Time-Dependent Radiation Quality Factor <Q> of Galactic Cosmic Rays in Deep Space and Shielding Environments: Modeling and Measurements

TL;DR

The paper quantifies how the galactic cosmic ray LET spectra and the radiation quality factor <Q> evolve with solar modulation and shielding, using BON20 GCR fluxes modulated by φ and GEANT4-based transport to compute $D$, $H$, and $\langle Q\rangle$ in deep space and spherical shielding. It introduces ACR and radial-gradient corrections to align BON20 outputs with long-term CRaTER and Liulin-MO measurements, validating the approach across thin and thick shielding. The results show <Q> is strongly controlled by shielding thickness, weakly by solar activity, and reflect complex, element-specific responses of D_Z, H_Z, and <Q>_Z across the GCR spectrum. This provides a practical, time-resolved dataset for mission design and risk assessment in deep-space and planetary environments. The work also offers physical explanations for how light and heavy GCR elements differentially shape radiobiological impact as solar activity varies.

Abstract

Understanding the long-term variation of the galactic cosmic ray (GCR) radiation environment is critical for assessing radiation risks in space exploration missions. In this study, we systematically model the linear energy transfer (LET) spectra of GCRs and the corresponding radiation quality factor, <Q>, in deep space and shielding environments. The Badhwar-O'Neill 2020 (BON20) model is used to represent GCR fluxes under different solar modulation potentials (phi), which characterize the level of solar activity. GCR interactions with spherical shielding of different thicknesses are simulated to obtain the LET spectra, absorbed dose, dose equivalent, and <Q>. We present a comprehensive dataset of these quantities for a range of phi values and shielding thicknesses. The results show that <Q> depends strongly on the shielding thickness but only weakly on solar activity. Furthermore, model predictions are validated against long-term measurements from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) orbiting the Moon, and the Liulin-MO detector on board the ExoMars Trace Gas Orbiter (TGO) orbiting Mars. In this comparison, we consider factors for anomalous cosmic ray (ACR) contributions and radial gradients of both GCRs and ACRs, applying scaling factors of 6.3% at 1 AU and 11.0% at 1.5 AU to the calculated absorbed dose rate. With these corrections, the modeled absorbed dose rate and <Q> exhibit consistent temporal variations with the observations under both thin and thick shielding conditions. Moreover, we investigate the distinct temporal evolution of <Q> for light and heavy GCR nuclei, revealing how solar modulation influences the elemental radiation quality factor across GCR species. These results offer new insights into the temporal and environmental dependence of the space radiation quality factor, with implications for radiation dose estimate and crewed mission design.

Figures (9)

• Figure 1: Schematic diagram of the shielding setup adopted in this study. The layers shown here correspond to two-dimensional plane cuts. (a) In the first method, we employ 16 distinct spherical shells, each with a specific shielding thickness ($T_\mathrm{shield}$). The inner radius of the shielding layer ($r_\mathrm{in}$, shown in the plot) is fixed at 1 m. (b) In the second method, we use one single spherical shell configuration with a total thickness of 100 g/cm$^2$ and split it into 101 concentric layers. In both approaches, isotropic primary GCRs are injected into the system. Particle fluxes inside the shielding (Method 1) or at the inner boundary of each layer (Method 2, also see a zoomed-in view at its lower-right corner) are used for dose calculations in a 1 mm thick spherical water "detector" with an inner radius of 175 mm, which is located at the center of the shielding sphere.
• Figure 2: Shielding thickness distribution of TGO/Liulin-MO. (a) Probability distribution function. (b) Cumulative distribution function. In both panels, the original TGO/Liulin-MO shielding thickness distribution taken from semkova2021results is shown in blue. The rebinned distribution functions corresponding to the first and second methods are shown in orange and black, respectively.
• Figure 3: Deep-space GCR spectra in October 2019 (solar minimum between SCs 24 and 25) and the corresponding LET spectra. (a) GCR energy spectra of different species in BON20, with the modulation potential $\phi=398$ MV used as the model input for this period. (b) LET distributions ($L \equiv \mathrm{d}E/\mathrm{d}x$) in water as functions of particle kinetic energy $E$ for different species of GCRs. Panels (a) and (b) share the same legend shown at the bottom-left corner of panel (a). (c) Converted LET spectra of GCRs in deep space, derived from the results shown in panels (a) and (b). Curves with dotted points denote the modeled LET spectra for individual particle species; the dark-blue curve with triangles represents the LET spectrum summed over 26 elements (from H to Fe) in BON20, and the purple curve with squares shows measurements from the CRaTER D1 and D2 pair. Characteristic peaks in the LET spectrum for specific elements (H, He, C, O, and Fe) are marked. Detailed notations are listed at the bottom-left corner of this panel. (d) $\langle Q \rangle$ as a function of $L$ (for LET), taken from icrp60.
• Figure 4: Absorbed dose rate ($D$), dose equivalent rate ($H$), and the radiation quality factor $\langle Q \rangle$ under shielding conditions. (a)–(c) $D$, $H$, and $\langle Q \rangle$ obtained via the first method, shown as functions of the aluminum shielding thickness ($x$-axis) and solar modulation potential ($y$-axis). (d)–(f) Same parameters plotted in a same style as in panels (a)–(c), but obtained via the second method. (g)–(i) $D$, $H$, and $\langle Q \rangle$ as functions of the aluminum shielding thickness ($x$-axis) for fixed modulation potentials: $\phi=400$ MV (green), 700 MV (magenta), and 1000 MV (purple). (j)–(l) $D$, $H$, and $\langle Q \rangle$ as functions of the solar modulation potential ($x$-axis) for fixed aluminum shielding thickness values: $T_\mathrm{shield}=0$ g/cm$^2$ (i.e., deep space, in brown), 5 g/cm$^2$ (blue), 50 g/cm$^2$ (red). In each panel from (g) to (l), results from the first and second methods are shown as solid lines and dashed lines, respectively.
• Figure 5: LET spectra of GCRs from both modeling and measurements in October 2019 (solar minimum between SCs 24 and 25). (a) Modeled and measured LET spectra. The modeled LET spectrum for the CRaTER D1 and D2 pair with a thin aluminum shielding thickness of 0.22 g/cm$^2$ is shown in blue, with the corresponding measured spectrum plotted as a purple curve with squares. The modeled LET spectrum for TGO/Liulin-MO, based on the shielding thickness distribution in Figure \ref{['fig01:TGOthick']}, is shown in orange, with the corresponding measurement plotted as a brown curve with diamonds. (b) Logarithmic differences between the modeled and measured LET spectra for CRaTER (blue) and TGO/Liulin-MO (orange).