CRITICAL EXPERIMENT OF THORIUM LOADED THERMAL CORES AT KUCA (1) A NEW CRITICAL EXPERIMENT OF THORIUM LOADED CORE WITH HARDER NEUTRON SPECTRUM IN KUCA

In order to perform integral evaluation of 232Th capture cross section, a series of critical experiments for thorium-loaded and solid-moderated cores in KUCA had been carried out. In these experimental cores, H/235U nuclide ratio ranged about from 150 to 315, and 232Th/235U nuclide ratio ranged about from 13 to 19. In this study, a new critical experiment with Th loaded core in KUCA, which had about 70 of the H/235U ratio and 12.7 of 232Th/235U ratio, was carried out. As results, the excess reactivity was 0.086 ± 0.003 (% dk/k) and the keff was 1.0009 ± 0.0003, where the effective delayed neutron fraction was 7.656E-3. The keff was also calculated by MVP3.0 with different nuclear libraries. The respective calculations with JENDL-4.0, JENDL-3.3 and ENDF/B-VII.0 lead to 1.0056 ± 0.0086 (%), 1.0048 ± 0.0085 (%) and 1.0056 ± 0.0086 (%).On the other hand, the further MVP3.0 calculations, where only the 232Th cross sections were taken from JENDL-4.0, JENDL-3.3 or ENDF/B-VII.0 but all other nuclides were done from JENDL-4.0, were carried out to examine an impact of the difference of 232Th cross section among these nuclear libraries to the keff. The keff calculated with respective 232Th cross sections from JENDL-3.3 and ENDF/B-VII.0 was 1.0038 ± 0.0086 (%) and 1.0040 ± 0.0086 (%).


INTRODUCTION
In discussing the feasibility of a thorium-based reactor system from an engineering perspective, it is necessary to verify and evaluate the impact of thorium (Th) utilization on the accuracy and reliability of core nuclear characteristic parameters such as criticality, conversion rate, and fuel balance.Improving the accuracy of the nuclear characteristics of Th is an important R & D step in the Th utilization reactor system.However, compared to the currently uranium / plutonium-based light water reactor system, the Th-based nuclear reactor system has not been sufficiently researched on the following two viewpoints.One is to evaluate the reliability and uncertainty of cross section of related nuclides including 232 Th in the nuclear data library.The other is the effect of the cross section uncertainties on the nuclear characteristics in the Th-based reactor core.
The authors have systematically carried out critical experiments on Th loaded cores using Kyoto University Critical Assembly (KUCA).In KUCA, the 9 critical experiments have been carried out with 3 type H/ 235 U nuclide ratios (about 150, 210, 315) and 3 type 232 Th/ 235 U nuclide ratios in a Th loaded fuel shown in Table I [1].Integral evaluations of thorium loaded thermal neutron systems and 232 Th capture cross sections has been performed via those critical experiments.
In this study, from the viewpoint of expanding critical experimental data, an experiment was conducted by a Th fuel loaded core with 70 of H/ 235 U and 12.7 of 232 Th/ 235 U ratio at KUCA.Section 2 outlines the critical experiment at KUCA, Section 3 describes the numerical analysis and sensitivity analysis for the criticality, and Section 4 concludes.

Table I.
List of experiments conducted by KUCA with thorium fuel loaded core.

Core Configuration with Thorium loaded fuel at KUCA
KUCA solid moderator core is able to consist of enriched uranium fuel plate and various moderator plates (i.e.polyethylene and graphite).Figure 1 shows the schematic view of KUCA solid moderator core.In order to vary the neutron spectrum of the irradiation field, the H/ 235 U nuclide ratio in the unit cell is varied by the combination of the U-Al alloy fuel plates (EU) and the moderator plates.The enrichment of the uranium is about 93 wt %.The width of the plates have 2 inch square.The thickness of the fuel plates has 1/16 inch.In this study, a new critical core consisted of two type fuel elements.One was a Th loaded fuel element (referred to as "Th fuel"), and the other was a driver fuel element ("Driver fuel").Figure 1 shows the configuration of Th fuel and the Driver fuel.The Th fuel consisted of 27 unit cells and sandwiched by a upper and a lower polyethylene reflector.The unit cell has three EU plates, one Th plate of 1/8" thickness and two polyethylene plates of 1/8" thickness.The Driver fuel has 49 unit cells and the unit cell was composed of one EU plate and two polyethylene plates.The experimental core was consisted of 37 Th fuels and 17 Driver fuels shown in Figure 2.Where "C" means a control rod and "S" means a safety rod.In addition, the partial driver fuel element which has 17 or 19 unit cells were loaded to adjust an excess reactivity of the critical core.The Th fuels were loaded at the center of the core and surrounded by the Driver fuels and the partial driver fuels.

Results of Critical Experiments
In order to obtain an effective multiplication factor of the core described in the previous section, excess reactivity measurement was performed 6 times by the reactor period method, respectively.In each measurement, the C1 and C2 control rods were set to the upper limit and the C3 control rod was adjusted to the critical position.And the C3 control rod was drawn to the upper limit from the critical position and the reactivity was inserted into the core.The results of measured excess relativities and the control rod position are shown in Table II.Here, the kinetics parameters using the reactivity measurements were calculated by the continuous energy Monte-Carlo code MVP3.0 [2] with the JENDL-4.0 [3].The parameters are shown in Table III.As the result, the excess reactivity was 0.0865 ± 0.0026 (%dk/k) and the keff was 1.0009 ± 0.0003.

Table II. Measured excess reactivity.
Table III.Kinetic parameter.

Criticality with various nuclear data libraries
Numerical analysis for the criticality (keff) in the critical experimental core was performed using MVP3.0,JENDL-4.0,JENDL-3.3 [4], and ENDF / B-VII.0 [5].The Monte Carlo runs performed for 5,000 active and 100 inactive batches with 20,000 histories per batch.The numerical results of the keff are shown in Table IV.The respective calculations with JENDL-4.0,JENDL-3.3 and ENDF/B-VII.0 lead to 1.0056 ± 0.0086 (%), 1.0048 ± 0.0085 (%) and 1.0056 ± 0.0086 (%).The calculate results have bias of about 0.39 (%dk/k) to 0.47 (%dk/k) compared to the experimental result.This bias are consistent with the analysis of previous experimental results for criticality [6].On the other hand, the differences of calculated keff between JENDL-4.0 and other libraries are less than 0.08 (%dk/k).The average neutron spectrum in the Th loaded region is shown in Figure 4.The present core has harder neutron spectrum than the previous cores.

Impact of 232 Th cross section for criticality calculation
The further MVP3.0calculations, where only the 232 Th cross sections were taken from JENDL-4.0, JENDL-3.3 or ENDF/B-VII.0 but all other nuclides were done from JENDL-4.0, were carried out to examine an impact of the difference of 232 Th cross section among these nuclear libraries to the keff.The results are shown in Table V.The keff calculated with respective 232 Th cross sections from JENDL-3.3 and ENDF/B-VII.0 are 1.0038 ± 0.0086 (%) and 1.0040 ± 0.0086 (%), respectively.The differences of the keff due to 232 Th cross section change from JENDL-4.0 are obtained to be 0.180 (%dk/k) of JENDL-3.3 and 0.162 (%dk/k) of ENDF/B-VII.0

Table V. Effect of 232 Th cross section change on keff calculation.
The main contribution of keff difference is 232 Th capture cross section.To discuss the changes of keff, the differences of 232 Th capture cross section between JENDL-4.0 and other libraries are shown in Figure 5.
Comparison between JENDL-4.0 and JENDL-3.3, the capture cross section in JENDL-3.3 is larger than JENDL-4.0 from energy range of 0.1 (eV) to 40 (eV), and it is smaller than JENDL-4.0 in the energy region higher than 40 (eV).Here, the major difference of the capture cross section is "resonance valley" with a small cross section.The difference of capture cross section between JENDL-4.0 and ENDF / B-VII.0 is small.In addition, the energy region below 3.3 (keV) has the same value. 0.E+0 5.E-3 1.E-2 2.E-2 2.E-2 3.E-2 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0  In order to quantitatively evaluate the contribution of the cross section difference for the keff, the sensitivity coefficient for effective multiplication factor defined by the following equation were calculated by sensitivity calculational code SAGEP [7].

S = 𝑑 𝑘
Where, ψ is adjoint neutron flux, neutron flux, F is operator for fission in neutron diffusion equation, and A is operator for leakage, absorption and scattering in neutron diffusion equation.By using the sensitivity coefficient and the cross section difference, it is possible to evaluate the energy depend contribution "R" of the change in effective multiplication factor.
Figure 6 shows the contribution of the keff difference due to the 232 Th capture cross section change when the nuclear data library is changed from JENDL-4.0 to JENDL-3.3 and ENDF / B-VII.0.In JENDL-3.3, it is observed the effect of increasing the capture cross section in the thermal energy region and decreasing the keff, and the effect of decreasing the cross section and increasing the keff at the energy region above the second resonance.Since these effects cancel each other, the difference of the keff between JENDL-4.0 and JENDL-3.3 is small.On the other hand, in ENDF/B-VII.0, the difference of the keff between JENDL-4.0 and ENDF / B-VII.0 becomes small due to the effect of increasing and decreasing the effective multiplication factor in the energy region above 3.3 keV.The difference of the keff by the library change are almost the same, but the energy-wise contribution of cross section is different.

CONCLUSIONS
In this study, from the viewpoint of expanding critical experimental data, the Th fuel loaded core with 70 of H/ 235 U and 12.7 of 232 Th/ 235 U ratio was newly constructed at KUCA.In order to obtain an effective multiplication factor of the core described in the previous section, excess reactivity measurement was performed 6 times by the reactor period method, respectively.As the results, the excess reactivity was 0.0865 ± 0.0026 (%dk/k) and the keff was 1.0009 ± 0.0003.
In order to evaluate the impact of of the difference of 232 Th capture cross section among JENDL-4.0,JENDL-3.3 and ENDF/B-VII.0 to the keff, the sensitivity analysis were carried out.In the evaluation, only the 232 Th cross sections were taken from JENDL-4.0, JENDL-3.3 or ENDF/B-VII.0 but all other nuclides were done from JENDL-4.0.As the results, the differences of the keff due to 232 Th cross section change were obtained to be 0.180 (%dk/k) of JENDL-3.3 and 0.162 (%dk/k) of ENDF/B-VII.0.To quantitatively evaluate the contribution of the cross section difference to the keff, the sensitivity coefficients for keff were calculated by sensitivity calculational code SAGEP As the results, The difference of the keff between JENDL-4.0 and other libraries were almost the same, but the energy-wise contribution of the cross section change was different. -

Figure 1 .
Figure 1.Schematic view of KUCA solid moderator core.

Figure 2 .Figure 3 .
Figure 2. Configuration of Th fuel and Driver fuel

Figure 4 .
Figure 4. Neutron spectrum in each core.

Figure 5 .
Figure 5. Differences of 232 Th capture cross section.