1 Introduction

According to the definition of the International Atomic Energy Agency (IAEA), radiation protection can be defined as “the protection of people from harmful effects of exposure to ionizing radiation and the means for achieving this” [1]. When using ionizing radiation, it is necessary to ensure that the radiation burden on the personnel is as low as reasonably achievable, without exceeding the exposure limits. This principle is called ALARA (as low as reasonably achievable), and it can be achieved in three ways: by time, by distance and by shielding. The first two ways are obvious, however, using shielding materials is not always trivial, because the effectiveness of different materials as shielding depends on the type and energy of the source of radiation. Alpha and beta particles are easy to be protected from, however, shielding against neutron and gamma radiations is a more complex task. In general, light materials have good properties for shielding neutrons and heavy materials are good against photons. The production of neutrons is usually accompanied with the production of secondary photons as well, therefore, the selection of shielding materials should be a compromise. As sources of neutron and gamma radiation are used in more and more areas of research, development, industry and medicine, new shielding materials are developed, which are usually optimized for the given application. Concrete has been used as a proper neutron shielding material for decades. Recently also special types of radiation shielding concrete with alternate constituents [2] and fibre-reinforced concrete materials containing nano—TiO2 [3] have been developed. The later one serves as a combined neutron—gamma shielding material. To effectively protect against both neutron and gamma radiation, there exist also foam metal matrix composites [4] combining W and B4C or glasses containing Gd2O3 [5] or B2O3 [6]. Due to their low atomic weight plastic composite materials can also serve for shielding, such as the polypropylene composite containing colemanite, tincal and ulexite, which were investigated in [7]. As for the Slovak university of technology, there is a significant experience of using NEUTRONSTOP [8], which is high-density polyethylene containing natural boron.

A university involved in radiation shielding must be capable of investigating basic and new shielding materials both experimentally and through simulations. Thanks to the advances in the development of stochastic radiation transport methods and information technology, performing Monte Carlo codes using MCNP6 [9] or Monaco from the SCALE6 [10] package is not such time and computation power consuming as it was 10–15 years ago. A significant challenge that still remains is that simulations and experimentally achieved results must be verified between each other with an acceptable precision. Since only limited relevant experimental studies have been published regarding the investigation of new radiation shielding materials there is a significant interest in the development of new experiments.

2 Overview of the Mini Labyrinth experiment

2.1 General overview

The Mini Labyrinth experiment, which results from the cooperation of the Slovak University of Technology in Bratislava (STU) with the Brno University of Technology in Czechia the Vinča Institute of Nuclear Sciences in Serbia, was designed to demonstrate the basic principles of radiation shielding and allows using new shielding materials to evaluate their properties for gamma and neutron attenuation. The Mini Labyrinth experiment is inspired by the ALARM-CF-AIR-LAB-001 ICSBEP [11], benchmark experiment originally developed and constructed at the Russian Institute of High Energy Physics (IHEP). In the original Labyrinth experiment a 252Cf source was placed within the centre of the doorway aperture of a labyrinth constructed from concrete blocks with additional plates of polyethylene or borated concrete.

The STU Mini Labyrinth is approximately a 1 to 13 scale version of the original ALARM-CF-AIR-LAB-001 Labyrinth, with the dimensions of the whole experimental setup (table, on which it is installed) 274 × 120 × 150 cm3. The geometry and the dimensions of the Mini Labyrinth workplace are shown in Fig. 1. The Mini Labyrinth itself has a dimension of 96 × 44 × 50 cm3 is made from 6 × 12 × 25 cm3 C-shape NEUTRONSTOP C5 shielding blocks (purple), which are placed on a reinforced particleboard desk (green). There is also a solid graphite block (grey) consisting of 8 plates on the table and it is used to produce thermal neutrons from the PuBe, AmBe or 252Cf neutron source from the block (red). To open and close the graphite block for source loading and unloading, a special sliding mechanism (yellow) is used, made from aluminium profiles and wheels. Another possibility is to insert the neutron source from the left side of the Labyrinth using a plastic source holder (orange) with or without moderator. This position also servers to insert the neutron source for a measurement with plastic solid state track detectors, which do not require extra moderator. Real photos of the Mini Labyrinth are shown in Fig. 2.

Fig. 1
figure 1

Top view and dimensions of the Mini Labyrinth experimental workplace

Full size image
Fig. 2
figure 2

Photos of the Mini Labyrinth workplace

Full size image

2.2 Measurement zones of the Mini Labyrinth

The Mini Labyrinth is an educational experiment and its objective is to demonstrate the fundamentals of radiation shielding. A good educational experiment must be clearly defined, easy to explain and variable. Therefore the Mini Labyrinth was designed with two source positions, to generate fast or thermal neutrons. In this paper, the V3-50-R version of the Mini Labyrinth. Results of previous simulations and measurements on the V2-25-L version of the Mini Labyrinth can be found in [12, 13]. In the latest design the name V3-50-R implies that it is the 3rd geometry configuration, with 50 cm high NEUTRONSTOP elements and the source is loaded from the right side, i.e., from the solid graphite block. This design servers for thermal neutron measurement and uses 15 measurement positions, divided into three zones. These zones are illustrated in Fig. 3. The dimensions can be seen in Fig. 1.

Fig. 3
figure 3

Measurement zones of the Mini Labyrinth

Full size image

Zone 1 serves to measure the horizontal profile of the produced thermal neutrons and consists of 7 measurement positions with 10 cm spacing. Zone 2 and 3 serve to investigate neutron absorption and scattering effects inside the Mini Labyrinth. Zone 2 is perpendicular to the graphite block and consist of four measurement positions (P8–P11). The neutron spectrum in this zone consists of direct (from the source) and scattered neutrons. The last four measurement positions (P12–P15) in Zone 3 are located behind the first and the second corner of the Mini Labyrinth. Here the majority of neutrons is expected to be scattered, because there is a very low probability of thermal neutrons passing through multiple layers of NEUTRONSTOP. For this experiment, the PuBe radioisotope neutron source with the emission rate of 5.22 E5 n/s was used.

3 Simulation and measurement methodology

3.1 Simulation setup

3.1.1 SCALE 6 simulation model

The analysis presented in this paper consists of measurements and simulations. The simulation part was carried out using the Monaco code of the SCALE6 system [10]. For this analysis the detailed 3D model of the laboratory, where the Mini Labyrinth experiment is located, was created. The geometry of the model is shown in Fig. 4.

Fig. 4
figure 4

SCALE 6 geometry model of the laboratory with the Mini Labyrinth experiment

Full size image

The model consists of the detailed description of the Mini Labyrinth, but also includes the most important parts of the laboratory, such as walls, crane, tables and other experimental configurations, such as the workplace for the measurement for neutron emission rate or neutron Fermi age and diffusion length. In SCALE 6, the neutron source was modelled as a combined neutron-gamma source. The neutron probability distribution was modelled as a continuous function (see Fig. 5) and the gamma probability distribution was modelled using the 3.43 MeV, 3.94 MeV and MeV discrete energies sampled according to their probability (see Fig. 6). The calculations were performed as fixed source problems in forward mode, without variance reduction techniques. Although it was possible to use the CADIS methodology for variance reduction, the authors were interested in several responses and regions of the laboratory, therefore the approach with weight reduction would require multiple adjoint sources and significant optimization. The investigation of adjoint sources will be part of the next analyses. Here, to achieve good convergence of the source 20,000 source particles were used and the calculation was performed in 500 batches, leading to the total number of 10 M histories. This number was sufficient to meet all statistical tests for the desired neutron responses.

Fig. 5
figure 5

Neutron emission spectrum of the PuBe neutron source used in the simulations

Full size image
Fig. 6
figure 6

Photon emission spectrum of the PuBe neutron source used in the simulations

Full size image

Since the calculation was carried out as a neutron-gamma radiation transport, the 27n18g ampx type coupled neutron-gamma multigroup cross-section library (XS) was used, originally processed based on ENDF/B-VII.1 [14] evaluated data and include in the SCALE6 distribution. This multigroup XS library consists of 27 neutron and 18 gamma energy groups. One rough calculation was also performed with the more detailed 200n47g XS library, but no significant deviations were found in the precision compared to 27n18g, therefore the authors favoured the faster calculation with 27n18g XS library. To collect the neutron responses 3D rectangular meshtallies were used. There were two types of meshtallies in the model, one rough (10 × 10 × 20 cm3) through the whole model, to catch the shape of neutron fluxes in the whole model, and one smooth (1 × 1 × 1 cm3), covering the area around the Mini Labyrinth experiment, for the comparison with the measurement. The smooth meshtallies covered the total area of 5.76 m2 and consisted of 4.6 M elements. This meshtallies was also divided into two energy regions, the thermal part, below 0.625 eV and the remaining part of the spectrum. It means, that in each geometry element of the mesh, the neutron flux is a function of space and energy φ = f(x, y, z, E). The SCALE 6 system makes possible of calculating the neutron fluxes in mesh elements for each of the 27 energy groups, but it would significantly slow the calculation down. Therefore, the fluxes per each mesh element were calculated only in two energy groups, for the thermal and for the rest of the energy spectrum.

3.1.2 SCALE 6 calculation cases

The complexity of the calculated meshtallies made possible to gather a huge amount of data. After required operations with the data, because the raw data were too detailed, several parameters could be derived from the original meshtallies. In our case, the operations with the meshtallies were carried out using an inhouse C++ utility developed for this purpose. The parameters derived from the neutron meshtallies can be divided into the following categories:

  • Neutron flux vertical profiles

    • They represent the simulated values of neutron fluxes extracted from the meshtallies for a specific X–Y position. They are graphically presented as functions of neutron flux vs. Z position. The positions for which the profiles are extracted range from the bottom to the top of the measurement position of the SNM-11 detector. The profiles were calculated for all 15 measurement positions.

  • Thermal to total neutron flux ratios

    • These ratios is the thermal neutron flux divided by the total neutron flux in the specific measurement position. For the sake of brevity, these ratios are presented in percentage, where 100% represents that all neutrons are thermal.

  • Maps of neutron fluxes

    • These maps are simulated 2D (in this case X–Y) heat-maps of thermal or total neutron fluxes for a specific vertical (Z) position in the model. The heat-maps were visualized using the Meshview SCALE 6 utility and they are presented for the vertical position, in which the centre of the neutron source is located.

  • Comparison of thermal neutron count rates with the measurement

    • In this graph, the simulated value is the sum or the average of the vertical profile of thermal neutron flux in the given measurement position. The measured value is the sum of counts over measurement time. For the comparison normalised relative values are used.

It should be noted that the flux profiles and the maps of fluxes were calculated also for the gamma radiation and these values were used to estimate the radiation situation in the laboratory and compare them with those obtained from the personal dosemeters of the workers, however these results are not presented in the paper.

3.2 Measurement setup

The measurement in each zone and position was performed using the SNM-11 detector. It is a B-10 coated corona detector, produced in the Russian federation, with a length of 30 and the diameter of 1.8 cm. The measurement of the thermal neutron count rate consisted of two steps. In the first step, the measurement was performed with a Cd tube on the SNM-11 detector to cut the thermal part of the spectrum. In the second step the Cd cover was removed from the detector to measure neutrons of all energies and the measurement was repeated without moving the detector. The thermal neutron count-rate was then calculated by subtracting the values with Cd cover from the case without Cd cover. The results from the detector were evaluated using the custom-made four channel analyser and EMConfig software, obtained from the NUVIATECH company [15]. For each measurement position, 3 × 15 min measurement was performed where the neutron counts were saved for every second for three different measurement channels, representing three discrimination levels of the detector. In case of each channel 1024 bins were used, where 1 bin represents 7 mV in case of discrimination level 1, the counts from the first 30 bins were omitted and therefore the results represent the sum from bins 31–1024. In case of discrimination level 2, the range of bins was 26–1024 and in case of level 3, 21–1024. These values were selected based on our previous experience.

4 Results

The results presented in this chapter are divided into four sub-chapters following the categories of investigated parameters listed above.

4.1 Neutron flux vertical profiles

The neutron flux profiles fore measurement zones 1–3 are shown in Figs. 7, 8 and 9. In case of each zone a; represents the total and b; represents the thermal neutron flux profiles. As it can be seen from the results for zone 1, the magnitude of the neutron flux profile is a function of position, and the curves are almost symmetrical. The largest values were achieved for position 4, which is situated in front of the neutron source, and the smallest values for positions 1 and 7, which are at the edge of the graphite prism. In case of thermal neutrons, the results are similar, but the effect of neutron moderation in graphite can be seen. The difference between central and peripheral positions is smaller compared to the total fluxes. This was due to the larger distance between the source and the detector in positions 3 and 5, which led to increased moderation effect since the neutrons travelled through more graphite. However, in case of positions 1, 2, 6, 7, the further increase of moderator also increases the absorption of neutrons. The profiles also identified the influence of the measurement desk. This can be seen from the increase of reflected neutrons for Z values between 70 and 90 cm.

Fig. 7
figure 7

Comparison of simulated vertical neutron flux profiles in zone 1

Full size image
Fig. 8
figure 8

Comparison of simulated vertical neutron flux profiles in zone 2

Full size image
Fig. 9
figure 9

Comparison of simulated vertical neutron flux profiles in zone 3

Full size image

Measurement position 2 is showing similar behaviour, however, the curves are flatter, and the effect of reflected neutrons is not visible. This is mainly caused by the fact, that the majority of neutrons in this zone is already reflected and their spectrum is softer. A very interesting behaviour can be seen from measurement Zone 3. While the maxima of the curves in the previous zones were achieved at the level of neutron source, between Z position 90 cm and 110 cm, in measurement Zone 3 it was different. Since this zone was behind the NEUTRONSTOP shielding blocks, the contribution of direct neutrons from the source was almost zero and only reflected neutrons were present and those, which flew over the NEUTRONSTOP material. This can be seen from the increase of neutron count rate below Z position 75 cm and over Z position 125 cm. Between Z positions 75–125 cm the uncertainties are higher than the values of neutron fluxes and there is practically no difference between measurement positions.

4.2 Thermal neutron rates

The results of simulated thermal neutron rates in 15 measurement positions are shown in Fig. 10. The values presented in the figure are the ratios of the integral neutron flux below 0.625 eV and the integral neutron flux over the whole energy spectrum. As in the previous case, it is interesting to split the results to the 3 measurement positions, i.e. Zone 1—in front of the graphite prism, Zone 2—in the corridor of the Mini Labyrinth and Zone 3—behind the first walls of the Mini Labyrinth. From the comparison of values in Zone 1, consisting of measurement positions P1–P7, we can see that the thermal neutron rate varies between 50 and 55%. It can be also seen that closer the measurement positions was to the source, less thermal neutrons were produced. It means, that by increasing the volume of the graphite prism, even higher thermal neutron rate can be achieved, however, the total neutron flux would be decreased, due to absorption of thermal neutrons. Another important finding is the slight asymmetry of the value distribution between positions P1–P7. Considering the fact, that the graphite prism was symmetrical, the neutron source was placed in the centre and the measurement positions P1 and P7 were in the same distance from the source, we assumed similar results between positions P7 and P7, but due to the reflection of neutrons from the walls of the laboratory, higher thermal neutron rate was achieved in position P1. It means, that the walls of the laboratory reflected moderated neutrons back to the Mini Labyrinth. From the results in Zone 2 (P8–P11), we can see that the thermal neutron rate decreased as a function of distance from the source. This was mainly caused by the fact that the reflected neutrons inside the Mini Labyrinth were absorbed on 10B in the NEUTRONSTOP shielding material. In this zone, the thermal neutron rate decreased from 50% in P8 to 42% in P11. An interesting phenomenon can be seen from the results obtained for Zone 3, consisting of positions P12–P15. Here the thermal neutron rate started to increase from approximately 39% in P12 to 43% in P15. This can be explained by two effect. First of all, due to high absorption of thermal neutrons in NEUTRONSTOP, there were only very few direct thermal neutrons from the source in zone 3 and the thermal neutrons here came from the reflection of fast neutrons on the NEUTRONSTOP material. Another possible cause of the increase could be the reflection of neutrons from the walls of the room. It should be also noted, that the increase could be also a result of the calculation statistics, because the standard deviation of results for these measurement positions is comparable or even higher than the difference between the simulated values.

Fig. 10
figure 10

Thermal neutron rates in the dedicated measurement positions

Full size image

4.3 Maps of neutron fluxes

To see how the thermal neutron rate changes from another point of view, also a 2D map of thermal neutron rates can be analysed, which is shown in Fig. 11. As it was previously discussed, the thermal neutron rate strongly decreased inside the Mini Labyrinth. This phenomenon can be also seen from Fig. 11. The figure presents that there was a strong reflection of thermal neutrons from the walls, both from the top and the right part of the region shown in Fig. 11. Another interesting fact is the very low penetration of thermal neutrons inside NEUTRON stop material, which is caused by the high absorption cross-section of 10B. This phenomenon causes significant problems reaching low statistical error of the calculation and meeting the statistical tests requires very long calculation time.

Fig. 11
figure 11

Map of the thermal neutron rates in the Mini Labyrinth

Full size image

The maps of thermal and total neutron fluxes around the Mini Labyrinth measurement desk are shown in Figs. 12 and 13. From these figures we can confirm the effect of neutron reflection from the walls of the laboratory. This effect is visible also from the total fluxes, but is more obvious from the map of thermal fluxes. Due to this effect, the distribution of thermal neutron flux was influenced and there were more thermal neutrons in the area above the graphite prism than in the area below. In terms of uncertainties, it should be concluded, that the standard deviation of the neutron fluxes in the area inside and around the Mini Labyrinth was lower than 5%, but there were zones, where the standard deviation exceeded 50%. These zones were inside the graphite prism and inside the NEUTRONSTOP material.

Fig. 12
figure 12

Map of the thermal neutron flux in the Mini Labyrinth

Full size image
Fig. 13
figure 13

Map of the total neutron flux in the Mini Labyrinth

Full size image

4.4 Comparison of count rates with the measurement

The last group of results is related to the comparison of normalized count rates between the simulation and the measurement with the SNM-11 corona neutron chamber. The results are presented in Figs. 14, 15 and 16. In each of the graphs the measured value is compared with the simulated one. The difference between the figures is that the results for each level of discrimination are presented separately, one per each graph. In each of the figures the measured values were normalized and were compared with two types of simulated values. “SCALE—SUM” representing the values normalized from the sum of all calculation voxels of the 3D mesh corresponding to the measurement position. “SCALE—AVG” is the case, where the normalization is done based on the average values from these calculation voxels. “SNM” stands for the measurement. The simulation and measurement results are presented with their ± 1σ standard deviation.

Fig. 14
figure 14

Comparison of simulated and measured thermal neutron count rates for discrimination level 1

Full size image
Fig. 15
figure 15

Comparison of simulated and measured thermal neutron count rates for discrimination level 2

Full size image
Fig. 16
figure 16

Comparison of simulated and measured thermal neutron count rates for discrimination level 3

Full size image

The figures are showing a consistent trend in case of all three discrimination levels, however, the smallest cumulative relative deviation from the simulation was achieved in case of discrimination level 2. In case of this discrimination level, the relative deviation varied between 0.25% and 19.69% and the average relative deviation was 9.58%. In case of discrimination level 1, the relative deviations varied between 0.21% and 20.59% with the 20.59% average relative deviation. In case of the least suitable discrimination level 3, the deviations were in the range of 1.87% and 44.67% with the 14.57% average. Taking the ± 1σ standard deviation of the simulations and the measurements into account, the deviations between calculations and simulations were statistically significant only in case of measurement positions 4, 9, 10 and 11. In case of 11 out of 15 positions the deviations were statistically insignificant and can be judged as acceptable. The same applies for all discrimination levels. Taking into account the ± 2σ confidence interval, all deviations are statistically insignificant. One of the possible cause of higher deviations in case of positions 4, 9, 10 and 11 could be the incorrect placing of the detector to the measurement position. Further investigation showed that a ± 1 cm uncertainty of the position may cause deviations even higher than the simulation statistics. Considering the evaluation of simulated results based on the sum and the average values of neutron count rates, it can be concluded that both methods can provide statistically the same results and the simulation model is acceptable for the verification of measured values.

5 Conclusion

This paper presents the results of the measurement and the simulation of thermal neutron count rates in the Mini Labyrinth experiment developed at STU. The measurements were carried out using the SNM-11 boron coated corona neutron chamber in 15 measurement positions inside and outside the V3-50-R version of the Mini Labyrinth. The PuBe Neutron source was installed in the graphite prism that ensures that at least 50% of the neutrons leaving its volume have energies in the thermal region. The simulation part of the analysis was carried out using the Monaco code from the SCALE 6 package, where the full model of the whole laboratory, in which the Mini Labyrinth experiment is located, was created. The simulation results were collected using a fine 3D grid of meshtallies from which several neutron flux related quantities were extracted using an inhouse C++ utility, visualised using the Meshview auxiliary SCALE 6 tool and compared with the simulated results. The analysis of thermal neutron rates and 2D maps of neutron fluxes identified significant room effects resulting from the reflection of moderated neutrons from the walls of the laboratory. This phenomenon also led to asymmetries of thermal neutron fluxes in the Mini Labyrinth. Due to the very good shielding properties of the NEUTRONSTOP material, from which the walls of Mini Labyrinth were constructed, there are almost no direct thermal neutrons inside the Mini Labyrinth and the ones measured in these positions are coming from reflections either on the walls of the laboratory or on the NEUTRONSTOP material. The comparison of measured and simulated count rates in 15 positions showed a very good agreement. In case of 11 out of 15 positions the deviations were statistically insignificant considering the ± 1σ confidence interval and can be judged as acceptable. The remaining four positions were statistically insignificant considering the ± 2σ confidence interval. It was found out that the increased deviations in case of 4 measurement positions may have been caused by incorrect placing of the detector into measurement position. To overcome such issues in the future, an automated source handling robot is being installed, which will be capable of 3 axis movement and positioning the detectors with a precision of ± 1 mm. After this upgrade, the Mini Labyrinth will be ready for further investigations and for online and offline education as part of regular and special lectures of radiation protection at STU. In the next steps also the effect of placing special moderator and shielding materials into the Mini Labyrinth will be evaluated with active and passive solid state track detectors.