Radiation dose and its protection in the Moon from galactic cosmic rays and solar energetic particles: at the lunar surface and in a lava tube

The GCRs are composed of energetic particles with a broad spectrum of energy and elements. About 98% are nuclei components and 2% are electrons and positrons. Among the nuclear components, ∼87% are protons, ∼12% are helium ions and ∼1% are nuclei of Z > 2, i.e. the HZE particles (e.g. Simpson 1983, George et al 2009). When these GCR charged particles enter the solar system, they interact with the outbound streams of the solar wind. GCR fluxes in the heliosphere vary between two extremes which correspond in time to the solar maximum and minimum activities. Solar activity and GCR fluxes are anticorrelated, the maximum of the particle intensity occurs during solar minimum conditions and the minimum exposure is reached at times of large solar activity.

In this study, we checked the elemental contribution to effective dose equivalent dividing it into Z = 1 (H), 2 (He), 3–10 (Li–Ne), 11–20 (Na–Ca) and 21–26 (Sc–Fe). The following equations were used to describe the differential spectra of GCR ${J_{{\text{GCR}}}}\left( {R,{\text{ }}W} \right)$ (m⁻² s⁻¹ sr⁻¹ (GeV/n)⁻¹) (Matthiä et al 2013).

$$\begin{equation*}{J_{GCR}}\left( {E,{\text{ }}\varphi } \right) = \frac{{{C_i}{\beta ^{{\alpha _i}}}}}{{{R^{{\gamma _i}}}}}\frac{{{A_i}}}{{{Z_i}}}\frac{1}{\beta }{\left( {\frac{R}{{R + {R_0}}}} \right)^{0.02W + 4.7}},\end{equation*}$$

$$\begin{equation*}{R_0} = 3 \times {10^{ - 4}}W + 0.37.\end{equation*}$$

Here subscript $i$ is the GCR element, $R$ is the particle rigidity (GV), $\beta$ is the ratio of particle speed and light speed, Z is the atomic number, A is the mass number, $W$ is the mean sun spot number for taking into account the influence of solar modulation and C (cm⁻² s⁻¹ sr⁻¹ GV⁻¹), $\alpha$ and $\gamma$ are fitting parameters given in the literature (Matthiä et al 2013). In this study, we calculated using $W$ = 0 (in 2010) and, 118.5 (in 2001) for the minimum and maximum phases of solar activity, respectively. Statistics of all ions are fixed to 1.0 × 10⁵ particles for the lunar surface (figure 1) and 5.0 × 10⁵ particles for the vertical hole (figure 2) to obtain the total dose rate by merging their dose rates.

Figure 3 shows the energy spectra of GCR hydrogen and helium determined by these equations. The fluxes during the solar maximum phase are lower than that during the solar minimum phase, and the peak energies are smaller. The GCR source particles are nuclei from hydrogen to iron with energies between 10 MeV n⁻¹ and 100 GeV n⁻¹. The spectrum at the lunar surface differs from the original GCR spectrum interacting with the surface and producing secondary particles. Figure 4 shows the calculated results for the proton flux at the surface during the solar minimum phase. The spectrum in the low energy region (<300 MeV) is almost flat so that the flux of secondary proton exceeds that of the primary protons below 300 MeV.

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Occasionally, the solar surface releases large amounts of energy in explosive outbursts on a wide electromagnetic band from radio waves, soft and hard x-rays, gamma rays, and highly energetic particles. In these SEP events, strongly varying magnetic fields from the solar corona accelerate the solar materials. Coronal particles with energies up to several GeV or higher escape into the interplanetary space spiraling around the interplanetary magnetic field lines. The energy spectra of particles observed in SEP events on Earth greatly depend on the size of the SEP events and its location on the sun relative to this connection. The measured flux of SEP varies from event to event up to about 5–6 orders of magnitude and also shows a large variability in energy spectra and elemental composition, having the potential to expose space crews to life threatening exposures. The occurrence is closely related to the solar activity cycle with a higher probability for the active phase of solar activity.

Most of particle energies in SEP events are typically less than 10 MeV n⁻¹. As protons with several MeV or lower energies have a short range, such protons will be shielded easily by shielding materials. However, in the worst case, large SEP events include a large amount of protons with GeV range energies.

There are anomalously large emissions of particles among SEP events which are sometimes observed as GLEs by Earth's ground neutron monitors since incident particles have sufficiently high energy at the top of the Earth atmosphere to generate a nuclear cascade producing an increased background intensity from cosmic radiation origin. The most extremely intense SEP events during the last five solar cycles were the November 1960 GLE event with a flux of 8 × 10⁹ cm⁻² and the August 1972 one with 5 × 10⁹ cm⁻². In this work, we took the results estimated by Mewaldt et al (2012) for the recent three large events in solar cycle 23, July 14, 2000, October 28, 2003 and January 20, 2005 as benchmarks.

The following two equations of the differential energy spectrum of the GLE proton ${J_{{\text{GLE}}}}\left( E \right)$ are used to describe GLEs.

$$\begin{equation*}{J_{{\text{GLE}}}}\left( E \right) = K{E^{{\gamma _1}}}{\text{exp}}\left( { - \frac{E}{{{E_0}}}} \right){\text{ }}\left( {E \leqslant \left( {{\gamma _1} - {\gamma _2}} \right){E_0}} \right)\end{equation*}$$

$$\begin{equation*}{J_{{\text{GLE}}}}\left( E \right) = K{E^{{\gamma _2}}}\left[ {{{\left\{ {\left( {{\gamma _1} - {\gamma _2}} \right){E_0}} \right\}}^{\left( {{\gamma _1} - {\gamma _2}} \right)}}\exp \left( {{\gamma _1} - {\gamma _2}} \right)} \right]\end{equation*}$$

$$\begin{equation*}\left( {E \geqslant \left( {{\gamma _1} - {\gamma _2}} \right){E_0}} \right).\end{equation*}$$

Here K, ${\gamma _1},$ ${\gamma _2},$ and ${E_0}$ (MeV n⁻¹) are the fitting parameters from the literature (Mewaldt et al 2012). As shown in figure 5, the intensity and the slope are different in each event. The energy range was fixed as 10 MeV n⁻¹–100 GeV n⁻¹ the same as for the GCR source. The energy spectra for 2000 and 2003 events bend at around 100 MeV, while the event in 2005 shows a simple power law spectrum. The energy spectrum slope of the 2005 event is much steeper than slopes from events of 2000 and 2003, although the 2005 event is similar in the GCR energy spectrum. Statistics of GLE protons are fixed as 1.0 × 10⁷ particles.

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The effective dose equivalents from GCR irradiation at the lunar surface are summarised in table 2. 'Others' in table 2 contains secondary ions and particles except neutron. The effective dose equivalents in solar minimum and maximum phases were 416.0 mSv yr⁻¹ and 160.5 mSv yr⁻¹, respectively. Although the GCR exposure evaluation highly depends on the model and environment, our results were generally consistent with previous estimations (e.g. Ballarini et al 2006, Slaba et al 2011, Zeitlin et al 2013, Dobynde and Shprits 2020).

The career exposure limit of crews on the ISS is given in table 3 (JAXA 2013). Strategic radiation shielding is encouraged for long term stays in the radiation environment found at the lunar surface. As seen from table 2, the contribution due to the secondary particles is ∼20% of the total exposure due to GCR particles at most. This implies that the contribution of the lunar surface to the radiation exposure by producing secondary particles is not so high.

Figure 6 shows the contribution of various elements to both the effective dose equivalents at solar minimum and maximum phases. Note that each contribution in this figure includes the contribution of their secondary particles. In spite of the fact that the fluxes of Z > 2 particles are only ∼1%, the radiation exposure from those particles was larger than 50% of the total. It is obvious that the evaluation of HZE particles is essential.

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The effective dose equivalents due to direct exposure to the three GLEs are summarised in table 4. These results and their ratios are consistent to previous estimations (Benghin et al 2005, Hayatsu 2012). The solar event of July 14, 2000 yielded the largest effective dose equivalent of 2190 mSv among the three events. This value is so large that body damages are expected. On the other hand, radiation protection by shielding materials effectively reduces radiation doses by the GLEs since the GLEs are dominated by relatively low energy particles (Slaba et al 2011). A large contribution of low energy particles can also be expected by the small values of secondary doses in table 4. It is clear that shielding is fundamental.

Other contributor to the lunar exposure is radioactive elements. Long time exposure to high energy particles produces cosmogenic nuclides such as ²²Na, ²⁴Na, ²⁶Al, ⁵⁴Mn and ⁵⁶Co. These radioactive elements emit gamma-rays providing radiation exposure as well as natural radioactive elements of K, Th, and U series. Here, the cosmogenic nuclides of ²²Na, ²⁴Na and ²⁶Al, which have relatively large intensities on the lunar surface (Reedy 1978), and the natural radioactive elements were taken into account to obtain the effective dose equivalent. The production rates of the cosmogenic nuclides were based on Reedy (1978). The abundances of the natural radioactive elements on the lunar surface have been measured by gamma-ray spectrometers onboard lunar orbiters (e.g. Lawrence et al 2000, Prettyman et al 2006, Kobayashi et al 2010, Yamashita et al 2010, Naito et al 2019). They become maximum at around Fra Mauro with values of ∼4300 ppm K, 13 ppm Th and 7.3 ppm Th (Prettyman et al 2006, Yamashita et al 2010). These maximum abundances were assumed for estimation.

The effective dose equivalent due to the radioactive elements was calculated as ∼0.3 mSv yr⁻¹. It is found that the contribution of the radioactive elements is low comparing to those of GCR and GLE particles.