# Modeling the effectiveness of radiation shielding materials for astronaut
protection on Mars

Dionysios Gakis  Dimitra Atri

###### Abstract

The surface of Mars is bombarded by energetic charged particles of solar and
galactic origin with little shielding offered by a thin atmosphere and lack of
a global magnetic field. As space agencies around the globe are planning for
crewed missions to the planet, one has to account for a number of factors, a
major one being the impact of ionizing radiation on astronaut health. Keeping
optimal exposure below acceptable radiation dose levels is crucial for good
health and survival of the crew. In this study, our goal is to understand the
radiation environment of Mars and describe the main strategies to be adopted
to protect astronauts from the harmful impacts of cosmic radiation.
Specifically, we investigate the shielding properties of various materials in
the Martian radiation field (Solar Energetic Particles and Galactic Cosmic
Rays) using the GEANT4 numerical model. Our results indicate that H-rich
materials show a similar response against cosmic rays and are the best
shields, whereas regolith has an intermediate behavior and therefore could be
used as an additional option, considering its practicability. Additionally, we
show that although aluminum is not as effective as other materials, it could
nonetheless be helpful when combined with other materials.

###### keywords:

Mars , radiation , shielding materials , human spaceflight

††journal: Life Sciences in Space Research

[inst1]organization=Department of Physics, University of Patras, Patras, Rio,
26504, Greece

[inst2]organization=Center for Space Science, New York University Abu Dhabi,
PO Box 129188, Abu Dhabi, UAE

[inst3]organization=Blue Marble Space Institute of Science, Seattle, WA,
98104, USA

##  1 Introduction

Ionizing radiation is one of the major hazards astronauts must face in long-
duration space missions. Other dangers include microgravity, absence of
oxygen, debris and isolation, but ionizing radiation ranks as one of the most
threatening because of its ability to penetrate shielding and causing
biological damage [1]. For this reason, awareness of space radiation and its
harmful effects is widely spread among the scientific community and is an
highly interdisciplinary endeavour.

Unlike the Earth, Mars lacks a thick atmosphere and a strong magnetic field
able to deflect particles and reduce radiation doses to low levels. Hence, we
must look for ways to protect human crews from these hazardous charged
particles. While radiation on the surface of Mars is of course much smaller
than when in deep space, the already accumulated doses in astronauts’ bodies
during their transfer to and from Mars make it inevitable to search for
strategies of mitigating exposure on Mars too.

Several techniques have been developed to protect astronauts from absorbing
immense amounts of radiation (e.g. [2]), the main being passive shielding,
which takes advantage of the energy loss through the mass of a shielding
material. In literature so far, aluminum and polyethylene have been well
tested in the Martian radiation field [3, 4]. Besides, the in-situ regolith
has also been suggested due to practicability [5, 6]. Other works like e.g.
[7] simulate radiation doses behind other materials too, but they are mostly
limited in the ISS or the deep space environment.

The purpose of this study is to outline the suggested radiation protection
techniques, focusing on the testing the effectiveness of various materials
against radiation, specifically on the surface of Mars. We re-examine the
effectiveness of materials commonly used in space missions and try other novel
ones. Additionally, we compare the efficiency of combinations of shielding
materials, trying to benefit from each one’s unique properties. To that end,
we employed the computational program GEANT4 to simulate the propagation of
energetic charged particles through matter.

This paper is organized as follows. Section 2 outlines the radiation
environment on the surface of Mars and Section 3 consists of the main
shielding strategies agencies have adopted for radiation mitigation. We then
describe our computational method in Section 4, present our results in Section
5 and discuss their validity in Section 6. Finally, we provide conclusions in
the last section (Section 7).

##  2 Radiation environment

Astrophysical radiation consists of photons and charged particles, which can
further be categorized as ionizing and non-ionizing. Both kinds of radiation
can damage living and non-living systems. However, protecting from non-
ionizing radiation is easy, since it can be easily blocked by any kind of thin
shield. On the other hand, ionizing radiation passes through substances and
alters them, producing a cascade of secondary particles, increasing with
increasing energy of incident radiation. For example, a single proton may
decay to kaons, pions, muons and other unstable particles, eventually
resulting in the exposure of neutrons, electrons, muons and other particles in
outer space, which are known to cause biological damage and pose health risks
to astronauts. Therefore, one of the main concerns during space missions is
protecting astronauts from the devastating effects of ionizing radiation.

###  2.1 Radiation sources

Radiation in interplanetary space and on the surface of Mars originates from
the Sun and from Galactic sources. Energetic processes in the sun release
energetic charged particles called Solar Energetic Particles (SEPs) and
background flux of charged particles from Galactic sources known as Galactic
Cosmic Rays (GCR). There may be local sources of radiation in form of
radioactivity in the Martian regolith, but their dose is much smaller and
extraterrestrial ones are the main source of health hazard; consequently we
focus on the latter.

SEPs are associated with solar flares and coronal mass ejections (CMEs) [8].
They consist mainly of protons (90-95%), followed by helium nuclei (5-8%),
along with some heavier nuclei (1%). Clearly, these percentages can only be
rough, as exact compositions differ a lot between events or even during a
single event [9]. The typical energy spectrum of an SEP event lies in the
range of some keV to hundreds of MeV, softer than GCR. In some extreme cases,
it can go up to 10 GeV [10, 11].

SPEs are rare and generally occur in phase with the solar cycle, at times of
maximum solar activity, despite the fact that some of them occur at any time
of the solar activity. They are produced during solar eruptions, at which
particles are accelerated to relativistic energies by the plasma [12].
Nonetheless, the exact mechanism of SPEs’ creation and the following effects
in the space weather have not yet been definitely determined. In other words,
they are quite unpredictable and might differ significantly by duration,
strength and fluence. Historically recorded events of exceptionally intense
solar activity include the Carrington event (September 1859), along with the
events of February 1956, August 1972 and September 1989. It appears that they
used to happen more often in the past; caution is then needed when
extrapolating to predict future events.

The other type of astrophysical radiation, GCR, has galactic origins. GCR are
accelerated by supernova shocks and interstellar magnetic fields before
entering the solar system. As a result, they are considered to have isotropic
flux (i.e. coming from every direction in the sky), and be nearly stable
through thousands of years. Their composition is similar, but different from
SEPs’: 87% protons, 12% alpha particles, 1% heavy nuclei ($Z>2$) [13]. Some
electrons are also observed (1%), but are often ignored due to their low
abundance in contrast to solar electrons. With an average energy of some GeV
per nucleon, GCR are deadlier than SEPs on a regular basis. It is possible
that a galactic cosmic ray is accelerated at kinetic energies as high as some
TeV [14].

The so-called HZE (high charge and energy) ions, coming from both radiation
sources, contribute significantly in radiation doses. HZE are in fact atoms of
low to medium atomic numbers (up until Fe), stripped off their electrons,
travelling freely through space at speeds near the speed of light. Despite
their small abundances, they are characterized by strong ionizing and
penetration power. They have the ability to penetrate deep inside matter, and
sometimes break apart inside materials, thus creating a cascade of secondary,
also highly energetic and charged, particles, dangerous for human health [15].
Shielding from this kind of cosmic particles is an extremely difficult task.

SPEs and GCR are anti-correlated at short timescales (months to years). At
periods of minimum flux of SPEs, GCR appear to have a peak in their intensity,
and vice versa (e.g. [16]). The proposed explanation to this behavior is the
following: at periods of minimum solar activity, the intensity of
interplanetary magnetic field (IMF) is reduced. As a result, it does not block
efficiently the incoming galactic cosmic radiation, which penetrates well
inside the solar region. The Badhwar-O’Neil 2010 model [17] is widely used to
account for the energy loss of GCR as they travel through the heliosphere,
considering factors like deceleration, diffusion and convection. In this
model, a parameter $\Phi$ of units MV is defined, in a way that a small value
of $\Phi$ corresponds to a large GCR flux. Typical values for solar minimum
condition are $\Phi=400-450$ MV and $\Phi=1000$ MV for a solar maximum, or
even $\Phi=1800$ MV for a very strong solar event [18].

###  2.2 Conditions on Mars

There have not been enough comprehensive measurements of the radiation
environment of Mars from orbit and from the surface. The MSL Radiation
Assessment Detector (RAD) instrument [19], launched as part of Curiosity
Rover, is currently estimating the radiation levels on the surface of Mars.
Located inside the Gale Crater (about 4 km deeper from the mean Martian
surface - elevation is estimated by Mars Orbiter Laser Altimeter, [20]), it
measures since August 2012 charged and neutral particles by GCR and SPEs,
accounting for both downward and albedo particles [21, 22, 23]. It is a highly
valuable experiment, since it provides results for dose rates, zenith angle
dependencies, diurnal and seasonal variations, among others [24, 25, 26]. An
extensive review on the knowledge acquired by RAD is given in [27].

Observations of Martian environment are available from satellites and surface
detectors (e.g. the Marie instrument on board 2001 Mars Odyssey [28]), but
they are limited in time (last decades). As for in-situ data, they are only
available during the last few years with MSL RAD. Because of that, our
knowledge about the situation on Mars is limited, which affects the total
planning of missions. We then give a short review of the actual known
conditions on Mars, coming from long-term observations or models, and as
validated by RAD measurements.

As a fist approach, the bulk of Mars reduces radiation exposure to half for an
astronaut placed on Mars mission in comparison to when located in deep space.
All upward-directed rays are absorbed by the mass of the planet. Hence,
radiation arrives isotropically over a solid angle of $2\pi$ steradians.

Secondly, Mars is surrounded by a very thin atmosphere, composed almost
entirely by carbon dioxide ($CO_{2}$) with traces of nitrogen, water vapor,
and oxygen. At a mean density of 0.020 $kg\cdot m^{-3}$, it is two orders of
magnitude thinner than Earth’s atmosphere [29]. This very thin atmosphere
offers some protection from radiation though, preventing particles of low
energy to reach the surface. The proton energy cutoff has been found to be
around 150-160 MeV (it may vary between 155 to 178 MeV depending on the column
density, [30]). In other words, only particles with energies above this
threshold may pass through the Martian atmosphere. Some SPEs have these low
energies and are thus retained away from the surface due to ionization
processes, as opposed to GCR, which have generally more energetic spectra. GCR
interact with the molecules of atmosphere before being stopped, and they
create secondary particles which can traverse all of the atmospheric layers.

The direction of the incoming solar particles plays a role as well.
Atmosphere’s protection increases at low altitudes. Near the horizon,
particles have to travel through longer paths within the atmosphere when
compared to radiation coming from near the zenith. To give a quantitative view
of the importance of the particle’s origin, the density of the atmosphere at
zero elevation for zenith angle $z=0$ is 16.0 $g\cdot cm^{-2}$, whereas it
increases to 120 $g\cdot cm^{-2}$ at $z=90^{\circ}$ [31], so the additional
protection is obvious. The above hold true for SPEs at most. GCR flux is
almost kept intact over varying incoming angles, because of their relatively
higher energies. The elevation has a similar effect, as corresponding
radiation paths are shorter for example at the top of a mountain, compared to
the mean elevation level or deep inside a crater. It becomes clear that
radiation varies from location to location [32]. It is then crucial to
determine precisely the area of the human activity during the astronaut stay,
as we further discuss in Section 3.2.

Other phenomena that occur inside the atmosphere of Mars have a minor effect
in the radiation condition on the planet. For example, [33] compared the
short-term modulations of GCR-induced doses caused by local atmospheric
pressure changes with the long-term solar modulation of GCR, and concluded
that although the high-pressure atmosphere results in lower radiation levels,
surface doses are mainly influenced by the second effect. Similarly, dust
storms have insignificant effect in radiation doses, because dust density is
much lower than atmospheric mean density [34, 35]. Negligible is also the
effect by diurnal thermal tides and seasonal atmospheric variations [24].

At last, Mars lacks a global magnetic field [36]. There is not an intrinsic
magnetic field like Earth’s. Only various regional magnetic fields have been
detected, with intensities of 30-60 nT. These magnetic fields are remnants of
the planet’s ancient magnetosphere. In Earth, the analog situation is an
active dynamo, located in the core of planet, which covers its bulk. As a
result, charged particles easily impinge on the top layers of the Martian
atmosphere, since there is not a mechanism (like the magnetic lines) able to
deflect them and divert them to trajectories away from the surface.

The principal radiation source of radiation on the surface of Mars is GCR. GCR
are always present and appear as an isotropic, highly predictable and nearly
constant background radiation, hard to shield against [23]. Although their
overall daily flux may be low, they become dangerous when they accumulate
during long missions. SPEs are less frequent, less energetic and can easily be
attenuated by the atmosphere, but can potentially deliver great doses in a
short period of time and cause illness or even death [37].

Summarizing, the radiation field on the red planet comprises mainly of primary
GCR, along with secondaries generated in atmosphere and scattered from surface
[38]. Furthermore, the radiation environment on Mars is similar to the one in
the vicinity of ISS, as it was evaluated by RAD. Despite the fact that charged
particles trapped by the Van Allen belts shape the radiation environment
around Earth, which is not the case on Mars, their mean quality factors (see
Appendix) are similar. The total dose rate is around 0.240 mGy/day for ISS
region and 0.213 mGy/day on Mars [39].

##  3 Shielding strategies

In environments outside of Earth’s protective zone, like the one experienced
on the surface of Mars, human crews are exposed to great amounts of radiation.
This exposure might be acute, meaning that substantial amounts of radiation
strike during a short time interval, or chronic (low-level radiation doses,
which become dangerous when they accumulate in large numbers). We would place
SPEs in the first kind of exposure, and GCR in the second one. Obviously,
either of those should be addressed, as they can lead in devastating effects
in the astronauts’ health (e.g. [40]). The sudden particle flux by a major
solar event might be lethal [41], and the constant hit of GCR particles on
human cells perhaps leads into long-term sicknesses, like cancer [42]. Given
the above, it comes as no surprise that scientists and space agencies have
developed many strategies against radiation.

However, we notice that at mean quality factor (see Appendix) $<Q>\,=2-3$
(e.g. [23], [39], [43]), the radiation levels on the surface Mars are not
usually that high. For example, the exposure levels are on average below the
exposure limits adopted by NASA [44] (still, a solar event may rise absorbed
doses to critical levels). Nevertheless, a typical journey to Mars takes 2 to
3 years. During that time period of space travel in the interplanetary region,
astronauts will be exposed to substantial doses of radiation. These already
accumulated doses make it necessary to try to mitigate radiation levels on
Mars as well, through some strategies, in order to maintain exposure levels
below allowed career limits. We present some of these strategies in the next
parts. Note that up until this time, sustaining radiation levels on space
below acceptable limits has not been reached adequately yet.

###  3.1 Shielding techniques

At present, two main radiation shielding techniques on space have been
proposed and implemented, to name passive shielding and active shielding.
Passive shielding utilizes a bulk material, inside of which the majority of
particles’ energy is deposited before reaching the human bodies. Instead, the
main idea behind active shielding is to use electrostatic or plasma shields
and confined or unconfined magnetic fields to avert charged particles from
their original direction, thus minimizing or avoiding irradiation [45]. Active
shielding is a practical solution, considering the weight launch limitations
of passive shielding. However, it is still in quite theoretical stages and
many steps are needed before it can be applied in large scale, although it is
used in some cases. Given that, we do not examine further this strategy in
this work. An interested reader may refer to [46] for a more thorough analysis
of its possible implementation on Mars.

We focus our analysis on the other type of shielding, the passive shielding.
In this case, the shielding material fulfils two purposes. It has to stop
highly energetic particles inside its volume and additionally, minimize the
formation of secondary particles. Since the radiation risk comes mainly from
the energy lost by incoming particles within a tissue or organ, materials,
with respect to their passive shielding properties, are characterized by their
stopping power. The stopping power is practically the incoming energy lost per
unit of thickness through a material. Bethe-Bloch formula calculates the
stopping power $-dE/dx$ of a material (density $\rho$) when a charged particle
(charge $z$ in units of electron’s charge) travels through its mass [47]:

$-\frac{dE}{dx}=0.1535\frac{MeV\cdot
cm^{2}}{g}\rho\frac{Z}{A}\frac{z^{2}}{\beta^{2}}\left[ln\left(\frac{2m_{e}\upsilon^{2}W_{max}}{I(1-\beta^{2})}\right)-2\beta^{2}-\delta-2\frac{C}{Z}\right]$
(1)

where $Z$ and $A$ are the atomic number and weight of the material,
$\beta=\upsilon/c$ is the normalized velocity of the projectile ($\upsilon$ is
the projectile’s velocity and $c$ is the speed of light), $m_{e}$ is the
electron mass, $W_{max}$ is the maximum energy transfer in a single collision
and $I$ stands for the mean excitation potential. The last two terms,
$-\delta$ and $-2C/Z$, are correction terms. $\delta$ is the density effect
correction and $C$ is the shell correction. The gradient of energy deposited
through a material is also called linear energy transfer (LET) and is caused
by inelastic collisions with the target electrons.

From the above, we conclude the stopping power of a material is proportional
to $\rho Z/A$. This condition is fulfilled by high-density substances made
from chemical elements of low atomic number. It follows that materials with
many electrons per unit of mass, little mean excitation energy and least tight
binding corrections are the best energy absorbers. Typical such materials are
the ones rich in hydrogen, like water ($H_{2}O$) and polyethylene ($CH_{2}$).
Especially, liquid hydrogen is assumed to offer great protection, but due to
poor mechanical properties of materials like that, aluminum is at present most
commonly used in aerospace. Note that no material stops effectively the cosmic
radiation. The engineering strategy is to take advantage of sudden drops of
penetrating energy for a given material and then try to mitigate exposure
further using other countermeasures.

Yet, passive shielding has a critical limitation: additional weights targeted
for shielding purposes increase the payload of the launched vehicle. More
massive spacecrafts need substantial amounts of energy to escape the gravity
of Earth and travel through space. So, it’s impossible to limitlessly increase
the amount of shielding materials until they provide adequate radiation
protection. Therefore, other alternatives are required too, utilizing the in-
situ resources and structures. Some suggested ideas are described in the next
section.

###  3.2 Other strategies

In general, shielding strategies are different for the surface of Mars and for
deep space transits (or for Moon missions). For instance, neutrons and gamma
rays dominate in the Martian environment due to interactions with the
atmosphere and soil [48, 49], while in deep space, protons are the radiation
type which dominates. So, it is logical to take advantage of the unique
features of each specific radiation environment and plan our strategy
accordingly.

An alternative is using terrain features (like craters, cliffs, caves or lava
tubes) as protective shields. This option lies to the fact that since rays
arrive isotropically, covering a part of sky reduces some percent of these
rays, thus reducing accumulated radiation doses. Doses are for example lower
inside craters, contrary to the top of mountains. Similarly, when located up
against a cliff, the majority of radiation comes from the diametrically
opposite side of the sky [50, 51].

Water-rich regolith acts as a great attenuator against neutrons of energies
less than 10 MeV, e.g. [52]. These neutrons undergo elastic scattering on the
hydrogen atoms in water or ice, get captured by the latter and are less able
to continue their journey or get back-scattered. This is an indirect method of
reducing albedo particles doses. Neutrons of energies around some MeV are of
significant biological importance, due to their ability to penetrate deeply
into matter [53]. Their biological quality factor (see Appendix) is $Q>20$, as
defined by the International Commision on Radiological Protection [54],
whereas for other particles like protons it is around $Q=1$. For this reason,
protecting from neutrons is a critical issue and should never be neglected.
Regions rich in subsurface or surface ice (e.g. polar or subpolar regions) are
then proposed as landing sites [52].

Moreover, the employment of local regolith has been suggested in literature
(e.g. [55]). Unconsolidated regolith may act as the basis to manufacture
bricks. These bricks, combined with some kind of epoxy, would constitute a
habitat. Other scenarios include piling regolith over dwelling [56] and
tunnelling (digging the subsurface to create protected living places) [2].
Although these approaches are interesting, further issues must be addressed,
such as the carry of the mechanical tools required for digging and
construction. En route stops on objects like the Moon to gather regolith seem
impractical for the time being.

Astronauts themselves should also be protected by adopting personal protection
measures. That is, astronauts must limit time spent outside of the habitat,
during walks or expeditions. Even when located inside the vehicle, they should
stay as protected as possible. Storm shelters, for instance, are places inside
the habitat which offer increased protection from radiation. They are useful
during solar events, when the magnitude of Sun-originated protons rises
enormously. The prompt forecast of the space weather would be useful in that
case, but it is still an open issue to model the solar activity precisely.

Apparently, radioprotection on Mars is not a straightforward practise.
Absorbed doses may shift according to a wide range of (probably unpredictable)
factors like location, season, atmospheric conditions, solar activity or
others. It is unavoidable to account for as many as possible scenarios and
solutions before determining each specification of a human mission to Mars.

Lastly, another suggested countermeasure, not however specifically related to
Mars, is the consumption of medical and dietary supplements by the astronauts,
in order to mitigate the effects of ionizing radiation. These supplements are
technically pills, which help human organism to respond better against
radiation exposure (e.g. [57]). It is then quite understood that
radioprotection is not a simple one-dimensional issue, but a whole spectrum of
different engineering, operational, and dietary designs are required to ensure
the safety of astronauts.

Table 1: Adopted composition of Martian atmosphere Chemical Compound | Molecular Percentage
---|---
$CO_{2}$ | 95.10
$N_{2}$ | 02.59
$Ar$ | 01.94
$O$ | 00.16
$CO$ | 00.06
$H_{2}O$ | 00.15
Based on data taken by Mars Fact Sheet [29]. |
Table 2: Adopted composition of Martian Soil Chemical Compound | Molecular Percentage
---|---
$SiO_{2}$ | 51.2
$Fe_{2}O_{3}$ | 9.3
$H_{2}O$ | 7.4
$Al_{2}CaK_{2}MgNa_{2}O_{7}$ | 32.1
Based on regolith definition of the OLTARIS model [58]. |

##  4 Method

Radiation risk derives principally from the energy lost by the particles in a
tissue. Particles with high energies pass through tissues and deposit parts of
their energy in those. Multiple computational programs are adopted by
researchers to calculate energy distributions at various points of a tissue or
organ, and to determine the beneficial effect of materials used as shields
against radiation.

In this work, we use the Geant4 toolkit for our simulations, developed by CERN
[59]. Geant4 is a Monte-Carlo numerical model that simulates particle
propagation, used for a variety of purposes (e.g. medical, engineering)
including space science. Geant4 is specifically applied to model interactions
of radiation with matter, since it includes a wide range of physics processes
(hadronic and EM interactions, decays etc.), and enables complex geometrical
configurations. Besides, [58] has shown good agreement between MSL RAD data
[23] and the Geant4 code. Geant4 model, in turn, results in compatible results
with other codes. Minor discrepancies between different codes may arise due to
alternative model setups, geometrical configurations, tally specifications or
other reasons.

As all charged particles interact with matter in different ways, a variety of
physics models has been constructed to describe these interactions. These
interactions may be electromagnetic or hadronic elastic and inelastic
processes. Apparently, an extremely accurate physics model is anti-correlated
with the CPU performance. In other words, fast simulations usually provide
imprecise results, and conversely. To maintain computational times under
logical limits, without though losing much accuracy, we have to select a
solution halfway. Specifically, we use the G4Hadron-PhysicsQGSP_BERT_HP model
for inelastic hadronic interactions and G4EmStandardPhysics_option3 for
electromagnetic ones. Both of these physics lists have been shown to provide
accurate enough results for space and medical purposes [58]. As for other
interactions (e.g. elastic hadronic, decay) we adopt the pre-defined models of
the Hadr07
example111https://gitlab.cern.ch/geant4/geant4/-/tree/master/examples/extended/hadronic/Hadr07.
Detailed specifications for the above models may be found in the Geant4
Physics Reference
Manual222https://geant4-userdoc.web.cern.ch/UsersGuides/PhysicsReferenceManual/html/index.html.

###  4.1 Geometry

Our geometry setup is similar to the one used in [60]. Fig. 1 depicts the
model we constructed to simulate Mars. Adopted Martian atmosphere and regolith
compositions used in our simulations are displayed in Tables 1 and 2
respectively. We used the Martian Fact Sheet data in the first case [29] and
the definition of the OLTARIS model in the latter [58]. Our model is set to
compute radiation about 4 km below the mean Martian surface, at which depth
the RAD instrument is located. In that way, we were able to compare and
validate our results.

Our simulation world, as it is called in the Geant4 documentation, is a
rectangular box which consists of 6 successive layers. Each layer is
considered homogeneous in composition and density. At first, a 10-m-thick
layer of the condensed atmosphere is defined. Setting an atmospheric layer at
its actual size (about 100 km) is not feasible, so instead we had to compress
it and assign its density accordingly, so that its linear thickness remains
constant. The second layer of the simulation world is also an atmospheric
layer, now having its normal density and a maximum length of 2 m. The tested
shielding material comes next, which is followed by another surface atmosphere
layer. The fifth layer is a water slab, which represents an astronaut located
inside a habitat on Mars. A final layer of regolith (thickness of 3 m), which
acts as a cemetery of survived particles, closes the simulation box. Table 3
summarizes the specifications of each layer.

In such a way, Mars is represented as series of absorbing layers, spanning
from the top of its atmosphere (about 100 km above mean zero elevation) up
until some meters below its surface. The layer 3, as above described,
represents the roof of a habitat. We test several potential materials of which
it may be constructed, and change the respective thicknesses as well, in order
to figure out how radiation responds to varying lengths of shield. As for a
human phantom, we use the water slab, since an average tissue is made almost
completely out of water. The two left dimensions of the simulation world (x
and y) are large enough to avoid the escape of particles, which could falsely
reduce the calculated doses.

We acknowledge that the adopted geometry is quite simplified. For example, we
could have defined multiple atmospheric layers to account for density and
temperature variations through altitude. However, setting an extremely
detailed model of Mars is beyond the scope of this study, since our aim is to
qualitatively distinguish materials in accordance to their shielding
properties. For this purpose, a model like the one we adopted will suffice.

Table 3: Martian geometrical configuration Layer | Content | Bulk density (g $\cdot$ cm-3) | Thickness (m)
---|---|---|---
1 | Condensed atmosphere | 0.023 | 10
2 | Surface atmosphere | 0.00002 | 1
3 | Shielding material | (varying) | (varying)
4 | Surface atmosphere | 0.00002 | 2
5 | Water | 1.0 | 1
6 | Soil | 1.7 | 3
Figure 1: Martian geometrical configuration used for simulations. It consists
of 6 successive layers: Layer 1 (Condensed atmosphere), 2 (Surface
atmosphere), 3 (Shielding material), 4 (Surface atmosphere), 5 (Water) and 6
(Soil). Primary radiation hits at the top of the layers. Figure 2: The SPE
proton spectra during the events of February 1956, August 1972 and September
1989. Based on data taken by [61]. Figure 3: The differential spectrum of GCR,
as calculated by [17]. Blue lines stand for protons, red for alpha particles
and green for heavier nuclei. Bright colors represent the conditions of
minimum solar modulation and lighter ones for maximum solar modulation
conditions.

###  4.2 Primary particles

As mentioned previously, the Geant4 model has been demonstrated to simulate
particle spectra on the surface of Mars accurately enough for many particles,
such as protons, alpha particles or heavy ions, as verified by the MSL RAD
instrument [58]. However, results concerning other types of particles, like
neutrons, are not that close.

We choose to compare the stopping power against a stream of many particles
rather than the behavior of a material on one particle solely. In that way, it
is ensured that there are not any random interactions between the material and
the particle, affecting the net shielding effect, but all arbitrary behavior
is averaged out. More precisely, an almost pencil beam (the angular
distribution is 0.003∘) consisting of 1,000,000 primary particles for SPEs and
100,000 ones for GCR hits the model at the top, just like cosmic radiation
comes from the outer space. The statistical error of the simulations scales to
$1/\sqrt{N}$, where N is the number of primary particles, therefore, the error
in the results is roughly 0.1-0.3%, which allows us for robust conclusions. A
point source generates a planar flux of the primary particles, downward
directed. The reason for this choice was to minimise the escape of particles
outside of the simulation worlds; that is why a not-isotropic initial beam was
tested.

We analyze the response of shielding materials against cosmic radiation coming
from both sources, as defined in Section 2.1 (SPEs and GCR). In the first
case, we use three major historic solar events as representatives: February
1956, August 1972 and September 1989. As solar eruptions show notable
differences with each other in terms of intensity, abundance, composition and
duration, different input events of them are required to better study their
effect. Fig. 2 depict the energy spectrum of solar protons produced by these
three events (data were obtained by [61]). On the other hand, the
Badhwar-O’Neil 2010 model ([17]) is used to obtain the background GCR
spectrum. Protons, alpha particles and iron nuclei (as a substitute for
heavier particles) are considered. The primary GCR spectrum used in our
simulations is shown in Fig. 3.

Table 4: Dose rates in the water layer induced by GCR particles (minimum solar conditions) for shielding materials Material | Dose rate ($\mu$Gy/day)
---|---
no shielding | 296.7
aluminum | 214.3
polyethylene | 192.9
water | 199.4
regolith | 212.6
carbon fiber | 207.7
liquid hydrogen | 152.0
cyclohexane | 194.5
PMMA | 199.4
Mylar | 204.4
Kevlar | 201.1
Table 5: Comparison of the dose rates ($\mu$Gy/day) in the water layer induced by GCR particles (minimum solar conditions) for shielding materials and their combinations with regolith Material | 10 g cm-2 material | 5 g cm-2 regolith, 5 g cm-2 material
---|---|---
aluminum | 214.3 | 215.9
polyethylene | 192.9 | 201.1
water | 199.4 | 204.4
carbon fiber | 207.7 | 212.6
Table 6: Comparison of the dose rates ($\mu$Gy/day) in the water layer induced by GCR particles (minimum solar conditions) for shielding materials and their combinations with aluminum Material | 10 g cm-2 material | 5 g cm-2 material, 5 g cm-2 aluminum
---|---|---
polyethylene | 192.9 | 202.7
water | 199.4 | 206.0
regolith | 212.6 | 212.6
carbon fiber | 207.7 | 214.3

##  5 Results

Figure 4: LET by the February 1956 solar event versus depth in the water layer
for no shielding material, aluminum, polyethylene, water, regolith, carbon
fiber and liquid hydrogen. All of the materials have an area density of 10 g
cm-2. Figure 5: LET by the August 1972 solar event versus depth in the water
layer for no shielding material, aluminum, polyethylene, water, regolith,
carbon fiber and liquid hydrogen. All of the materials have an area density of
10 g cm-2. Figure 6: LET by the September 1989 solar event versus depth in the
water layer for no shielding material, aluminum, polyethylene, water,
regolith, carbon fiber and liquid hydrogen. All of the materials have an area
density of 10 g cm-2. Figure 7: LET by the GCR particles (minimum solar
conditions) versus depth in the water layer for no shielding material,
aluminum, polyethylene, water, regolith, carbon fiber and liquid hydrogen. All
of the materials have an area density of 10 g cm-2. Figure 8: LET by the GCR
particles (minimum solar conditions) versus depth in the water layer for no
shielding material, polyethylene, cyclohexane, PMMA, Mylar and Kevlar. All of
the materials have an area density of 10 g cm-2.

As a first step, we ran the fundamental situation of our simulations, i.e. the
situation without any shielding material. Hence, radiation could travel freely
through the atmospheric layers before reaching the layer representing the
astronaut’s body, mimicking the actual conditions and natural shielding of
Mars. The resulting dose rate, induced by GCR, ranged in our model between
172.8 $\mu$Gy/day (maximum solar conditions) and 296.7 $\mu$Gy/day (minimum
solar conditions). These values are quite consistent with the RAD measurements
in detector E (plastic), which lie in the interval of $\sim$ 200 - 325
$\mu$Gy/day from MSL landing until late 2020 [27]. This consistency is
particularly encouraging considering the simplicity of the model we built and
shows that our outcomes should be compatible with other outcomes deduced by
much more complex models.

We continue with examining the effect of the shielding materials. The energy
deposited per depth versus the depth in the water layer, caused by three
typical solar events, are shown in Fig. 4, 5 and 6 for some specific
materials. The materials tested are aluminum, polyethylene, water, regolith,
carbon fiber and liquid hydrogen, and they are assigned the same area
thickness, 10 g cm-2. That way, we examine how helpful against cosmic rays a
material is, accounting simultaneously for its weight efficiency, as all of
them the simulated cases would have the same mass. For comparison, the
situation with no shielding material is given too. In Fig. 7 the behavior of
the same materials against the full GCR spectrum (protons, alpha particles and
helium ions) during solar minimum conditions (as a worst case scenario) is
presented.

Energies are definitely lower in the SPE-induced diagrams, since GCR are
characterized by a much harder spectrum. Additionally, some minor peaks and
overlaps are recognized. They could be attributed to the random interactions
of radiation with matter, which are quite visible due the low energies of
solar particles. In spite of that, some basic results may be inferred. For
instance, aluminum seems in all cases to be the worst shielding material,
among the ones tested, or, liquid hydrogen indeed maintains the exposure
levels at the lowest levels, as expected by eq. (1). Later on, we focus on the
GCR particles, which form the main field on Mars, as explained in Section 2.2.

We note that results by the GCR ions (Fig. 7) are compatible with the ones in
Fig. 4-6, by the SPEs. Again, liquid hydrogen poses as the best attenuator,
since it reduces roughly almost to half the absorbed doses in comparison with
the other materials. The rest of them have an intermediate behavior, reducing
radiation to about a third of the situation of no shielding at all. Our
results are in agreement with [56, 62], which also simulate the passive
shielding performance on the Martian field. In order of energy decrease,
materials are ranked as: liquid hydorgen, polyethylene, water, carbon fiber,
polyethylene, aluminum. Even the differences between the curves of the
simulated materials in Fig. 7 are almost identical with the respective
differences in the plots of Fig. 3 of [56]. As mentioned above, the
statistical error in the simulations is about 0.3%, and thus, we can
confidently assume that these deviations (at minimum $\sim$1-2%) do not come
from the random nature of the Monte Carlo calculations, but illustrate the
particular behavior of each material against radiation instead.

We now turn our attention on regolith’s performance. As mentioned, regolith
could significantly assist on the radiation shielding purposes, as it would
reduce the required payload. Thus, assessing the extent at which Martian
regolith could fulfil this purpose is an important issue. Our results suggest
that its behavior against charged particles is similar to aluminum’s (it is
slightly more effective). We remind that the same thickness in g cm-2 is
simulated here. Other materials, like the hydrogen-based ones, diminish
absorbed doses more, but the difference is only small (though definitely
larger than the statistical uncertainties). Consequently, regolith is
classified as a relatively quite effective materials against SPEs and GCR.
Previous studies deduce similar outcomes. In particular, [63, 56, 64] conclude
that $\sim$1 m of regolith shielding provides adequate protection, but
increasing the thickness attenuates radiation more gradually; in order to keep
effective dose below the safety limits more than 3 m of regolith are required.
Mixing regolith with graphite epoxy is proposed by [6], becuase of the
hydrogen compounds epoxy contains.

We further examine the performance of some materials, similar to polyethylene,
as well. Precisely, these hydrogen-rich materials are: high-density
polyethylene ($(C_{2}H_{4})_{n}$), cyclohexane ($C_{6}H_{12}$), PMMA
($(C_{5}O_{2}H_{8})_{n}$), Mylar $(C_{10}H_{8}O_{4})_{n}$) and Kevlar
$(C_{14}H_{14}N_{2}O_{4})_{n}$). Their plots are given in Fig. 8. We conclude
that they respond to radiation almost identically, and only minor differences
are noticed. This is of course expected, due to their analogous chemical
identity.

A quantitative comparison of the shielding effects of each one of the above
mentioned materials can be found in Table 4, where we present the GCR-induced
(minimum solar conditions) dose rates (see Appendix) in the water layer. As
noted above, the resulting doses for the hydrogen-based are very close to each
other, while liquid hydrogen maintains by far the lowest dose (51% of the dose
without passive shielding).

We continue by simulating combinations of passive shielding materials. As a
first scenario, we consider how efficient the piling up of regolith on top of
the habitat would be, compared to having the material of the habitat solely.
Outcomes are demonstrated in Fig. 9 and Table 5. Solid lines in Fig. 9
represent 10 g cm-2 of a material and dotted lines 5 g cm-2 of regolith
followed by 5 g cm-2 of the material. We see that combinations with regolith
are less helpful against the charged particles. In spite of this, they still
reduce incoming radiation at some considerable extent and differences between
the solid and dotted lines in Fig. 9 are only small ($<$ 0.1 MeV/mm). Regolith
properties are actually comparable with the aluminum’s, which means that the
obtained plot of the sequence 5 g cm-2 of regolith and aluminum is quite
similar with the one coming from 10 g cm-2 of aluminum. This is another
confirmation of the similar performance between regolith and aluminum. These
qualitative considerations are also supported by the dose rates in Table 5,
where it is shown that the combinations of regolith allow slightly larger dose
rates.

Figure 9: LET by the GCR particles (minimum solar conditions) versus depth in
the water layer for combinations of regolith (aluminum, polyethylene, water
and carbon fiber). Solid lines represent 10 g cm-2 of a material and dotted
lines 5 g cm-2 of regolith followed by 5 g cm-2 of the material. Figure 10:
LET by the GCR particles (minimum solar conditions) versus depth in the water
layer for combinations of aluminum (polyethylene, water, regolith and carbon
fiber). Solid lines represent 10 g cm-2 of a material and dotted lines 5 g
cm-2 of the material followed by 5 g cm-2 of aluminum.

Next, we perform similar simulations with aluminum combinations (Fig. 10 and
Table 6). The reason behind this options lies in the fact that the most parts
of spacecrafts are currently being constructed with aluminum; its performance
against cosmic radiation is then of notable interest. The plots of Fig. 10
indicate that polyethylene, water and carbon fiber mitigate radiation doses
more effectively solely, than when replaced with aluminum of the same weight.
5 g cm-2 of the regolith followed by 5 g cm-2 of aluminum indicate an almost
identical behavior with the energy deposition by 10 g cm-2 of a regolith, as
stated above. We have to mention though, that although aluminum’s
characteristics result in a bit higher doses, dissimilarities with different
materials are not large enough to exclude aluminum from a suitable shielding
material. On the contrary, we propose taking advantage of combinations of
aluminum with other material in order to reduce radiation doses, as suggested
in Fig. 10 and the values in Table 6.

##  6 Discussion

Despite its simplicity, our model has been demonstrated to provide a
sufficient simulation of the radiation conditions on Mars. We show that our
results are compatible with already published ones, either with alternative
and more complex models or with the actual measurements by RAD instrument
onboard Curiosity rover. Therefore, we infer that our above described results,
coming from the computational outputs, have a high degree of confidence. In
this Section, we discuss other parameters that could affect the outcomes.

At first, the Martian temperature at the equator can vary from -113∘ C during
the night to 17∘ C during the day [65]. Additionally, the atmosphere
experiences a thermal tide by the heat of the Sun on dayside and an infrared
cooling on the nightside. According to [33] though, their effects in the
radiation doses should be small compared to other factors like the solar
modulation. Therefore, we do not investigate any variations of absorbed dose
with respect to the temperature.

It is also worth to mention that the passing of cosmic rays through materials
has an important effect to the nature of the materials. The most
characteristic examples are the sensitivity of the electronic equipment to any
kind of radiation, and of course, the harmful effect of rays to human organs,
which rise to the creation of illnesses like tumors. An in-depth study of the
energy distribution of charged particles on the Martian environment is maybe
required to assess the damage on different substances, however, exploring
these effects in our simulations is beyond the scopes of this paper.

The regolith’s varying properties could potentially influence our decisions on
where to locate a human habitat on Mars as well. For example, the value of its
density has been derived in the literature from thermal inertia measurements,
or indirectly from rover measurements or from assumptions about the grain
density and the pore space, and there is a full range of values that can be
attributed to regolith’s density. The composition of Martian regolith can vary
itself too; near the poles of the planet regolith is found in combination with
water and ice, whereas near the surface it is mostly composed out of silicon.
In other words, we cannot adopt one composition model, as the regolith’s
characteristics depend strongly on the location. Nevertheless, despite the
fact the exact features of regolith may vary a little, it has been shown in
previous studies about Martian regolith [6] and about Moon’s regolith, which
is comparable to Martian [66, 67] that small changes don’t affect
significantly shielding properties. All subgroups of Martian soil have
basically the same shield protection, and so, analyses for in-situ resources
used for radioprotection can be reasonably made with a single Martian regolith
model.

Lastly, we note that the discussion about the real effectiveness of passive
shielding materials in space will become more established as soon as
experiments will be compared against models. For instance, [68] performed
experiments of polyethylene in a simulated Martian atmosphere and examined the
fabrication of composite materials based on Martian regolith using
polyethylene as a binding material. Inevitably, every coding model implicitly
makes a number of necessary simplifications of the actual conditions of an
environment, in order to keep simulation times manageable. Therefore, it is
always possible that some of the theoretical conclusions could be premature or
over-interpreted at some extent. Future work should shed more light on the
field.

##  7 Conclusions

Protection from radiation is a top priority in planning long-duration missions
in outer space. Especially on Mars, protecting astronauts from the hazardous
cosmic rays is absolutely necessary due to the continual bombard of Galactic
Cosmic Rays throughout the duration of the mission. A combination of
measurements and model calculations in context of Mars are needed to fully
understand the radiation effects on human health. Additionally, optimization
and validation of radiation mitigation strategies is absolutely essential for
preparing any human expedition of the red planet.

There is an ongoing effort to find suitable materials to protect astronauts
from radiation in deep space environments, like during the planned human
journeys to Mars. Likewise, the MSL RAD measurements have allowed us to
develop coding models of the Martian radiation environment and validate the
obtained results. Nevertheless, there is a lack in literature in combining
these two efforts, i.e. determining the behavior of passive shielding
materials specifically in the Martian radiation field. This study aims to
foster that need. We examined a number of materials in the Martian environment
according to their passive shielding properties, using both GCR and some
typical SPEs as input spectra. Apart from the most widely used materials in
spacecrafts and missions so far, we also tested a range of innovative
materials, not previously thoroughly analyzed for their radiation properties
or considered as an option precisely on Mars. As a next step, we moved on to
simulating combinations of materials with the common aluminum and the
potentially useful Martian regolith.

For that purpose, we developed a model of Mars using the Geant4 toolkit, in
which the planet was represented by a series of absorbing layers (atmosphere,
shielding material, water as a substitute of a human, and soil). To gauge the
accuracy of our model, we examined any sources of error and crosschecked the
resulting dose rates with the respective values by RAD, finding a significant
consistency. As a result, although such a slab-plane model has a much simpler
geometrical configuration compared to other published models used, we can
safely argue that our model can nonetheless provide us with valuable answers
to our research problem. Having an additional reliable and simple model of
radiation on Mars, which can run under reasonable computational times, is
quite valuable for a demanding and complicated task like protecting astronauts
there from the dangerous cosmic radiation.

Our simulations suggest that the richer a material is in hydrogen, the more
energy it absorbs. The most commonly used material in the aerospace field,
aluminum, is not as effective as water, carbon fiber or polyethylene, but its
still reduces a significant part of incoming radiation. We found that hydrogen
and carbon-based compounds have an analogous behavior against cosmic rays.
Lastly, we propose regolith combinations as an alternative option for
shielding purposes, in order to keep launch mass requirements reasonable,
although regolith’s response against charged and energetic particles is not
ideal, but sufficient enough.

The in-depth study of the radiation environment on Mars is more than needed in
order to plan and carry out successful human missions there. The engineering
approach is to prepare all systems for the worst case scenario, therefore more
work must be done in the space radiation field. Besides the obvious importance
of this kind of this research for human spaceflight, we remark that studying
the radiation field on Mars has many implications for astrobiology and the
possible mechanisms through which life could possibly have emerged on the red
planet.

## Acknowledgments

We thank the members of the Geant4 collaboration who developed the software
(geant4.cern.ch) used for this work. This work was supported by the New York
University Abu Dhabi (NYUAD) Institute Research Grant G1502 and the ASPIRE
Award for Research Excellence (AARE) Grant S1560 by the Advanced Technology
Research Council (ATRC).

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## Appendix

There is not an absolute way to calculate radiation risk. Some physical
quantities have been established to assess it. Usually, the following three
ways are adopted to measure radiation:

  * 1.

Dose ($D$): It is defined as the energy absorbed per mass, regardless of the
type of radiation. It is often measured in centi-Grays
($1\,cGy=0.01\,Gy=1\,rad$).

  * 2.

Equivalent dose ($H$): It is represented by dose multiplied by a correction
factor to account for the type of radiation. Its common unit is centi-Sieverts
($1\,cSv=0.01\,Sv=1\,rem$).

  * 3.

Effective dose ($E$): It is defined as equivalent dose multiplied by a factor
considering the part of the body irradiated.

More precisely, for all $i$ particles, each one of energy $E$, the dose at
depth $x$ is given by:

$D=\sum_{i}\int_{0}^{\infty}S_{i}(E)\Phi_{i}(x,E)dx$ (2)

$S_{i}(E)$ is the stopping power of the material and $\Phi_{i}(x,E)$ is the
flux of particles. Similarly, the equivalent dose is calculated by multiplying
the above relation with the weighting factor $Q_{i}(E)$ corresponding to the
particle type, as mentioned previously:

$H=\sum_{i}\int_{0}^{\infty}Q_{i}(E)S_{i}(E)\Phi_{i}(x,E)dx$ (3)

$Q_{i}(E)$ is computed by the linear energy transfer of each particle. Lastly,
the total effective dose for a human body is the weighted average for all
organs (subscript $o$ stands for organ and $w$ is the weighting factor [69]):

$E=\sum_{o}w_{o}H_{o}$ (4)

Hence, radiation quantities are corrected according to factors like the energy
spectrum intensity, composition and the tissue(s) impacted. Still, many
uncertainties arise when determining the radiation effects on astronauts.
Radiation risk varies for example as per other aspects like age, gender or
individual susceptibility.

The quality factor Q is introduced due to the fact that different radiation
types are not equally hazardous, even if they deposit the same energy. For the
dose equivalent, x-rays stand as the reference radiation type, at $Q=1$.
Electrons and photons have the same $Q$, while for protons it is $Q=2$. On the
other hand, helium nuclei are much more dangerous ($Q=20$), which is also the
value for 1 MeV neutrons. Neutrons’ $Q$ is decreasing for other energies. In
general, the absorbed dose is related to the energy lost by the incident
particles, although there are some exceptions to this behavior.

Finally, ICRP Publication 60 [70] introduced a mean radiation quality factor
$<Q>$ to distinguish between different radiation environments and gauge the
severity of them. $<Q>$ is calculated by dividing the total dose equivalent by
the total absorbed dose.