1 Introduction

The neutron radiation environment in space is complex, and the neutron energy is complicated which is ranging from eV to GeV [1, 2]. Currently, a multi-sphere neutron spectrometer is mainly used to monitor the neutron dose equivalent (rate). The multi-sphere neutron spectrometer, also called Bonner ball, was proposed by Bonner in 1960 [3]. Due to its low resolution, but wide measurement range, isotropy, and easy measurement, so it is often used for neutron spectrum measurement [4,5,6,7,8]. Conventional multi-sphere neutron spectrometers are more sensitive to neutrons with energy below 20 MeV and have almost no response to neutrons with energy above 20 MeV. Therefore, high-energy neutrons may cause dose underestimation [9,10,11]. Birattri developed the LINUS meter, enabling it to be used for neutron radiation field measurements at 400 MeV. Afterward, the researchers improved the structure of the instrument and designed single-ball multi-count neutron spectrometers, rotating multi-sphere neutron spectrometers, and use water and boric acid as moderating materials for the neutron spectrometer [12,13,14,15,16]. But these multi-sphere neutron spectrometers all have certain problems such as a large number of slowing balls, inconvenient to carry, and possible ball interference in the measurement process [17, 18]. Therefore, for the conventional multi-sphere neutron spectrometer, our team designed a pumped water multi-sphere neutron spectrometer [19,20,21,22,23,24]. The aim is to solve the problem of the low sensitivity of high-energy neutrons, and to solve problems such as ball interference, making it more portable.

The pumped water multi-layer concentric neutron spectrometer uses 304 stainless steel as the casing material of the detector which will cause some problems. For example, stainless steel material leads to mass increase and the response function is not solved accurately. Therefore, the focus of this paper is to study the influence of stainless steel shell on the detector response function, and to find a more excellent shell material to improve the accuracy of the detector measurement of pum** and injecting multilayer concentric spherical neutron spectrometer.

2 Materials and methods

2.1 Water-injection multi-sphere neutron spectrometer

The structure of the pumped water multi-layer concentric neutron spectrometer is shown in Fig. 1 [19,20,21,23,24]. The overall structure of the spectrometer is a multi-layer concentric spherical shell made of 304 stainless steel with a maximum diameter of 45.6 cm, and the thickness of each layer of 304 stainless steel is 3 mm. A 2705 type 3He proportional counter (Built-in air pressure of 10 atmospheres) manufactured by LND company is placed in the center. By pum** 5 water layers, 32 kinds of water layer thickness variation schemes can be designed. According to the difference of the neutron moderating ability of different water layer thicknesses, the relationship between the counting rate response of the thermal neutron detector and the neutron energy spectrum was analyzed to obtain the incident neutron energy spectrum. In addition, in order to measure high-energy neutrons, a layer of lead auxiliary material has been added to the spectrometer. The water layer combination method uses binary for mnemonic, 1 means there is water and 0 means no water. For example: 10Pb010 indicates that the first and the fourth layers have water, Pb means the lead layer, and the other layers are empty. The minimum mass of the spectrometer is 53.79 kg (no water) and the maximum mass is 97.64 kg (full water).

Fig. 1
figure 1

Pum** water-type multi-layer concentric neutron spectrometer model

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2.2 Calculation of response function of pumped water multi-layer concentric neutron spectrometer

The size of the neutron surface source directly affects the calculation of the response function of the pumped water multi-layer concentric neutron spectrometer. So when calculating the neutron energy response function of the detector, it is assumed that the incident neutron beam is a parallel single energy beam, and the cross-section is circular. For a moderator layer combined with a diameter d cm of the outermost moderator material, a 3He proportional counter with a volume of the V is placed in the center, then the formula for the fluence energy response of the moderator layer combination is [25]:

$$R_{d} (E) = \frac{M}{{\Phi (E)}}$$
(1)

In the formula, \(R_{d} (E)\) is the response function when the maximum diameter of the moderator combination is d cm, M is the neutron detector count and \(\Phi (E)\) is the neutron fluence with energy E. When using FLUKA to calculate the response function of the detector, assuming that the protons generated in the 3He sensitive volume are all recorded. Using the RESNUCLEi card to record the number of P(proton) or T(tritium) produced by the 3He (n, p) T reaction in the 3He sensitive volume, that is The corresponding energy response value can be obtained [8]:

(2)

The response function of 18 water layers is calculated, as shown in Fig. 2. The results showed that, for water layer combinations of 00Pb000, 01Pb000, 10Pb000, 11Pb00, there is a peak in the 10−2–10−1 MeV interval.

Fig. 2
figure 2

Pum** water multi-layer concentric neutron spectrometer response function (18 water layer combinations)

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2.3 Sandwich structure and double layer structure model

For the response function of a multi-layer concentric spherical neutron spectrometer with pum** water, the peak value exists at 10−2–10−1 MeV, the FLUKA program was used to simulate the effect of different metal materials on the neutron fluence energy response under different thickness. The simulation model is shown in Fig. 3: (a) is a 3He spherical proportional counter in the center of the sandwich structure, 3 cm thick water layer, 1 cm metal material (lead, stainless steel, aluminum), 2 cm thick water layer; (b) is a double-layer structure with a variable thickness of the water layer and auxiliary materials.

Fig. 3
figure 3

A simulated structure of the effects of metallic materials on neutrons: a sandwich structure; b double layer structure

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3 Results and discussion

3.1 Influence of sandwich combinations

According to the model in Fig. 3a, the influence of 304 stainless steel (SS), Pb, Lead Glass, Al and Al2O3 as auxiliary materials on the response function of the thermal neutron detector is simulated using FLUKA as shown in Fig. 4. In Fig. 4, when the neutron energy is 10−8–10 MeV, Pb and Lead Glass as an auxiliary material does no effect on the response of the thermal neutron detector with the increase of thickness. With the increase of Pb thickness in the energy range of 10 MeV–1 GeV, the neutron fluence energy response of the thermal neutron detector gradually increases. The main reason is that inelastic scattering is mainly after 10 MeV, while the elastic scattering of lead is very low before 10 MeV. For stainless steel as auxiliary materials, the neutron injection response of the thermal neutron detector in the energy range of 10−8–1 MeV gradually decreases with the increase of thickness, but it gradually increases in the energy range of 10–1 GeV. But neither Al nor Al2O3 affects the detector’s response function.

Fig. 4
figure 4

Effect of Pb, stainless steel (SS), lead glass, Al and Al2O3 as auxiliary materials on the response of neutron detectors

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3.2 The effect of the two-layer combination

According to Fig. 3b model, FLUKA was used to simulate the influence of the thickness of the lower water layer and the auxiliary material on the detector response function. The simulation results are shown in Fig. 5. Under the double-layer combination, when the auxiliary material is stainless steel, the response function of the central thermal neutron detector has a peak value when the middle energy is 10−2–1 MeV, no matter the thickness of the water layer or the thickness of the stainless steel increases. When the auxiliary material is Pb and Lead Glass, no matter how the water layer changes, the response function of the thermal neutron detector is always in the smooth phase throughout the energy range (10−8–103 MeV), and no breakpoint appears. Therefore, the stainless steel under the double-layer combination will not only reduce the response function of the thermal neutron detector in the energy range of 10−8–10−2 MeV, but also cause the phenomenon of the response function to increase in the energy range of 10−2–1 MeV. But Al and Al2O3 have no effect on the detector response function.

Fig. 5
figure 5

Effect of thickness change of the water layer and auxiliary material thickness on the detector response under double-layer structure

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3.3 Improved response function of pumped water multilayer concentric neutron spectrometer

According to the structural model of the detector in Fig. 1, the response function of the detector was simulated when the stainless steel shell was replaced with aluminum and lead glass by the pumped water multi-sphere neutron spectrometer. As shown in Fig. 6, compared to stainless steel, aluminum and lead glass to improve the detector response function between 10−8 and 1 MeV. The response function of the aluminum shell has a small peak in the range of 10−2–10−1 MeV, but it is greatly reduced compared to the stainless steel shell; the lead glass shell has basically no peak in the energy range of 10−2–10−1 MeV, and the lead glass has a detector response between 10 MeV and 1 GeV slightly higher than the case due to the lead content in the lead glass.

Fig. 6
figure 6

Response function of pumped water multi-sphere neutron spectrometer after changing spherical shell

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4 Conclusion

In this paper, the effects of aluminum, aluminum oxide, lead glass, 304 stainless steel, and their constituent materials on the response function of the 3He detector are simulated by Monte Carlo methods. The following main conclusions are drawn:

  1. 1.

    Aluminum and aluminum oxide do not affect the response function of the detector under the double-layer combination and sandwich combination, while lead glass only increases the detector’s response function value to high-energy neutrons.

  2. 2.

    Aluminum, aluminum oxide and lead glass as the shell of the multi-layer concentric sphere neutron spectrometer pumped with water will make the response function of the detector smoothly, thereby making its energy spectrum measurement more accurate.

  3. 3.

    304 stainless steel and its constituent materials will make the detector response function step-like under the double-layer combination, and its value will be affected under the sandwich combination, which mainly manifests as the value decreases in the energy range of 1 eV–1 MeV. And in the energy range of 10 MeV–1 GeV, the internal value increases.

  4. 4.

    Two improvement directions are provided for the pumped and injected multi-layer concentric spherical neutron spectrometer in the future, aluminum shell is used to replace the stainless steel shell as the supporting material, and the built-in structure of the spectrometer does not change.