1 Introduction

Space exploration has developed rapidly, and significant progress has been made in the past decades. Mars has become a hotspot for deep-space exploration missions. Mars exploration programs have been carried out, to learn about the evolution of Mars and for determining whether life exists on Mars [1]. The manned mission to Mars has also been on schedule [2]. A key factor that must be considered for manned space exploration missions is the space radiation, which is caused by galactic cosmic rays (GCRs) and solar particle events (SPEs) [3,4,5]. In the space, energetic particles can penetrate spacecraft and harm the instruments and astronauts [6]. Radiation-related health risks constitute a serious challenge for long-term manned space exploration missions [7, 8]. GCRs are mainly composed of charged nuclei, such as protons, \(\alpha\) particles, and heavier nuclei with a broad range of energies, from sub-MeV to hundreds of TeV [9, 10]. SPEs mainly consist of protons and \(\alpha\) particles, with relatively lower energies compared with GCRs. Owing to the planet’s thin atmospheric layer and the lack of a global magnetic field [11], the radiation intensity on Mars is much higher than that on Earth. Knowing the radiation environment on Mars and the radiation dose that is likely to be received by astronauts is very important for future manned missions to Mars [11, 12]. This knowledge will allow decision-makers to accurately assess the corresponding health risks and is likely to provide a reference for designing radiation-protection gear [13, 14].

The radiation environment on Mars is complex and is defined by several factors. The shielding effect of the Mars atmosphere is much weaker than that of the Earth atmosphere. As a result, energetic particles in GCRs and SEPs can penetrate the Mars atmosphere, reaching the planet’s surface. Owing to the irregularity and infrequency of SPEs, only GCRs were considered in this study. The interaction between GCRs and atmospheric molecules generates many secondary particles, which further interact with the planet’s atmosphere, resulting in the complex radiation spectrum on the Mars surface. Albedo particles that are produced on the planet’s surface also contribute to the radiation environment. The three main components of the radiation environment on the Mars surface were considered in this study. The Curiosity rover has carried out a long-term scientific exploration on Mars since it successfully landed on the planet in 2012. At the same time, an onboard radiation assessment detector (RAD) has been collecting radiation-related information on the Mars surface, including the particles’ spectrum and the absorbed dose rate [15].

Some studies have shown that long-term exposure to the space radiation can harm humans [2]. Radiation can directly and indirectly affect DNA molecules in the human body, causing cell death or mutation and increasing the risk of cancer [16,17,18] and other diseases. The National Aeronautics and Space Administration (NASA) categorized the health risks owing to the space radiation into four groups: (1) degenerative tissue effects, (2) carcinogenesis, (3) acute and late central nervous system (CNS) effects, and (4) radiation-related syndromes [19]. Accurate calculation of the radiation dose received by astronauts is necessary for assessing the health risks associated with the space radiation. However, it is difficult to directly calculate the particles’ spectra on the Mars surface and the associated radiation dose. Monte Carlo simulations can be used for addressing this problem. Some transport codes have been used for studying the radiation environment in the space and on Mars, such as HZETRN [20, 21], HETC-HEDS [22], FLUKA [23], PHITS [24], MCNP6 [25, 26] and Geant4 [27,28,29,30]. In Ref. [20,21,22,23,24,25,26], Slaba et al. studied the radiation environment on the Mars surface using these tools. Most of these studies have mainly focused on simulating the radiation environment on the Mars surface. Our work addresses two aspects of this research area. First, we used the G4QMD model to deal with the inelastic scattering of GCRs in the Mars atmosphere and soil, and for obtaining the particles’ spectra on the Mars surface. Then, based on the simulated particles’ spectra, we calculated the radiation dose received by a typical human body. To our knowledge, this is the first study attempting to estimate the radiation dosage to individual organs of a typical human on the Mars surface. The results and conclusions of this study can be used when planning future manned Mars exploration missions.

2 The radiation environment on Mars

2.1 Model setup

To reduce the simulation time, a simple geometrical model consisting of a cylinder (radius, 1 km) was built, to represent the Martian environment. The cylinder was divided into 12 layers to represent the Martian regolith and atmosphere. The first layer from the bottom corresponded to the Martian regolith (thickness, 3 m; density, 1.7 g/cm\(^3\)) [21]. The second layer was 4-m-thick, representing the atmospheric conditions on the Mars surface. From the third layer to the twelfth layer, each layer was 1-m-thick, and the column densities of the different layers were 11.820, 5.915, 2.624, 1.069, 0.395, 0.131, 0.035, 0.009, 0.003, and 0.001 g/cm\(^2\), respectively. The overall column density of these layers was approximately 22 g/cm\(^2\) [21, 31, 32], representing the Mars atmosphere. The detector was a cylinder (radius, 1 km; thickness, 3 mm) and was positioned1 m above the soil, for detecting and registering the Mars radiation environment. The planet’s soil and atmosphere components were derived from Ref. [21] and are listed in Table 1. Primary GCRs were incident from the top of the geometrical structure, in the isotropic fashion. Once a particle passed through the detector, the information about the event was recorded, including the particle’s type, its kinetic energy, and its angle of incidence.

Table 1 Modeled soil and atmosphere components of Mars [21]
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The radiation environment simulations were performed using the Geant4-10.5.1 package (version10.5.1). This code is a track structure code that was developed at CERN for simulating the passage of particles through matter [29, 30]. It provides many models that can be chosen by the user according to the specific application, and it has been widely used in high-energy physics, medical physics, and radiobiology. The physical parameters that were used for simulating the interaction between GCRs and the Mars medium are listed in Table 2. The Emstandard_opt3 physics list was used for describing the electromagnetic interactions of photons, leptons, hadrons, and ions, with energies in the 1 keV-10 PeV range [33]. The G4HadronPhysicsQGSP_BIC_HP physics list [34] was used for describing the inelastic scattering of nucleons and mesons with nuclei, for energies in the 0 eV–100 TeV range. In this physics list, the quark gluon string model (QGS) was used for describing high-energy hadronic interactions (12 GeV–100 TeV range). The binary cascade model (BIC) was used for dealing with nucleon-nucleus interactions at intermediate energies, and high-precision neutron models (HPs) were used for dealing with neutron-nucleus interactions involving energies below 20 MeV. For the inelastic interactions of nuclei, the G4QMD model that was validated in our previous work was used [35]. In this model, all nucleons were considered as participant particles, and each nucleon was treated as a Gaussian wave packet. Equations of the particles’ motion were derived based on the time-dependent variation principle [36]. A detailed description of these models can be found in the Geant4 Physics Reference Manual [36].

Table 2 The physics list
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In this study, only GCRs were considered as contributing to the radiation environment of Mars. GCRs mainly consist of protons, \(\alpha\) particles, and heavy ions. Although the proportion of heavy particles is very small, they are important for radiation protection, owing to their high relative biological effectiveness (RBE). In our simulations, particles with atomic numbers \(Z=1\)–26 were considered for GCRs. The energy spectra of these particles were calculated using the GCR model developed by Matthi\(\ddot{a}\) et al. [10]. In that model, a single parameter W was used for describing the modulation effect of solar activity [10]. A part of the primary GCR spectra used in the simulation is shown in Fig. 1. The modulation parameter W was calculated according to the Oulu neutron monitor count rate (from http://cosmicrays.oulu.fi/) during the period from August 2012 to January 2013, and an average value (\(W=56\)) was used in this work.

Fig. 1
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(Color online) A part of the primary GCR spectra used in the simulation

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2.2 Results

When GCRs pass through a planet’s atmosphere, many neutrons and photons are induced owing to the interactions between the GCRs and atmospheric molecules. The simulated neutron and photon spectra on the Mars surface are plotted in Fig. 2, together with the experimental data [21, 37]. As shown in this figure, the simulation results for neutrons were slightly higher than the corresponding experimental data, for energies below 100 MeV/n, while the simulation results for photons agreed well with the RAD data. For neutrons and photons, the average relative deviations of the simulation results from the corresponding experimental data were 60.8% and 56.0%, respectively.

Fig. 2
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(Color online) Simulated and measured photon and neutron spectra, for the Mars surface

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The simulation results for the charged particles’ spectra, for zenith angles smaller than \(30^{\circ }\), are plotted in Figs. 3 and 4. Heavy particles can be divided into several groups, for proper comparison to the RAD data [15]. Evidently, the simulated spectra of protons, \(\alpha\) particles, and particle groups \(Z=6-9\), \(Z=9-13\), and \(Z=14-24\) were consistent with the corresponding RAD data, and the corresponding average relative deviations were 27.7%, 37.9%, 40.9%, 60.7%, and 40.1%. For the particle groups \(Z=3-5\) and \(Z>24\), the simulation results were slightly lower than the measured data. However, the simulated spectra of deuterons, tritons, and \(\,^3{\mathrm{He}}\) were much lower than the corresponding RAD data, and the average relative deviation was approximately 90%. These particles are pure secondary particles generated in reactions between primary GCRs and atmospheric molecules, and the observed discrepancy might be owing to the lower generation cross sections. Based on the previous work, the cross sections for light fragments simulated by the G4QMD model were lower than the experimental data [35].

Fig. 3
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(Color online) Simulated and measured charged particles’ spectra, for zenith angles smaller than \(30^{\circ }\): a protons, deuterons, and tritons, b alpha particles and \(\,^3{\mathrm{He}}\)

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Fig. 4
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(Color online) Simulated and measured charged particles’ spectra, for zenith angles smaller than \(30^{\circ }\): a Li–Be–B and C–N–O; b particle groups \(Z=9\)–13, \(Z=14\)–24, and \(Z>24\)

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Heavy charged particles incident from the entire upper hemisphere were also recorded in the simulation, and the simulated spectra for zenith angles smaller than \({90}^{\circ }\) are plotted in Fig. 5. Compared with the spectrum within the \(30^{\circ }\) zenith angle, for light particles, the flux averaged over the \(90^{\circ }\) zenith angle was close to the flux for zenith angles below \(30^{\circ }\). However, for heavy particles, the flux for the zenith angles below \(90^{\circ }\) was slightly smaller than the flux for zenith angles below \(30^{\circ }\). The spectra of electrons, muons, and pions were also calculated, owing to their significant contributions to the absorbed dose, and are plotted in Fig. 6.

Fig. 5
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(Color online) Simulated spectra of particles, for zenith angles smaller than \(90^{\circ }\): a protons, deuterons, tritons, \(\,^3{\mathrm{He}}\), and alpha particles. b Li–Be–B, C–N–O, F–Al, Si–Cr, and Mn–Fe

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Fig. 6
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(Color online) Simulated spectra of electrons, pions, and muonsm, for zenith angles smaller than \(90^{\circ }\)

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3 Radiation dose received by a typical human body

Accurate estimation of the dose received by astronauts is an essential precondition for successful manned deep-space exploration missions. In addition, with the wide use of nuclear technology in material physics and medical physics [38,39,40,41,42,43,44,45,46], it is also important to be able to calculate the radiation dose received by a typical human in the corresponding radiation environment. Based on the prior simulation results, we calculated the radiation dose that would have been received by astronauts on the Mars surface.

According to the International Commission on Radiological Protection (ICRP) [47], the equivalent dose for a tissue, \(H_T\), is defined by

$$\begin{aligned} H_T=\sum _R W_R D_{T,R} \end{aligned}$$
(1)

where \(D_{T,R}\) is the absorbed dose for tissue T caused by radiation R, and \(W_R\) is the radiation weighting factor for radiation R. The effective dose, E, is defined as

$$\begin{aligned} E=\sum _T W_T H_T \end{aligned}$$
(2)

where \(W_T\) is the tissue weighting factor for tissue T. Tables 3 and 4 list the values of \(W_T\) and \(W_R\), respectively. The ICRP recommends that the effective dose received during occupational exposure and in public should not exceed 20 mSv/y and 1 mSv/y [47], respectively.

Table 3 Tissue weighting factors \(W_T\) (extracted from Ref [47])
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Table 4 Radiation weighting factors \(W_R\) (extracted from ref [47])
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3.1 Model setup

The geometrical simulation model is shown in Fig. 7. The human phantom model [48] was borrowed from the Geant4 advanced example “human phantom” and placed on the Mars surface. A cubical regolith (10 \(\times\) 10 \(\times\) 6 m\(^3\)) was built, with the density of 1.7 g/cm\(^{3}\). Then, the simulated particles’ spectra within the \(90^{\circ }\) zenith angle (in Figs. 5, 6) were used for simulating primary particles and projecting them onto the surface from the top of the geometrical model. For each step in the simulation, the energy deposited by different particles into different human body organs was recorded. After the simulation, the values of the total deposited energy, the absorbed dose, and the equivalent dose delivered by different particles to different organs were calculated. In the simulation, the total sampling number of each primary particle was set to 5 million. For each scenario, the simulation was repeated six times, and the uncertainties shown in this paper represent, in each case, one standard deviation from the corresponding mean.

Fig. 7
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(Color online) Geometrical simulation model

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3.2 Results

Fig. 8
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(Color online) Radiation received by a human body on the Mars surface: a distribution of the radiation energy deposition in the body organs, b distribution of the absorbed dose in the body organs, c distribution of the equivalent dose in the body organs. The horizontal coordinate represents different organs: 1-Brain, 2-Head, 3-Heart, 4-LeftAdrenal, 5-LeftArmBone, 6-LeftClavicle, 7-LeftKidney, 8-LeftLeg, 9-LeftLegBone, 10-LeftLung, 11-LeftScapula, 12-LeftTeste, 13-Liver, 14-LowerLargeIntestine, 15-MaleGenitalia, 16-MiddleLowerSpine, 17-Pancreas, 18-Pelvis, 19-RibCage, 20-RightAdrenal, 21-RightArmBone, 22-RightClavicle, 23-RightKidney, 24-RightLeg, 25-RightLegBone, 26-RightLung, 27-RightScapula, 28-RightTeste, 29-Skull, 30-SmallIntestine, 31-Spleen, 32-Stomach, 33-Thymus, 34-Thyroid, 35-Trunk, 36-UpperLargeIntestine, 37-UpperSpine, 38-UrinaryBladder

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Figure 8 shows the radiation dose received by different human body organs, for a typical human staying on the Mars surface for one year. The distribution of the deposited energies in the body organs is plotted in Fig. 8a. Evidently, the energy deposited in the trunk was the highest, reaching \((9.05 \pm 0.04)\times 10^{12}{\mathrm{MeV/y}}\). The body part receiving the second highest amount of the radiation energy were legs, with the deposited energy per leg reaching \({(2.02\pm 0.02)\times 10^{12}}{\mathrm{MeV/y}}\). This large deposition occurred because the mass and volume of the trunk and legs were larger than those of the other body parts. The amount of energy deposited in the head and skull was also high; however, the amounts of energy deposited in smaller organs, such as left/right adrenal and thyroid glands, were among the lowest. Figure 8b shows the simulated absorbed dose distribution across the different body parts. The distribution of the absorbed dose differs significantly from the distribution of deposited energy. The absorbed dose was the highest for the brain, reaching 62.0 ± 1.7 mGy/y, followed by the thyroid and skull. The absorbed doses for the thymus, upper spine, left/right lung, and left/right clavicle were also relatively high; however, the absorbed doses for the lower body organs were relatively low; for example, the absorbed doses for the left/right leg and leg bone were approximately 35 mGy/y. Evidently, the difference between the doses received by the different organs was significant, because primary particles were incident from above; consequently, some smaller-energy particles only affected the superficial layers of the human body. Thus, upper-body organs, such as the brain and the thyroid gland, received higher radiation doses than lower-body organs. The average absorbed dose for the entire body was 43.8 ± 0.4 mGy/y. Taking the quality of different radiation sources into account, we calculated the equivalent doses for the different organs, and the results are shown in Fig. 8c. The equivalent dose for the brain was the highest, reaching 234.1 ± 8.0 mSv/y, agreeing well with the corresponding RAD data [31]. For the skull, adrenal, and upper spine, the equivalent doses were also relatively high, all above 200 mSv/y. For the leg bone, the equivalent dose was the lowest, just 116.4 ± 1.7 mSv/y. The average equivalent dose for the entire body was approximately 153 mSv/y, much lower than the corresponding RAD data. We posit that this difference could be attributed to the fact that a typical human body is much larger than the RAD detector, and because the mass distribution in the body is not uniform. The lower part of the body and inner organs received less radiation, so that the average equivalent dose for the entire body was lower than the corresponding RAD data.

Fig. 9
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(Color online) Contributions of different particles to the radiation dose received by the human body

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To analyze the contributions of different particles to the radiation dose received by the human body, we extracted the deposited energy and the absorbed dose in the human body owing to electrons, photons, pions, muons, protons, \(\alpha\) particles, and heavy ions (\(Z\ge 3\)), respectively. The results are plotted in Fig. 9, except for photons, because their contribution was far less than those of other particles. The energy deposited by protons was (1.08 ± 0.01)\(\times 10^{13}\) MeV/y, accounting for 56.1% of the total energy deposited in the human body. The second largest contribution was that of electrons; the corresponding deposited energy accounted for 22.6% of the total energy deposited in the body. The energies depositions by \(\alpha\) particles, heavy ions, pions, and muons were smaller, accounting for 6.1%, 3.6%, 6.6%, and 3.9% of the total deposited energy, respectively. The contribution of neutrons to the total deposited energy was only 0.07%, much lower than that of protons. This was because the reaction cross section of neutrons with matter was very small, and most of the deposited energy was owing to secondary particles. The contributions of the different particles to the absorbed dose were similar to those for the deposited energy. However, for the equivalent dose, the situation was different. \(\alpha\) particles contributed mostly to the total equivalent dose, which reached 53.7 ± 1.3 mSv/y, accounting for 35.1% of the total equivalent dose. The equivalent doses owing to protons and heavy ions were 49.1 ± 0.6 mSv/y and 31.9 ± 0.7 mSv/y, accounting for 32.1% and 20.9% of the total equivalent dose, respectively. The contributions of electrons, pions, muons, and neutrons were slightly smaller, accounting for only 6.5%, 3.8%, 1.4%, and 0.24% of the total equivalent dose, respectively. Although the deposited energies owing to \(\alpha\) particles and heavy ions were not very high, they were the main contributors to the equivalent dose. This was because the radiation weighting factors of \(\alpha\) particles and heavy ions were much larger than those of the other particles. Therefore, it is necessary to consider heavy ions in GCRs, when designing future manned deep-space exploration missions.

It can be observed from Figs. 2, 3 and 4 that the simulated spectra of deuterons, tritons, and \(\,^3{\mathrm{He}}\) were much lower than those of the measured data. To assess the effect of the differences on the calculated doses to the human body, we multiplied the spectra by a scaling factor, for matching with the measured data, and recalculated the dose. The absorbed dose and the dose equivalents for the body organs, based on the scaled spectra, increased by approximately 22% on average, compared with the previous results. The average absorbed dose and the dose equivalent for the human body were 54.0 mGy/y and 191.6 mSv/y, respectively. The results show that these particles strongly affect the dose calculation, and the models in the Geant4 package should be improved for better describing nucleus-nucleus interactions.

4 The shielding effect of the Martian soil

The simulation results suggest that the dose that would have been received by astronauts on the Mars surface is much higher than that received on the Earth surface. Therefore, appropriate radiation protection measures are necessary. When astronauts will carry out long-term exploration missions on the Mars surface, it is likely that they will use Martian soil to build shelters, for protecting themselves from radiation. Thus, the shielding effect of Martian soil is worth investigating.

4.1 Model setup

A hollow cube (5 \(\times\) 5 \(\times\) 3 m\(^3\)) was built and placed in the Mars soil, and the human phantom was placed in the cube. The thickness of the soil above the human phantom, denoted by d, was adjustable. In the simulation, we considered 9 levels of the soil thickness, namely \(d=0.1\) m, 0.3 m, 0.5 m, 0.7 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, and 3 m; for each one of these scenarios we computed the dose received by the human body. The primary particles were projected from the top of the soil according to the simulated particles’ spectra on the Mars surface. The tissue energy deposition owing to different particles was recorded.

4.2 Results

Fig. 10
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(Color online) The dose on the human body, at different depths under the Mars surface

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The radiation doses on the human body at different depths under the Mars surface are plotted in Fig. 10. The deposited energy and dose rate on the Mars surface were also included for comparison. Evidently, with increasing the soil depth, the deposited energy, absorbed dose, and equivalent dose in the organs all decreased rapidly. At the depths of 0.1 m, 0.5 m, and 1.0 m, the absorbed dose was lower by 7.6%, 41.3%, and 71.1%, respectively, compared with the dose on the Mars surface. The reduction rate of the absorbed dose decreased as the soil thickness continued to increase. As shown in Fig. 10c, the equivalent dose in the organs dropped faster than the absorbed dose at small depths. For example, at the depth of 0.1 m, the equivalent doses on the brain and whole body decreased by 30.6% and 28.1%, respectively. We attribute this to the fact that energetic heavy ions collided with the Mars soil and broke into lighter fragments, with smaller radiation weighting factors. The variation of the effective dose with the soil depth was similar to that of the dose equivalent and at the soil depths of 0.1 m, 0.5 m, and 1.0 m, the effective dose on the entire body was 121.0 ± 9.7 mSv/y, 67.6 ± 7.9 mSv/y, and 35.0 ± 2.4 mSv/y, respectively. At the depth of 1.5 m, the average equivalent dose and effective dose on the entire body were 17.4 ± 0.5 mSv/y and 17.9 ± 2.4 mSv/y, respectively, lower than the dose limit of 20 mSv/y for occupational exposure. At the depth of 3 m, the equivalent doses received by different organs were between 2.0 mSv/y and 3.8 mSv/y, and the effective dose on the entire body was 2.7 ± 1.0 mSv/y, still higher than the dose limit for public exposure. To confine the effective dose below 1 mSv/y, the thickness of the soil needs to be larger than 3 m.

5 Conclusion

In this study, we first simulated the radiation environment on the Mars surface using the Geant4 toolkit. In the simulation, a simple geometrical model and G4QMD physics model were used. The simulation results for neutrons, photons, protons, \(\alpha\) particles, and particle groups \(Z=6\)–8, \(Z=9\)–13, and \(Z=14\)–24 were in a reasonable agreement with the corresponding RAD data, with average deviations of 60.8%, 56.0%, 27.7%, 37.9%, 40.9%, 60.7%, and 40.1%, respectively. However, for deuterons, tritons, and \(\,^3{\mathrm{He}}\), which are pure secondary particles, the simulation results were much smaller than the corresponding RAD data, which might have been owing to the underestimation of the production cross sections in the G4QMD model. In addition, the particles’ spectrum from the entire upper hemisphere was also obtained.

Based on the simulated radiation environment, we calculated the radiation dose received by the human body on the Mars surface. The results showed that the doses absorbed by different organs differed significantly from each other. The absorbed doses for the brain, thyroid, and skull were relatively high, but the doses for the legs and male genitalia were much lower. The average absorbed dose and equivalent dose of the entire body were 43.8 ± 0.4 mGy/y and 152.9 ± 2.0 mSv/y, respectively. Further analysis showed that most of the dose was induced by \(\alpha\) particles, protons, and heavy ions. The shielding effect of the Mars soil on radiation was also studied. With increasing soil depth, the deposited energy, absorbed dose, and equivalent dose for the organs decreased rapidly. At the depth of 1.5 m, the effective dose for the entire body was 17.9 ± 2.4 mSv/y, lower than the dose limit recommended by the ICRP for occupational exposure. However, for confining the effective dose to the safe range for public exposure, the soil thickness should exceed 3 m.