Fusion Neutronics Experiments for Thorium Assemblies

2.1 ²³²Th reaction rates

The experimental method of activation of γ-ray off-line measurement of ²³²Th reaction rates is used. The activation γ-rays are measured by using an HPGe γ spectrometer.

The ²³²Th capture reaction rate (THCR) indicates the fuel breeding, that is, the production rate of fissile ²³³U (²³³Pa decay). THCR can be deduced by measuring 311.98 keV γ rays emitted from ²³³Pa [6, 7]. The reaction process is as follows:

The ²³²Th fission (with threshold of 0.7 MeV) reaction rate (THFR) indicates energy amplification and neutron breeding. The fission fragment yield correction method is used [8]. THCR can be deduced by measuring 151.16 keV γ rays emitted from the decay of ^85mKr from ²³²Th (n, f) reaction. The reaction process is as follows:

The ²³²Th(n,2n) ²³¹Th (with threshold of 6.5 MeV) reaction rate (THNR) indicates neutron breeding. THNR is obtained from measuring 84.2 keV γ rays emitted from ²³¹Th [9]. The reaction process is as follows:

The ²³²Th reaction rates are deduced from the measured activity and corrections, which include detection efficiency of the HPGe γ spectrometer, cited value of branching ratio, D-T neutron yield during irradiation, self-absorption of gamma rays in the foils, ^85mKr yield only for THFR, etc. The ²³²Th reaction rates are normalized to one source neutron and one ²³²Th atom.

2.2 Breeding properties

The breeding ratio in the conceptual design of subcritical blanket is more than one [1]. The experiment on breeding properties of thorium is used to support the design [17]. The breeding properties are relevant to the reaction type, cross section, and neutron spectrum. The breeding properties contain the fuel breeding and neutron breeding. The fuel breeding is derived from the reaction rate ratio of ²³²Th capture to fission, and neutron breeding from the ²³²Th(n,2n) and fission reaction rates. The different neutron spectra are constructed by using the macroscopic assemblies in which the material is relevant to that of the conceptual design. The breeding properties under different assemblies are obtained and analyzed from the measured ²³²Th reaction rates.

2.3 Neutron spectra

The neutron spectra leaking from the ThO₂ cylinders of different thickness are measured by the proton recoil method and the liquid scintillator [16]. The n-γ pulse shape discrimination is based on the cross-zero method. The spectra are resolved by using iterative method, and their range is from 0.5 to 16 MeV.

3.1 Polyethylene shell

One can assume the elastic scattering cross sections of H and C, which are widely used as standard cross sections [18] to be reliable. The polyethylene (PE) shell is adopted for checking the method of measuring the ²³²Th reaction rates. The inner radius (IR) and the outer radius (OR) of the PE shell are 80 and 230 mm [11], respectively. Five slices of ThO₂ (concentration > 99.95%) foils are put in the radial channel at 0° to the incident D⁺ beam, as shown in Figure 1. The mass and size of foils are about 4.2 g and ϕ30 × 1 mm, respectively.

A D-T fusion neutron source is located in the center of the shell. The 14 MeV neutrons are produced by a neutron generator at INPC. The energy of D⁺ beam bombarding a T-Ti target is 225 keV. An Au-Si surface barrier semiconductor detector is at an angle of 178.2° to the incident D⁺ beam in the drift tube and used to measure the absolute yield by counting associated α particles [19, 20]. D-T neutron yield is about 3 × 10¹⁰/s.

3.2 Depleted uranium shell

In the conceptual design of a subcritical blanket based on thorium, the neutrons from the U reaction process are used to maintain the Th/U fuel cycle. The depleted uranium (DU) shell is adopted for studying Th reaction. The IR/OR of the DU shell is 131/300 mm [12]. Six slices of ThO₂ samples are put in the radial channel at 90° to the incident D⁺ beam, as shown in Figure 2. ThO₂ samples are foils made from ThO₂ powder filling a plexiglass box with IR/OR of 9/9.5 mm. The mass of ThO₂ powder is about 0.45 g, and the thickness is about 0.7 mm. The D-T neutron source is located in the center of the shell.

3.3 ThO₂ cylinders

3.3.1 ThO₂/DU cylinders

The thorium oxide (ThO₂) cylindrical assembly with the thickness of 150 mm is produced and consists of three ThO₂ cylinders with the thickness of 50 mm and the diameter of 300 mm. The ThO₂ cylinders are made by pressing ThO₂ powder using PEO (CH₂CH₂O) as the binder and their densities are 4.25–5.59 g/cm³ [9, 10]. The structure of the ThO₂ cylinders as benchmark is simple. To change neutron spectra in ThO₂ cylinders, the latter can be combined with DU cylinders. The combination of two ThO₂ cylinders and one DU cylinders is shown in Figure 3. Three slices of the ThO₂ samples are put in axial channel of the assembly. The front surface of the assembly is 113 mm from the center of a tritium target.

3.3.2 ThO₂ powder cylinder

Based on thorium oxide powder, the ThO₂ assembly is produced, as shown in Figure 4 [13, 14, 15]. ThO₂ powder fills a stainless steel/aluminum cylinder container with IR/OR of 93.4/96.2 mm. The height of the ThO₂ cylinder is 168.9 mm and the density 1.5 g/cm³. Five pieces of ThO₂ foils are put at 0° to the incident D⁺ beam and fixed using holders consisting of aluminum plate and stainless steel. The mass and size of ThO₂ foils are about 5.0 g and ϕ30 × 1 mm, respectively. The distance between the tritium target center and the front end of the cylinder is 78.8 mm.

3.4 Neutron spectra in three assemblies

The neutron spectra in PE, DU, and ThO₂ assemblies are simulated by using the MCNP4B code [21] with ENDF/B-VII.0 [22], in which the S (α, β) thermal scattering model in PE is considered. The angular dependences of the source neutron energy and intensity are calculated by “DROSG-2000” code [23]. The neutron spectra at foils with different distances d to the neutron source in three assemblies are relatively compared, as shown in Figure 5. The ordinate is a normalized neutron fraction, that is, the proportion of the neutron number in each energy segment to the one in the whole energy range [11, 13]. The results show that the differences of the fractions are very obvious, especially in the low-energy region.

4.1 ²³²Th reaction rates in PE shell

The PE shell assembly for measuring ²³²Th reaction rates is shown in Figure 1. THCR is deduced from measuring 311.98 keV γ rays emitted from ²³³Pa (its half-life is 26.967 days, it is obtained from ²³³Th decay). THFR is deduced from measuring 151.16 keV γ rays emitted from ^85mKr decay (its half-life is 4.48 hour), which is one of the fragments of ²³²Th(n,f) reaction, and using the fragment yield correction method. THNR is deduced from measuring 84.2 keV γ rays emitted from ²³¹Th (its half-life is 25.52 hour).

The experimental uncertainty of THCR is 3.1%, including neutron yield 2.5%, γ-ray detection efficiency 1.0% (HPGe-GEM 60P), self-absorption 1.0%, characteristic gamma branch ratio 1.0%, ²³²Th nucleus number 0.5%, and counting statistics 0.3–0.6%.

The experimental uncertainty of THFR is 5.3%, including neutron yield 2.5%, γ-ray detection efficiency 1.0%, self-absorption 1.0%, average fission yield of ^85mKr 4.3%, characteristic gamma branch ratio 0.7%, ²³²Th nucleus number 0.5%, and counting statistics 0.8–1.0%.

The experimental uncertainty of THNR is 6.8%, including neutron yield 2.5%, γ-ray detection efficiency 1.0%, self-absorption 1.0%, characteristic gamma branch ratio 6.1%, ²³²Th nucleus number 0.5%, and counting statistics 0.5–0.6%.

The experiment is simulated by using the MCNP code with evaluated nuclear data from different libraries, including ENDF/B-VII.0, ENDF/B-VII.1 [24] and JENDL-4.0 [25]. The model is completely consistent with the structure of the assembly; it takes into account the target chamber and experimental hall. The calculated statistical uncertainty is less than 1%. The ranges of C/E with ENDF/B-VII.0 are 0.96–1.02 for THCR, 0.95–0.97 for THFR, and 0.89–0.91 for THNR. The results show that the experiment and calculation for THCR and THFR are well consistent within the range of experimental uncertainties, respectively. It is shown that the γ-ray off-line method is feasible for determining the ²³²Th reaction rates.

The distributions of ²³²Th reaction rates obtained from the experiments and calculations with ENDF/B-VII.0 are shown in Figure 6. The reaction rate ratio of ²³²Th capture to fission gives fissile production rate in unit of fuel burn-up [12]. The relative ratios measured are about 10.76–20.17 with the increase of radius in PE shell.

The ratios of calculation to experimental values (C/E) are analyzed. The C/E ratios of ²³²Th reaction rates are shown in Figure 7, and the ²³²Th(n,f) reaction results for different evaluated nuclear data are shown in Ref. [11]. The calculations with ENDF/B-VII.0 and ENDF/B-VII.1 for THNR underestimate the experimental values. Meanwhile, large differences still exist in the ²³²Th(n,2n)²³¹Th cross sections among different evaluated data [26]. Fractions with different energies in the PE shell are calculated by using ENDF/B-VII.0, and neutrons of energy more than 6.5 MeV account for 33–48% in the whole energy range, as shown in Figure 5. Since the neutron spectra in the PE shell are reliable, it is suggested that ²³²Th(n,2n) reaction cross sections should be studied further.

4.2 ²³²Th reaction rates in DU shell

The DU shell assembly for measuring ²³²Th reaction rates is shown in Figure 2. The ²³²Th reaction rates are measured by the same method as described above.

The experimental uncertainties are 3.1% for THCR, 5.3–5.5% for THFR [6, 8], and 6.8% for THNR in DU shell.

The experiment is simulated using the MCNP code with different evaluated data, including ENDF/B-VII.0, ENDF/B-VII.1, JENDL-4.0, and CENDL-3.1 [27]. The distributions of ²³²Th reaction rates from the experiments and calculations with ENDF/B-VII.0 are shown in Figure 8. The ranges of C/E ratios with ENDF/B-VII.0 are 0.97–1.04 for THCR and 0.95–1.02 for THFR [8, 12], respectively. The results show that calculations and experiments are well consistent within the range of experimental uncertainties. The ratio of ²³²Th capture to fission is about 6.71–12.23 with the increase of radius in DU shell.

The C/E ratios of ²³²Th reaction rates with different evaluated data are shown in Figure 9. The calculations for THNR overestimate the experiments. Meanwhile, large differences still exist in C/E of THNR. The range of C/E with ENDF/B-VII.0 is 1.07–1.12. Fractions with different energies in DU shell are calculated by using ENDF/B-VII.0, and neutrons of energy more than 6.5 MeV account for 4–9% in the whole energy range, as shown in Figure 5. Since U(n,f) cross sections are standard in the wide energy range, it is suggested that U inelastic cross sections and ²³²Th(n,2n) reaction cross sections should be studied further.

4.3 ²³²Th reaction rates in ThO₂ cylinders

4.3.1 ²³²Th fission and (n,2n) reaction rates in ThO₂ cylinder

The ThO₂ assembly for measuring ²³²Th reaction rates in three ThO₂ cylinders with the thickness of 150 mm (without DU cylinder) is shown in Figure 3. The ²³²Th fission and (n,2n) reaction rates are measured by the same method as described above.

The experimental uncertainties are 5.3–5.5% for THFR and 7.1% for THNR [9, 10].

The ²³²Th reaction rates are calculated by using MCNP code with ENDF/B-VII.0. The ranges of C/E are 0.77–0.91 for THFR, and 0.92–1.0 [12] for THNR, respectively. The results show that the calculations generally underestimate the experiments for THFR. The PEO influence on THFR is described below. The distributions of ²³²Th reaction rates by the experiments and calculations are shown in Figure 10.

4.3.2 ²³²Th fission rates in ThO₂/DU cylinders

Experimental and simulative studies of THFR are carried out on three sets of ThO₂/DU cylinder assemblies to validate the evaluated thorium fission cross section and code [9, 10]. The size of each ThO₂ cylinder and DU cylinder is ϕ300 × 50 mm. The ThO₂ cylinders with PEO contents of 7.28, 1.1, and 0.55% are named as number 1, number 2, and number 3, respectively. The DU cylinder is named as number 4. Three sets of cylinder assemblies are combined with different cylinders, and named as “3 + 2 + 1,” “4 + 2 + 1” (as shown in Figure 3) and “3 + 4 + 2 + 1” assembly, respectively.

THFR in the axial direction of the assemblies is obtained by using the activation method as described above, with experimental uncertainties about 5.6–5.9%.

THFRs are calculated by using MCNP code with ENDF/B-VII.0 and ENDF/B-VII.1. The calculations are 5–21% smaller than experimental ones, while the calculations with ENDF/B-VII.0 show better agreement with experimental ones. C/E distributions in the three assemblies are presented in Figure 11. The influence of the PEO in the ThO₂ cylinders is also evaluated by MCNP simulation employing ENDF/B-VII.0. The results show that the PEO influence on THFR under the measured level is negligible.

In order to gain more experimental results, it is necessary to design a new integral experiment employing thorium transport medium in which the ingredient is single and precisely known, and to determine THFR based on more kinds of fission products, as described below. The stage results could provide reference for the evaluation of neutron-induced thorium fission cross section, and the conceptual design margin of the subcritical blanket.

4.3.3 ²³²Th reaction rates in ThO₂ powder cylinder

The ThO₂ power cylinder assembly for measuring ²³²Th reaction rates is shown in Figure 4. The ²³²Th reaction rates are measured by the same method as described above.

The experimental uncertainties are 3.1% for THCR, 5.5% for THFR, and 7.0% for THNR in the ThO₂ powder cylinder.

The experiment is simulated by using the MCNP code with different evaluated data [10, 11]. The C/E ratio of ²³²Th reaction rates with ENDF/B-VII.0 are shown in Figure 12. The ranges of C/E ratio are 0.96–0.98 for THCR, 0.96–0.99 for THFR, and 0.74–0.76 for THNR. The results show that calculations and experiments for THCR and THFR are well consistent within the range of experimental uncertainties. The distributions of ²³²Th reaction rates in the experiments and calculations are shown in [13, 14, 15].

The calculations for THNR underestimate the experiments. Fractions with different energies in ThO₂ powder cylinder are calculated by using ENDF/B-VII.0, and neutrons of energy more than 6.5 MeV account for 62–72% in the whole energy range, which is the largest among the assemblies, as shown in Figure 5. The suggestion described above is that ²³²Th(n,2n) reaction cross sections should be studied further.

4.4 Breeding properties

4.4.1 Fuel breeding

The primary conversion rate is one of the important parameters in the conceptual design of subcritical blanket. The relative reaction rate ratio of ²³²Th capture to fission as the fissile production rate indicates fuel breeding in the fuel burn-up unit [12]. The ratios of ²³²Th capture to fission measured in PE shell, DU shell, and ThO₂ powder cylinder are obtained.

The ratios are about 10.76–20.17 with the increase in radius of the PE shell. It is demonstrated that the fuel breeding efficiency under the neutron spectra in the PE shell is quite high.

The ratios are about 6.71–12.23 with the increase in radius of the DU shell. It is demonstrated that the fuel breeding efficiency under the neutron spectra in DU shell is high.

The ratios are only about 0.11–0.19 with the increase in radius of the ThO₂ powder cylinder. It is demonstrated that the fuel breeding efficiency under the neutron spectra in ThO₂ powder cylinder is low.

The results show that the ratios are relevant to neutron spectra in the assemblies. The ratios in the three assemblies are compared and shown in Figure 13.

4.4.2 Neutron breeding

The bred neutrons from ²³²Th(n,2n) and ²³²Th(n,f) react with thorium or relevant nuclides to maintain the Th/U fuel cycle. THNRs in three assemblies, that is, under different neutron spectra, are compared and shown in Figure 14. The results show that the ²³²Th(n,2n) reaction rates are relevant to the fraction of high-energy neutrons in the assemblies as described above, and the decreasing trend of THNR with the increase in distance to the neutron source are similar for three assemblies.

Since ²³⁰Th half-life (7.54 × 10⁴ years) is very long, measurement of ²³²Th(n,3n) ²³⁰Th (with threshold of 11.6 MeV) reaction rate by the activation method is very difficult. The ²³²Th(n,4n) reaction has high threshold 19 MeV and is not involved in this work.

The prompt neutron and delayed neutron yields from ²³²Th(n,f) reaction are about 3.7 and 0.0265 per fission at 14.1 MeV [28], respectively. THFRs in three assemblies, that is, under different neutron spectra, are compared and shown in Figure 15. From Figures 14 and 15, THNRs are higher than THFRs in the three assemblies.

4.5 Leakage neutron spectra

Three assemblies consist of the ThO₂ cylinders with thicknesses of 50, 100, and 150 mm (without DU cylinder), respectively, as shown in Figure 3. The front surface of the assembly is 0.22 m from the center of a T-Ti target. The leakage neutron spectra are measured by using a 50.8 mm diameter and 50.8 mm length BC501A liquid scintillator coupled to a 50.8 mm diameter 9807B photomultiplier [16]. The distance from the detector to the neutron source is 10.75 m. The detector is at a 0° to the incident D⁺ beam and arranged in shielding room. The influence of background neutrons is negligible.

The leakage neutron spectra from the three assemblies are measured. The spectra are normalized to one source neutron and unit area. The experimental uncertainties are 9.7% for 0.5–1 MeV, 6.7% for 1–3 MeV, and 6.3% for 3–16 MeV. The experiments are calculated by using MCNP code with ENDF/B-VII.0. The results show that the experiments and calculations are generally consistent within the range of experimental uncertainties, and the spectra (<5 MeV) should be analyzed further, as shown in Figure 16.