Effectiveness of Al and PE as Shielding Against GCR
The measurement of Bragg curves (i.e., dose versus depth) is crucial for characterizing the effectiveness of shielding materials. At the NASA Space Radiation Laboratory (NSRL), part of the U.S. Department of Energy, Bragg curves of 56Fe ions with energies of 986 MeV/n were measured in Al and PE materials. The results are published in (Giraudo et al.2018). We conducted a Monte Carlo simulation of these experiments using the PHITS code. A comparison of the simulated and experimental Bragg curves is shown in Fig. 3. It was observed that PHITS accurately reproduces the shape of the measured Bragg curves. The normalized curves show a decrease in dose with depth up to the Bragg peak, followed by a long tail. The results indicate that the initial dose decrease is greater for PE than for Al. Additionally, the tail dose before the Bragg peak is highest for Al and lowest for PE.
In our study, the slope of the curve was calculated for both Al and PE using the first and second values for each curve. The flux of the primary 56Fe ion in the two materials was computed with respect to depth, and the results are presented in Fig. 3. The shield material attenuates the flux of the primary 56Fe ion due to fragmentation effects, which generate secondary particles during penetration towards the Bragg peak position. At this position, 56Fe ions are completely absorbed, causing the flux to drop to zero. Consequently, the dose beyond the Bragg peak is mainly attributed to secondary particles, particularly light fragments.
We can note that the flux F(x) of the incident ions at a distance x in the shield can be written as (Durante et al.2019) :
Initial slope δD can be estimated by:
F0: Incident flux of 56Fe primaries. AT: Atomic weight of the shield. σ: Fragmentation cross-section. NA: Avogadro number, ρ: Target density.
It has been established that the shielding effectiveness of a material can be assessed by measuring the fraction of dose reduction from the initial slope of the Bragg curve of a 56Fe beam [6]. The percentage dose reduction per unit thickness can be calculated from the initial slope of the Bragg curve by extrapolation to zero depth. This initial slope is determined by fitting the Bragg curve points using a linear function. In our study, the initial slope for PE is 0.04 ± 1 cm⁻¹, and for Al it is 0.047 ± 1 cm⁻¹. The initial decrease in dose is more pronounced for PE, indicating that PE is a more effective shield against GCR than Al.
During the penetration of 56Fe ions into the shielding material, nuclear fragmentation occurs; producing secondary particles particularly lower Z fragments and neutrons. The PHITS code can separately simulate the different primary and secondary particles. We performed a simulation of the flux of the secondary neutrons in both Al and PE as a function of depth. The results, shown in Fig. 4, confirm that Al produces more neutrons than PE. Figure 4 shows that neutron flux rises with increasing thickness of shielding in both Al and polyethylene PE. Moreover, neutron generation is notably higher in Al shielding, suggesting that PE provides more effective protection compared to Al with respect to secondary neutrons.
Combination of Aluminum and Polyethylene
As GCR ions penetrate shielding materials, neutrons are inevitably produced during nuclear reactions. Neutrons are generally the most harmful secondary radiation to the human body, especially within the energy range of 10⁻² MeV to 10³ MeV. In this energy range, the radiation weighting factor of neutrons can exceed 20 (Valentin .2007). Analyzing neutron flux is the most straightforward and effective way to measure radiation, helping to determine which materials produce lower secondary neutrons.
Optimization of the Mass of Shielding
Minimizing the mass of the shielding system while maintaining the required level of efficiency is crucial, especially in space applications where weight limits are significant. By strategically combining materials, we can potentially optimize the shielding systems mass while providing adequate protection against GCR. We investigate the effectiveness of a shielding system using a combination of Al and PE. A 30 g/cm² Al slab is compared to a configuration of 15 g/cm² Al followed by 5 g/cm² PE. The focus is on evaluating the potential benefits for optimizing secondary neutron reduction.
The PHITS code is used to compute the neutron spectra behind the shielding system. Figure 5 shows the simulation geometry: the slab target is surrounded by a vacuum and irradiated with GCR beams incident perpendicular to its surface. The geometric thickness was determined based on the density of each material.
We used the Galactic Cosmic Rays spectrum provided by the Particle and Heavy Ion Transport code System (PHITS) during the solar maximum period. The GCR particles considered ranged from hydrogen (Z = 1) to nickel (Z = 28). Figure 6 presents a comparison between the flux of secondary neutrons after passing through 30 g/cm² of Al and the flux of secondary neutrons after passing through a combination of 15 g/cm² of Al followed by 5 g/cm² of PE. This comparison allows for the evaluation of the effectiveness of these two configurations in terms of secondary neutron production. Figure 6 shows that when the combination of Al and PE is used, the flux of secondary neutrons is reduced by approximately 30%. From the neutron physics aspects, PE (hydrogen-rich material), it can moderate the neutrons that have been produced in Al. This indicates a lower production of secondary neutrons with this combination compared to using Al alone.
Secondary Neutrons from GCR in Al and PE Shielding
We performed a simulation using the PHITS code with a GCR beam composed of protons, helium, oxygen, and iron ions passing through a slab of shielding material. These particles were chosen due to their abundance in GCRs. we computed the flux of secondary neutrons behind a 15 g/cm² thick Al and behind a 5 g/cm² thick PE shield. The results, presented in Fig. 5(a), show that the flux of secondary neutrons is higher after passing through the Al shield compared to the PE shield, indicating greater neutron production in Al. Figure 5(b) shows the secondary neutron flux behind a 15 g/cm² thick Al shield, indicating that neutrons are primarily produced by protons and helium ions from GCR.
Polyethylene Thickness Effect
In this study, the shielding effectiveness, in terms of secondary neutron production, of the combination of an Al slab of 15 g/cm² followed by PE slabs of various thicknesses (5, 10, 15, 25, 40, 50 g/cm² ) will be evaluated. The GCR particles considered ranged from hydrogen (Z = 1) to nickel (Z = 28). Figure 8 presents the results of the simulation. It shows the flux of secondary neutrons, where a slight increase in neutron flux is observed by increasing the thickness of PE, followed by a significant increase in flux for the thicknesses of 40 and 50 g/cm². This can be explained by the production of secondary neutron in PE material.
Multi-Layer Configuration
We investigated the impact of a multi-layered approach on shielding effectiveness, specifically focusing on the production of secondary neutrons. Using the PHITS code, we performed simulations to compute and compare the spectra of secondary neutrons produced behind different configurations: 15 g/cm² of Al combined with 5 g/cm² of PE. The configurations included a thick block of Al followed by a thick block of PE, a multi-layered Al followed by a thick block of PE, and a thick block of Al followed by a multi-layered PE. The multi-layered configuration was modeled in steps of 1 g/cm². The geometry used in the PHITS simulation is represented in Fig. 9.
We considered Galactic Cosmic Ray particles ranging from hydrogen (Z = 1) to nickel (Z = 28). As shown in Fig. 10, the simulation results indicate that multi-layering aluminum (Al) has no impact on the secondary neutron flux, whereas multi-layering polyethylene (PE) reduces the secondary neutron flux by approximately 10%. This demonstrates that the shielding effectiveness is enhanced when a multi-layer approach with PE materials is applied.