen source has intensity of 10 8 n/s, which gives mass of 43 mg of 252 Cf. The planned irradiation time equals 25 days, but it can be easily shortened or extended, depends on experiment specification.

Results
Section 3 presents results of the numerical modelling using the Monte Carlo Continuous Energy Burnup Code (MCB) for neutron transport and burnup simulation [1,12]. The calculations were performed for the two sets of nuclear data libraries i.e. ENDF/B-VII.1 and JEFF3.1 for comparative analysis. The supercomputer Prometheus of the Academic Computer Centre of AGH University was used for numerical simulations. The numerical precision of the obtained results is much below 0.5%. In the following subsections the characteristic of neutron spectra in the samples, mass evolutions of crucial isotopes ( 233 Pa, 239 Np, 233 U, 239 Pu) as well as power and activity evolutions are shown. Figure 4 shows the absolute neutron spectrum, while Figure 5 presents the relative neutron spectrum calculated in 100 energy group structures for ENDF/B-VII.1 nuclear data libraries at the beginning of irradiation. The shape of the spectrum is similar for both applied libraries and for particular time steps, as it is mainly formed by the Cf  neutron source and polyethylene thermalisation zones. The isotopic changes in 25 days of irradiation and the Cf decay do not influence it significantly. The differences between JEFF3.1 and ENDF/B-VII.1 libraries depend on the energy group but mostly they are below 1% on average, and below 0.25% for both samples. In the spectrum, two major peaks related to thermal and fast neutrons are presented. The main difference between the ThO 2 and UO 2 fuel samples comes from the flux depressions due to the radiative capture cross-sections on 232 Th and 238 U. The first large resonance for 232 Th appears at about 2 Â 10 À5 MeV and for 238 U À at about 7 Â 10 À5 MeV in the epithermal energy range, which is visible in Figure 4.  Tables 5 and 7. In general, the absolute neutron flux is higher in the case of the UO 2 fuel sample (1.27E+06 n/cm 2 · s) compared with the ThO 2 fuel sample (1.11E+06 n/cm 2 · s) due to the presence of fissionable 235 U in the fresh fuel composition and the surplus fissions in the thermal and epithermal energy range.

Mass evolution
The mass evolution of 233 Pa and 233 U for both nuclear data libraries and the sample segments is shown in    Figure 8. This is caused by the equilibrium between 239 Np formation from decay of 239 U and its further decay to 239 Pu. The axial distribution of 239 Np corresponds to the power distribution. At the end of irradiation for ENDF/B-VII.1 nuclear data libraries, the highest concen-tration of 239 Np was obtained in the central segment (1.80 Â 10 9 atoms) and the lowest concentration À in the peripheral segments (1.76 Â 10 9 atoms). The calculations with JEFF3.1 nuclear data libraries show the concentration of 239 Np higher by about 1%. The concentration of 239 Pu increases with the irradiation time due to its breeding from 238 U, which is shown in Figure 9. The highest concentration of 1.14 Â 10 10 atoms corresponds to the central segment of the sample and the lowest concentration of 1.11 Â 10 10 atoms À to the peripheral segment of the sample. JEFF3.1 nuclear data libraries in general show the concentration of 239 Pu higher by about 1%. The calculations also show some minor differences between the concentrations in the symmetric segments (1-5 and  Table 4. In addition, Tables 5, 6, 7 and 8 present the effective microscopic r eff (1/s) and macroscopic R eff (1/s · cm 3 ) reaction rates for the sample segments. The reaction rates for the isotopes present in the initial fuel composition ( 230 Th, 232 Th, 234 U, 235 U, 238 U) were calculated at the beginning of irradiation and for the formed isotopes ( 233 Pa, 233 U, 239 Np, 239 Pu) À at the end of irradiation. The radiative capture and fission reaction rates for both nuclear data libraries are shown. The axial distributions of the reaction rates show a similar shape as the power and the number of distributions of atoms for the investigated isotopes, which proves the reliability of the calculations. The reaction rates were presented as possible input for other calculations considering similar nuclear set-ups for various numerical tools used by research teams.   for ENDF/B-VII.1 libraries, which gives a difference of about 5%. In addition, the difference between the nuclear data libraries is much lower compared with the ThO 2 fuel sample and equals about 0.3%. The reason for the differences between the nuclear data libraries may be attributed to better knowledge on the isotope cross sections in the formation chain of 239 Pu than in the formation chain of 233 U. The final axial power distribution corresponds to the neutron flux distribution in the samples and it is consistent with theoretical predictions, i.e. the closer to the neutron source, the higher the power is.

Activity
The activity in the sample segments for both fuel types is shown in Figures 12 and 13. The activity is higher in the case of the UO 2 fuel sample due to the fissions on the residual 235 U and the formation of active fission products and due to the formation of minor actinides from the transmutations on 238 U. The difference in the activity at the end of irradiation equals about 52% for each segment of the sample. The activity increases more rapidly after the initial jump in the case of UO 2 and it reaches the equilibrium state faster at the end of irradiation. The

Discussion and summary
In the study, the design of irradiation experiments with a ThO 2 and UO 2 fuel sample was presented. The main   dneutron characteristics of the sample located in the available experimental set-up were calculated using the developed numerical methodology based on the Monte Carlo modelling. The methodology includes the reconstruction of the experimental set-up using the functionalities of the MCB code and the high-performance computing capabilities for numerical calculations using the Prometheus supercomputer. The numerical simulations shows that some improvements are necessary for better planning of irradiation experiments. The irradiation time for the ThO 2 sample should be longer in order to reach the equilibrium state of 233 Pa and to cover full period of 233 U production. In the study, only the irradiation time with the neutron source embedded in the assembly is considered. For the experimental measurements, the decay of the remaining 233 Pa and 239 Np should be also considered to estimate the number of atoms of bred fissionable isotopes, especially 233 U, after the source removal. The long-term activity of the samples should be also calculated for further technical and administrative maintenance of active fuel samples. Thus, the detailed analysis considering quantitative identification of the main isotopes contributing to the radiotoxicity of the spent Th fuel is recommended. Moreover, the experimental measurements using the detectors available in the radiometric laboratory should be performed not immediately after the removal of the neutron source from the assembly but after the removal and opening of the fuel rod for the sample extraction and preparation for measurements. The basic requirement of the experiments (uncertainties of the measurement results) will be defined after choice of the measurement methodology. The time for technical maintenance of the sample should be included in the numerical modelling. The numerical modelling should also contain analysis of the gamma spectra in the experimental set-up, especially in the in lead-filtered media.
In the future experiments, the use of many configurations of the core is foreseen. Firstly, for the spectrum thermalisation, not only polyethylene but also graphite rods may be applied. Secondly, the assembly can be loaded with depleted or natural uranium fuel rods. Thirdly, the radio isotopic Cf neutron source could be changed to e.g. Pu-Be source or even to D-T neutron generator. Finally, other irradiation positions of the sample are also possible, e.g. in the gap between the rods. The axial adjustment of the neutron source and the samples during long-term irradiations is also possible. The versatility of the assembly gives a perfect opportunity to perform many irradiation experiments for R&D on the thorium and uranium fuel cycle in a different material and geometrical environment, e.g. for the development of IV Generation nuclear reactors [13]. The use of lead may help to enhance the knowledge about the fuel behaviour in Lead-Cooled Fast Reactor and Accelerator Driven Systems [7,14], while the use of graphite À in High Temperature Gas Reactors [15]. The current study has a preliminary character in order to demonstrate the capabilities of the available experimental set-up towards integral irradiation experiments and it focuses on the numerical approach. On the other hand, the experimental measurements would also help to validate the numerical methodology developed, especially the crosssection libraries, which show some differences, especially in the decay and transmutation chain to 233 U.