A benchmark study of large-angle neutron scattering cross section of tungsten using two shadow bars technique at 14 MeV

. In fusion reactor design, neutron leaks intensively from blanket material through a gap. In this streaming phenomenon, backscattering cross section is known to be very crucial. In the present study, the author's team carried out a new experiment for benchmarking the large angle scattering cross section of tungsten using a DT neutron source of OKTAVIAN facility, Osaka University, Japan. Tungsten-containing material is under consideration as the radiation shield in a fusion reactor. The experimental geometry consists of a DT neutron source, two shadow bars, niobium foil, and a tungsten target. Four irradiations were performed at a neutron energy of 14 MeV using DT neutrons to extract only the contribution of large angle scattering cross section. By using two shadow bars, room return contribution was effectively suppressed. Consequently, only backscattering neutrons were measured by using a niobium foil. In the present benchmark study, obtained experimental data were compared with numerical calculations by MCNP6 using various nuclear data libraries, including JENDL-4.0, JENDL-5, JEFF-3.3, and ENDF/B-VIII.


Introduction
The challenging in ITER (International Thermonuclear Experimental Reactor) are due to the complicated structure of the blanket and the fact that it is bombarded strongly by generated DT neutrons. Leakage of a large amount of neutrons between the blanket materials must thus be anticipated. This neutron leakage considerably brings up material damage, gas production, and so on. Due to this issue, precise neutron transport through the gap in the blanket structural materials is crucial and it requires validation by the experimental benchmark study.
Previously, the accuracy of the benchmark experiment for neutron streaming/transportation was reported to be within 30% by Konno's experiment carried out for ITER design calculation [1]. The neutron streaming phenomenon was thought to dominantly be affected by back-scattering cross section, as proved in the DT beam neutron experiment for stainless steel by Ohnishi [2]. However, as is well known, only a few experimental studies related to this subject have been carried out in the past [3][4] due to the small reaction cross section, as shown in Fig.1, for instance.
For improving nuclear data, the present study examined the large angle scattering cross section experimentally by a new technique established in OKTAVIAN facility of Osaka University, Japan. Supported by the author's group, the two-shadow bars * Corresponding author: murata@see.eng.osaka-u.ac.jp technique was carried out in the benchmark experiment to examine a large-angle scattering reaction cross section at neutron energy of 14 MeV. Experiments were initially performed for iron [5][6]. Furthermore, a similar method was applied to tungsten.

Experimental method
An experimental room in OKTAVIAN facility is surrounded by a wall of 1 m thickness, in which high energy (14 MeV) neutrons are generated isotopically by a deuteron tritium (DT) reaction. Source neutrons spread till 55 cm distant from the source to the left base of the shadow bar, as seen in Fig. 2. It means, not only the target but also the wall and shadow bar were irradiated for 8 hours with neutrons, and the intensity of which is around 10 9 − 10 10 n/sec.
We used a cylindrical tungsten target having dimensions of 15 cm in diameter and 6 cm in thickness. The thickness of the tungsten target should be as thin as possible, because the number of multiple scattering reactions can be suppressed substantially. It is appropriate to employ around two mean free paths that make the contribution of one-time large angle scattering reaction dominant inside the target, keeping enough activity. As seen in Fig. 2, a shadow bar is a truncated cone shape made by iron that has a length of 50 cm. It is set up to suppress neutrons directly entering into the niobium foil set just behind the shadow bar, which can detect backscattered neutrons from the target. In order to extract only the backscattering neutrons, our research group developed a new benchmark method. This is called "two shadow bars technique" with two different diameters. Firstly, using a thin shadow bar (S1) with diameters of 2 and 3 cm for both sides respectively, the contribution of the large angle scattered neutrons is measured. Meanwhile, a thick shadow bar (S2) has 8.3 and 15 cm, respectively, to measure the contribution of the roomreturn neutrons, as shown in Fig. 3. In the tungsten benchmark study, niobium is employed as a activation foil due to its high threshold energy of 93 ( , ′ ) 92 reaction around 9.06 MeV and a high reaction cross section of 0.448 barn at 14 MeV. The crucial point is that niobium can measure neutrons only if the energy is beyond the threshold energy of 9 MeV [6].
Niobium foil dimensions are 5 mm in thickness and 3 cm in diameter, and the foil is positioned on the edge of the shadow bar close to target, as seen in Fig. 2. Only the scattered neutrons from tungsten can activate a niobium foil, and after the irradiation the induced radioactivity is measured by a Ge detector.

Simulation procedure
Four experimental irradiation systems in the benchmark study were numerically analysed by calculations with MCNP6 [12]. They correspond to two sizes of shadow bars (S1 and S2), and with target (TC) and without target (C).
The four systems are symbolized by S1TC (thin SB with target), S2TC (thick SB with target), S1C (thin SB without target), and S2C (thick SB without target). To consider the neutron transport paths in MCNP6 calculations, 3 flags (wall, shadow bar, and target) are set to reproduce all the neutron pathways as the total combination of 7 paths ( = 3C1 + 3C2 + 3C3). The details of the paths are described in Table 1 and Fig. 4.  These 7 paths can be applied to solid targets. Conversely, for liquid or flake targets, more than 7 paths should be required because they need a casing [13]. By subtracting all unwanted neutron path contributions, an extracted neutron path contribution of only from the target is given in path ③, expressed by CP in Eq. (1). The detail is given below.

S1TC -S2TC -(S1C -S2C) = CP
The detailed result will be given in the next section, however, for understanding each path contribution, we refer to Tables 2-5 in advance, which show calculated path contributions of neutrons passing through flagged cells in the tungsten (W) target. In path ①, neutrons pass only through the shadow bar, the contribution of which is determined only by the size of the shadow bar, not the size of the target. It shows that the neutron contributions are equal between S1TC and S1C, and S2TC and S2C. By subtraction of Eq. (1), the total reaction rate is completely disappeared. It is also the case for path ④ and ⑥. Neutrons pass only through the wall and shadow bar (path ④) and only the wall (path ⑥). Both are irrespective of the target.
In another case, neutrons in path ⑤ pass only through the wall and target, depending on the target's existence. Thus, it mostly disappears due to the equal value of S1TC and S2TC, and S1C and S2C. Consequently, the total reaction rate can be cancelled out. Oppositely, paths ② and ⑦ cannot be cancelled out easily due to not only depending on the shadow bar size but also on the target existence. However, fortunately, this path has a small contribution, so that it can be regarded as an experimental error. Finally, only path ③ contribution can be extracted from Eq. (1). This path includes neutrons that pass only through the target. Moreover, in case of without target (S1C and S2C) system, the reaction rates in paths ⑤ and ⑦ are non-zero due to the dominant wall contribution in the neutron scattering calculations. Compared to the path ②, the neutron passes through SB and the target has a zero value of S1C and S2C.  PATH S1TC S2TC S1C S2C S1TC-S2TC-(S1C-S2C) As mentioned in section 3, paths ①, ④, and ⑥ have the same value in S1TC and S1C (green), and S2TC and S2C (blue). Meanwhile, path ⑤ has almost the same value depending on the target's existence, between S1TC and S1C (grey), and S2TC and S2C (pink). It is noted additionally that the path's value of 0.00 is a decimal number less than 5 × 10 −12 , meaning that it has a small contribution to the reaction rate, and so that it is treated as zero. On the other hand, the value, 0, means the path is physically impossible and the value is really zero. Table 6 summarizes measured niobium activities compared to computational calculation results among four nuclear data libraries. S1TC-S2TC-(S1C-S2C) shows path ③, i.e., the backscattering contribution from the target. At first, we found the tendency of reaction rate among nuclear data libraries could be accounted for consistently as shown in Fig. 1. From the comparison result of simulation and experimental data, the tendency is found to underestimate the simulation data of all four data libraries compared to the experimental data. Recently released JENDL-5 shows better result instead of JENDL-4.0 and ENDF-B/VIII.0. Meanwhile, JEFF-3.3 shows the best result among data libraries, ~29% smaller than the experimental value, as shown in the table 6.  [14]. From the measured DDX, the angular differential cross sections (ADX) can easily be deduced as shown in Fig. 5.   5 shows consistency of Takahashi's ADX data with the present data seen in Table 6. It turns out to be excellent authentic data for verifying that the two shadow bars technique is an appropriate method to extract large angle scattering reaction cross section of tungsten.

Conclusion
Benchmark experiments of large angle scattering reaction cross section of tungsten were performed in OKTAVIAN facility with the two shadow bars technique. It was found that JENDL-4.0, JENDL-5, and JEFF-3.3 showed ~30% smaller than the experimental reaction rate value, while ENDF-B/VIII.0 shows a significantly smaller value (~1/3 of the experimental result). In addition, the present data confirmed the consistency of Takahashi's ADX data. In conclusion, our new method by using the two shadow bars technique was confirmed to work appropriately in examining the large angle scattering cross sections.