The neutron source

The D-T fusion neutron source was used in this experiment. Deuterium ions were accelerated using a high-pressure multiplier to achieve an energy of 300 keV, with the accelerator operating at a pulse frequency of 1.5 MHz and a beam current of 20 μA. The beam spot size was approximately 5–10 mm. These ions were then bombarded on a T-Ti target. The T-Ti target had a T/Ti ratio of approximately 1.6, with a reactive layer thickness of 1300 μg/cm². Neutrons with energies centered around 14.5 MeV were generated through the T(d, n)⁴He reaction. The neutron yield was approximately $1\times {10}^9\text{neutrons/s}$.

The measurement platform

The integral experiment platform, illustrated in Fig. 2, is composed of a neutron source, sample stage with precise positioning capabilities, sophisticated collimation system, suite of detectors, and digital data acquisition setup. To enhance the accuracy of neutron leakage measurements and effectively suppress background noise from environmental scattering, the main detector was strategically located in an adjacent hall. This strategic placement, combined with a multi-layer collimation system, ensures that the majority of the neutrons reaching the detector originate from the sample, thereby maximizing the local effect-to-background ratio.

The ⁹Be Sample

In the shielding integral experiment, the higher the purity of the sample, the better the test results obtained. The purity of the ⁹Be sample used in this experiment was 99.24%. Two disc-shaped samples with a diameter of 30 cm and thicknesses of 4.4 cm and 8.8 cm were customized and processed by the Northwest Rare Metal Materials Research Institute. A thickness of 13.2 cm was achieved by combining the two samples. Table 1 lists the specific sizes and parameters of the ⁹Be samples.

In the experiment, the positions of the neutron source and detector remained stationary, and angle variation was accomplished by moving the sample position, as depicted in Fig. 3. Keeping the direction of the outgoing neutron (from the sample center to the detector) fixed, modifying the position of the sample center on the quasi-line alters the direction of the incoming neutron (from the neutron source to the sample), thereby achieving a change in the angle between the incoming and outgoing neutrons. The leakage neutron spectra of ⁹Be samples were measured at six angles: 47°, 58°, 73°, 107°, 122°, and 133°. The three pairs of symmetric angles (47° and 133°, 58° and 122°, 73° and 107°) have identical angles between the incident neutron and D beam.

Fig. 3Full-screen View

Schematic diagram of measurement angle with ⁹Be sample

The collimation and shielding system

As shown in Fig. 2, the structure of the entire experimental hall is complex, resulting in a high scattering neutron background. The adoption of the collimator system effectively reduces the scattering background entering the detector. A collimator system consisting of a pre-collimator and a wall collimator was used in this experiment.

In the pre-collimator system, source neutrons may directly enter the collimator hole, scatter with the inner wall material, and be detected by the detector, thereby contributing to the background. To minimize this background, a set of copper shadow cones was employed in the pre-collimator system to block the direct entry of source neutrons into the collimator.

Figure 4 illustrates the effect spectrum and background spectrum of the ⁹Be sample with a thickness of 4.4 cm at 47°. As shown, for most experimental points, the effect-to-background ratio is greater than 10, demonstrating that the entire collimator system effectively suppresses the scattering neutron background.

Fig. 4Full-screen View

The TOF spectra from ⁹Be sample (4.4 cm) at 47° measured with sample in and sample out

The detector and data acquisition system

The spectrum of leaking neutrons was measured by TOF method in this experiment, corresponding to neutrons with energies above 0.8 MeV hitting the detector. A schematic of the detector and data acquisition system is shown in Fig. 5. Four detectors were used in the experiment: a 2 inch×2 inch EJ-301 liquid scintillation detector was used as the main detector to measure the TOF spectrum of the leaking neutron at different angles after the interaction of the neutron with the ⁹Be sample; two 0.5 inch×0.5 inch EJ-301 liquid scintillation detectors were used as monitors to directly measure the TOF spectrum of source neutrons and obtain the pulse time distribution; and a Si-C detector acted as an adjoint particle detector to measure the neutron yield of the source [34, 35]. In addition, there is a copper ring in the pipeline in front of the target. When the D ion beam generated by the ion source accelerated through the accelerator and passed through the copper ring, an induced charge was generated on the copper ring to form a pick-up signal, which was sent to the acquisition card after a fast preamplifier as the time signal of neutron generation.

Fig. 5Full-screen View

An electronic system for measuring TOF spectra in shielding integral experiment

A digital acquisition system was employed for data acquisition. Regarding hardware, a Pixie-16 acquisition card manufactured by XIA Corporation of the United States was utilized, and in terms of software, general acquisition software developed by the Experimental Nuclear Physics Group of Peking University was adopted [36]. The logic of the entire data acquisition process is shown in Fig. 5. Both the main detector signal and the two monitor signals were self-triggered. After the signal of any detector is triggered, a trigger signal is sent to the channel where the pick-up signal is located, and the channel collects and records the pick-up signal within 700 ns after receiving the trigger signal.

For every neutron produced by the T(d, n)⁴He reaction, an alpha particle is also produced in the opposite direction of the center of mass system. Therefore, the number of neutrons produced by the fusion reaction, known as neutron yield, can be deduced by measuring the number of alpha particles produced. The advantage of this method is that the detection efficiency of the semiconductor detector used in the measurement is basically 100%, the measurement accuracy is high, and absolute measurement can be achieved. Because the noise of the detector is restricted to the low-energy region and the counting rate ratio of alpha particles to noise exceeds 500, while the amplitude ratio is approximately 3, the plateau effect from scattered neutrons is negligible. The processed counting rates, representing the net peak counts after plateau subtraction, ensure accurate neutron yield estimation.Therefore, the Si-C detector was used to measure the alpha particles produced by the D-T fusion reaction.

The alpha particles produced by T(d, n)⁴He were measured using a Si-C detector at 135°, and the normalization coefficient was calculated. The neutron flux obtained in the unit solid angle in direction θ can be expressed by the following formula: ${\text{Φ}}_{\text{n}}\left(\theta \mathrm{,}{E}_{\text{d}}\right)=\frac{N_{\alpha }}{\text{Δ}{\text{Ω}}_{\alpha }}{A}_{\alpha }，$ (1) $A_{\alpha }=\frac{{\left(\frac{\text{d}\omega }{\text{d}{\omega }^{\prime }}\right)}_{\alpha }}{{\left(\frac{\text{d}\omega }{\text{d}{\omega }^{\prime }}\right)}_{\text{n}}}，$ (2) $\text{Δ}{\text{Ω}}_{\alpha }=\frac{\pi r^2}{R^2}\mathrm{,}$ (3) where $\text{Δ}{\text{Ω}}_{\alpha }$ is the solid angle between the Si-C detector and the D-T target. r is the beam limiting radius (0.16 cm); R is the distance between the detector and the beam limiting bar (90 cm); To calculate A_α (1.263), Eq. (2) is used, where ${\left(\frac{\text{d}\omega }{\text{d}{\omega }^{\prime }}\right)}_{\alpha }=1.19201$ and ${\left(\frac{\text{d}\omega }{\text{d}{\omega }^{\prime }}\right)}_{\text{n}}=0.943847$, determined based on an average deuteron energy (E_d) of 147 keV and an alpha particle emission angle of 135. These foundational values are derived from an internal technical document, which is not publicly accessible. However, key numerical parameters and calculation processes were included to ensure transparency and reproducibility. T(d, n)⁴He reaction neutron yield N_n and neutron flux Φ_n can be expressed as $\frac{{\text{Φ}}_n\left(\theta \mathrm{,}{E}_{\text{d}}\right)}{N_{\text{n}}}=\frac{\sigma (\theta )}{{\sigma }_{\text{tot}}}\mathrm{,}$ (4) where σ_tot is the total cross-section of T(d, n)⁴He reaction (3.984 b), σθ is the differential cross-section of T(d, n)⁴He reaction at θ (0.336 b at 0°). Finally, by substituting Eqs. (1), (2) and (3) into Eq. (4), the following can be obtained: $\frac{N_{\text{n}}}{N_{\alpha }}=\frac{A_{\alpha }{R}^2{\sigma }_{\text{tot}}}{\pi r^2\sigma (\theta )}=\frac{1.263\times {90}^2\times 3.984}{\pi \times {0.1565}^2\times 0.336}=1.576\times {10}^6\mathrm{,}$ (5) That is, for every alpha particle measured by the Si-C detector, a total of 1.576 × 10⁶ neutrons were generated in the entire space.

Calculation of source neutron energy and angular flux distribution

An accurate description of the energy spectrum and angular distribution of neutron sources is necessary for obtaining reliable simulation results. Owing to the complex environment of the experimental hall, it is difficult to eliminate the influence of the scattering neutron background on the experimental measurement results, which makes it challenging to measure the energy spectrum and angular flux distribution of the D-T neutron source through experiments. Therefore, a Monte Carlo simulation method was adopted in this study to obtain the energy spectrum and angular flux distribution of the D-T neutron source. The simulation was performed using the TARGET program [38] developed by the PTB Laboratory in Germany, considering the target structure parameters, material data, and incident beam parameters of the D-T neutron source. The calculated results are shown in Fig. 6. The neutron energy generated by the T(d, n)⁴He reaction gradually decreased with an increase in the angle, and the flux gradually decreased as the angle increased.

Fig. 6Full-screen View

(Color online) The angle-dependent energy distribution of the source neutrons

To verify the reliability of the simulation results, the angular flux of the neutron source is measured at several specific angles. A comparison between the measurement and simulation results is shown in Fig. 7, and the results indicates that the measurement results are in good agreement with the simulation results.

Fig. 7Full-screen View

A comparison of angular distribution between measurement and calculation

In the D-T neutron source, deuterium deposition on the target inevitably leads to D-D reactions. The counting rates of the accompanying particles from both reactions were measured using a SiC detector. In the simulations, we also included the neutron energy spectrum generated by the D-D reaction in the source term. However, its impact remains minimal, contributing only to 1.2% increase in the total flux detected by the main detector. This is primarily because the target is regularly replaced as the alpha counting rate from the D-T reaction decreases, thereby limiting the influence of the D-D reactions.

Calculation of source neutron pulse time distribution

The pulse time distribution of the source neutron was obtained by the Maximum Likelihood Expectation-Maximization (MLEM) solution spectrum using the source neutron time-of-flight spectrum measured by two monitors. The specific process is described in detail in Ref. [39].

Calculation of detector efficiency curve

The efficiency curve of the liquid detector was obtained using the NEFF program [40], which was developed by the German PTB laboratory. The geometric parameters of the detector crystal, the standard light response curve, and the energy threshold were considered in the calculations. Additionally, the absolute efficiency value of the detector was calibrated using 14.1 MeV neutrons generated by the D-T reaction. The calibration results were in good agreement with the theoretical calculation results, as shown in Fig. 8.

Fig. 8Full-screen View

A comparison of the simulation results from the NEFF code and the absolute efficiency points calibrated by monoenergetic neutrons

Simulation of ⁹Be leakage neutron spectrum

In the input card of MCNP-4C, the obtained neutron energy spectrum distribution, angular flux distribution, pulse time distribution, and liquid scintillator detector efficiency curve were described in detail to ensure accurate simulation results. In addition, the simulation model was simplified, and materials with little influence on the leakage neutron spectrum, such as the floor and walls of the hall, were discarded. Structures with a significant influence were retained, including the target structure, sample, shadow cone, pre-collimator, and wall collimator.

As shown in Fig. 9, the entire neutron transport model was simplified into a cylinder with a diameter of 1.5 m, and the target structure, collimator, and sample were modeled based on their actual structure and size. This model was used to simulate the leakage neutron TOF spectra at various angles. To simulate the background, the material of the sample was changed to air. The evaluated nuclear data of ⁹Be from the CENDL-3.2, ENDF/B-VIII.0, JENDL-5, and JEFF-3.3 libraries were adopted in the simulation, whereas the nuclear data of all other structural materials were obtained from ENDF/B-VIII.0 library.

Fig. 9Full-screen View

(Color online) A 3D model used for simulation by the MCNP code

The TOF spectra comparison between simulation results and experimental results

The experimental measurement results of the leakage neutron TOF spectrum after data processing were compared with the simulation results from the different libraries, as shown in Fig. 14.

Fig. 14Full-screen View

(Color online) Comparison of TOF spectra with simulation results and experimental results from different thickness ⁹Be samples

From the comparison of leakage neutron spectra, it is clear that:

1. The simulation results of the CENDL-3.2 library were higher than the experimental results between 200 ns–300 ns at small angles (47°, 58°, and 72°).

2. The simulation results of the JEFF-3.3 library were significantly lower than the experimental results at all angles of approximately 250 ns, especially in the direction of large angles (greater than 90°).

3. At large angles, especially 122° and 133°, the simulation results of each library were lower than the experimental results between 400 ns–600 ns.

Change of C/E value with flight time

By dividing the simulation results of the CENDL-3.2 library by the experimental results, the change in the C/E value with the flight time was obtained, as shown in Fig. 15. As can be seen from the figure, the simulation results of the CENDL-3.2 library in the range of 180–280 ns are higher than the experimental results, but lower than the experimental results in the range of 280–400 ns. At large angles, the simulation results were significantly lower than the experimental results in the range of 350–550 ns.

Fig. 15Full-screen View

(Color online) Calculation of C/E values for a single time-of-flight point in the CENDL-3.2 library

By dividing the simulation results of ENDF/B-VIII.0 library based on the experimental results, the results obtained are shown in Fig. 16. As can be seen, the C/E value of the ENDF/B-VIII.0 library decreases with an increase in flight time (energy decrease), and is higher in the high-energy region, while it is slightly lower in the low-energy region. This phenomenon becomes more obvious with an increase in angle and improves with an increase in the sample thickness.

Fig. 16Full-screen View

(Color online) Calculation of C/E values for a single time-of-flight point in the ENDF/B-VIII.0 library

The results obtained by dividing the simulation results of the JENDL-5 library by the experimental results are shown in Fig. 17. The trend of C/E values in the JENDL-5 library was generally the same as that in ENDF/B-VIII.0 library, where the simulation results were higher in the high-energy region and lower in the low-energy region.

Fig. 17Full-screen View

Calculation of C/E values for a single time-of-flight point in the JENDL-5 library

By dividing the simulation results of the JEFF-3.3 library by the experimental results, the results obtained are shown in Fig. 18. It can be seen that the simulation results of the JEFF-3.3 library are generally lower than the experimental results.

Fig. 18Full-screen View

(Color online) Calculation of C/E values for a single time-of-flight point in the JEFF-3.3 library

Comparison and analysis of C/E values in different energy regions

The NDPlot program was used to obtain the outgoing neutron spectra of 14.5 MeV neutrons in the CENDL-3.2 library at different angles after interaction with ⁹Be samples, and the results are shown in Fig. 19. The choice of 14.5 MeV neutrons corresponds to the average energy of neutrons at forward angles in the D-T reaction, making it representative for cross-sectional analysis. It can be observed that the outgoing neutron has only two reaction channels: elastic scattering and the (n, 2n) reaction. Owing to the relatively light mass of Be, the elastic scattering neutron energy generated by the interaction between neutrons and Be decreased significantly with an increase in the exit angle.

Fig. 19Full-screen View

(Color online) Double differential spectrum of 14.5 MeV neutron incident ⁹Be sample given by CENDL-3.2 library

Therefore, the secondary neutrons at each angle are first divided into elastic scattering and (n, 2n) reaction energy regions according to the outgoing neutron energy. Considering the actual pulse width of the pulsed neutron beam, the elastic scattering peak is about ±10 ns (approximately 1/10th of the bottom width of the pulse time distribution). Additionally, according to the shape of the neutron energy spectrum derived from the (n, 2n) reaction in Fig. 19, the (n, 2n) emitted neutron spectrum is further subdivided into two energy regions, namely:

1. (n, 2n) reaction high-energy region, corresponding to the tail of the elastic scattering peak to the 2.8 MeV energy region;

2. (n, 2n) reaction low-energy region, corresponding to 2.8 MeV to the detector measurement threshold of 0.8 MeV energy region.

The integral comparison of the experimental and simulated results across different energy ranges yields the C/E values listed in Table 3.

Trends of C/E Values Across Different Energy Ranges with Angle and Thickness Variation

The trends of the C/E values for different energy ranges in various databases as a function of the angle and thickness are shown in Figs. 20 and 21. From these figures, we can observe the following.

Fig. 20Full-screen View

(Color online) The trend of C/E values of different reactions changing with angle

Fig. 21Full-screen View

(Color online) The trend of C/E values varying with thickness in different reactions

1. The C/E values from the JEFF-3.3 database were significantly lower than those from the other three databases, and were generally less than 1. This was particularly evident in the (n, 2n) energy range at larger angles, where the C/E values were consistently below 0.9.

2. In the elastic scattering energy range, all four databases show a marked decrease in the C/E values as the angle increases. At angles of 47 and 58, the C/E values were approximately 1.1, while at 122 and 133, they decreased to approximately 0.85. The C/E values from ENDF/B-VIII.0 database were slightly higher than those from the other three databases. At smaller angles of 47, 58, and 73, the C/E values for all databases exhibited a gradual increase with increasing thickness, whereas at larger angles (107, 122, and 133), the C/E values remained relatively constant with respect to thickness.

3. For the CENDL-3.2, ENDF/B-VIII.0, and JENDL-5 databases, the C/E values in the high-energy region of the (n, 2n) outgoing neutron spectrum were greater than 1 at small angles and increased with the thickness. At larger angles, the C/E values approached 1 with minimal changes as the thickness increased. In the low-energy region of the (n, 2n) outgoing neutron spectrum, the C/E values were close to 1 at small angles but less than 1 at larger angles, with a slight increase observed as the thickness increased. Among these databases, the CENDL-3.2 database shows the most pronounced variation in C/E values with angle, with the highest values at small angles and the lowest at large angles.

Result Analysis

To analyze the large deviations in the C/E values described above, the NDplot program was used to extract and compare relevant ⁹Be data from the CENDL-3.2, ENDF/B-VIII.0, JENDL-5, and JEFF-3.3 databases.

1. The (n, 2n) reaction cross-section curves from all four databases were extracted and compared, as shown in Fig. 22. In the JEFF-3.3 database, the (n, 2n) reaction cross-section was derived by summing the cross-sections of the 16 reaction channels (MT = 875 to 890). It is apparent that the (n, 2n) cross-section in JEFF-3.3 is significantly lower than those of the other databases around 14.5 MeV. At this energy point, the cross-section values extracted from the CENDL-3.2, ENDF/B-VIII.0, JENDL-5, and JEFF-3.3 databases are 0.4783 b, 0.4783 b, 0.4760 b, and 0.4424 b, respectively. The cross-section value for JEFF-3.3 is more than 7% lower than those of the other three databases, which is likely the main reason for the significant deviation between the simulation results and experimental data for JEFF-3.3.

Fig. 22Full-screen View

(Color online) The cross section of ⁹Be(n, 2n) reaction from different nuclear data libraries

2. The elastic scattering angle distributions for neutrons interacting with ⁹Be at 14.5 MeV were also extracted and compared for the four databases, as shown in Fig. 23. Overall, the evaluated databases tend to overestimate the differential cross-sections at smaller angles (47°, 58°, and 73°), and underestimate them as the angle increases. At smaller angles, the differential cross-section deviations for all four databases are relatively small and consistently higher than the experimental data. At 107, the ENDF/B-VIII.0 and JENDL-5 databases predict larger differential cross-sections compared to CENDL-3.2 and JEFF-3.3. At 122° and 133°, the values from all four databases are closely aligned. However, at larger angles, particularly at 133°, all databases significantly underestimate the differential cross-section, as shown by comparisons with experimental data from the EXFOR database.

Fig. 23Full-screen View

(Color online) The distribution of ⁹Be(n, el) reaction from different nuclear data libraries