Galactic cosmic rays (GCRs) are high-energy particles originating from outside the solar system, consisting primarily of protons, helium nuclei, and heavier ions [1]. These particles travel at close to the speed of light and can penetrate spacecraft shielding, posing significant radiation risks to both astronauts and electronic equipment [2]. GCR radiation poses a significant concern for long-duration space missions, such as a Mars expedition, due to the extended exposure duration and the current inadequacy of shielding technologies to effectively mitigate the impact of such high-energy particles [3]. Understanding and accurately predicting GCR radiation doses are therefore critical for ensuring the safety of future manned missions to Mars and beyond.

The radiation environment in free space differs significantly from that on Earth’s surface. On Earth, the shielding effect of the ground limits GCR exposure to a 2 π geometry. Furthermore, the presence of Earth’s magnetic field and atmosphere significantly reduces the harmful effects of GCR radiation on humans and the environment. However, once outside the protective shield of Earth, during interplanetary travel, humans are exposed to substantially higher levels of GCR radiation, which poses serious health risks [4]. For example, in the International Space Station (ISS), typical GCR dose rates range from 90 to 110 μ Gy/day, excluding the influence of the South Atlantic Anomaly (SAA). In deep space near Earth, typical GCR dose rates increase to 250–500 μ Gy/day, reflecting the significantly higher radiation levels encountered during interplanetary travel [5]. In terms of observational data, the Radiation Assessment Detector (RAD) on board the Mars Science Laboratory (MSL) provided valuable observations of the GCR radiation doses during the spacecraft’s journey to Mars [6]. [3] reported measurements of the energetic particle radiation environment inside the MSL during its cruise to Mars from 6 December 2011, to 14 July 2012, offering important insights for future human missions to Mars. In addition, several GCR modulation models have been developed to predict GCR radiation doses under various conditions. These include the Badhwar-O’Neill (BON) model, the Heliospheric Modulation Model (HelMod), and the Cosmic Ray Effects on Micro-Electronics (CREME96) model, among others (e.g., [2,7]). These models estimate radiation exposure by incorporating factors such as solar modulation, spacecraft shielding, and particle transport [8]. However, the discrepancies between the observed and simulated data highlight the need for further refinement of these models [9].

The radiation environment in free space and exposure to GCR radiation are considered among the primary health risks for future long-duration human exploration missions [5]. [10] estimated the GCR radiation dose rates around the lunar surface, using a GCR radiation dose calculation model. Although the modeling results generally agreed with spacecraft observation, they underestimated the observations in the year 2012 (indicated as underestimation of the model in 2012 hereafter). In this study, following [10], we employ numerical simulations using the GCR modulation model developed in previous work [11–13] to calculate the GCR energy spectra for the four predominant GCR nuclei (protons, helium, oxygen, and iron ions) during the Earth-to-Mars transit. By combining these simulation results with the FDCCs from ICRP Publication 123 [4,14,15] and considering the contributions of different elements (based on the contribution percentages in Table 1 of [10]), as well as the underestimation of the model in 2012, we derive time-dependent GCR absorbed dose rates during the transit period, accounting for all 26 GCR nuclei. In Section 2, we introduce the methodology for calculating the GCR radiation dose during a flight to Mars. In Section 3, we present the calculated results and compare them with observations. Finally, in Section 4, we provide a summary and discussion of our study.

In the following, we present observational and numerical results for the radiation absorbed dose rates of GCRs during a flight to Mars (in silicon). The MSL spacecraft was launched to Mars on 26 November 2011. During most of the 253-day, 560-million-kilometer cruise to Mars, the RAD instrument made detailed measurements of the energetic particle radiation environment inside the spacecraft [23]. In the following, we use the dosimetry data from the MSL-RAD silicon detector B, as our model focuses on the dose rate from GCR charged particles in free space (excluding neutral particles such as neutrons), which aligns with the measurement capability of detector B. The data are sourced from the digitization of Figure 5 in [23], with the radioisotope thermoelectric generator (RTG) background already subtracted. The radiation measurements during the 7-month cruise to Mars exhibit characteristic variability patterns - including ∼ 27-day solar rotation effects, Forbush decreases, and SEP spikes. We have filtered the dataset by removing the five identified SEP events to ensure our analysis focuses exclusively on GCR-induced variations. A complete list of these SEP events can be found in the cruise phase analysis by [24]. Considerable work has been done comparing the measured and calculated dose rates (e.g., [25,26]). [3] reported that the BON11 GCR flux model used the HZETRN radiation transport code to calculate the dose rate of GCRs during the flight to Mars and estimated the contribution from pions and their decay products (including muons, electrons, and γ rays) during the flight to Mars [27,28].

Figure 1 shows the GCR radiation absorbed dose rate (in silicon) with the horizontal axis tracking the spacecraft’s transit time from Earth to Mars. The silver solid line with solid circles represents the absorbed dose rate detected by MSL-RAD/B, while the black solid line shows the smoothed result. As can be seen from the figure, the observed values of absorbed dose rate exhibit relatively severe fluctuations, which may be caused by local disturbances in the space environment. The blue solid and dash-dotted lines represent the modeling results from the BON11 model, without and with pion contributions, respectively [3].

In order to calculate the absorbed dose rates, we performed numerical simulations to solve the modulation model, i.e., the Parker transport equation of GCRs in the heliosphere, Equation 1, during the MSL spacecraft’s traveling from the Earth to the Mars. Figure 2 illustrates the interplanetary conditions, including the solar tilt angle, magnetic turbulence magnitude ( δ b ) , sunspot numbers, and spacecraft position in heliosphere, as a function of time during the Earth-to-Mars transit period (December 2011 - June 2012). These parameters – solar tilt angle, magnetic turbulence magnitude ( δ b ) , and spacecraft position in heliosphere – are also key inputs for our model of GCR modulation. The top panel shows the computed tilt angle of the heliospheric current sheet (HCS) for the new model from the WSO (http://wso.stanford.edu/Tilts.html). The second panel shows the square root of the magnetic field variances (magnetic turbulence magnitude) calculated following [10]. The third panel shows the monthly sunspot number from the WDC-SILSO (https://www.sidc.be/SILSO/datafiles). The bottom panel shows the radial distance of the MSL spacecraft from the Sun (https://omniweb.gsfc.nasa.gov/coho/helios/heli.html). In summary, the period was characterized by a fluctuating heliospheric current sheet (HCS) tilt, which is inversely related to radiation intensity; that is, the greater the tilt, the weaker the radiation. There was also increasing magnetic turbulence, which similarly correlates with weaker radiation as its magnitude grows. Additionally, there was a near-term decrease in sunspot numbers, despite the ongoing ascent of the current solar cycle, and this reduction in sunspot activity is associated with weaker radiation. Conversely, there was an increase in solar distance, which is directly related to radiation intensity; the greater the distance from the Sun, the stronger the radiation observed. During this period, the overall variation in absorbed dose rates (in silicon) is the combined effect of these several factors. We input these parameters into our numerical model to obtain numerical results.

In Figure 1, we present the GCR absorbed dose rates (in silicon) as predicted by our model. The red dashed line represents the absorbed dose rates due to the four main GCR species-hydrogen (H), helium (He), oxygen (O), and iron (Fe)-calculated using simulations based on the GCR modulation equation, denoted as D t m a i n . The red dotted line corresponds to the absorbed dose rates for a comprehensive set of 26 GCR particles, as forecasted by the model, labeled D t m o d . The red solid line illustrates the modeled results after correction, D t c o r r , which incorporates the 2012 underestimation factor, as detailed by [10]. The red dash-dotted line depicts the results, D t i n t , obtained by scaling the corrected dose rates D t c o r r with an optimized scaling factor α = 1.286 . This scaling factor α was determined by forcing the model mean to equal the observational data, which corresponds to a relative difference R D = 2.51% against the observational average. The silicon detector B detects a mixed radiation field of GCR and secondary particles inside the spacecraft, whereas our model is specifically for charged GCR in free space. Therefore, we propose that this scaling is primarily due to the secondary charged particle radiation resulting from GCR interactions with the spacecraft, which is not accounted for in our model. Additionally, other factors, such as uncertainties in estimating less abundant particle species, organ-averaging, and the constant water-to-silicon conversion coefficient, could also partially contribute to the observed discrepancy.

The results from Figure 1 indicate that, after correcting for the underestimation noted by [10], the results of D t c o r r closely align with the BON11 model without pions, both of which are slightly lower than the MSL-RAD/B observed data, showing a reduction of ∼ 20% compared to the background trend value inferred from the MSL-RAD/B observations within expected uncertainties. In contrast, the BON11 model with pions yields results that are very similar to the background trend value of the observations. These findings suggest that the secondary charged particle radiation (e.g., from pions) produced by GCR interactions inside the spacecraft during the journey to Mars significantly impacts the overall radiation dose rate. Assuming that the influence of secondary charged particle radiation produced by interactions of GCRs within the spacecraft can be represented by a scaling factor, we have adjusted our model D t c o r r , the scaling factor α = 1.286 to match the observed data, thus creating the scaled model D t i n t . We acknowledge that detector E provides a more comprehensive measure of the total dose, including neutral secondaries, and is recommended for future studies aiming to model the complete internal radiation field. Our analysis demonstrates that the results of the model D t i n t are in good agreement with the background trend value of the observations. Specifically, the GCR radiation levels exhibit a general, albeit slight, decreasing trend. This is consistent with the approach to the solar maximum of Solar Cycle 24 during this period [24], a pattern that is captured by both our model and the MSL-RAD observations. Furthermore, by comparing the interplanetary environment during the flight shown in Figure 2 with our radiation simulation results in Figure 1, it is evident that the modulation of GCRs is complex and influenced by multiple interplanetary factors.

In this study, we calculate the charged GCR radiation absorbed dose rate during a flight to Mars in free space, based on the GCR radiation dose rate model developed in previous work by [10]. Firstly, we use the GCR modulation model to calculate the differential flux j ( r , E , t ) of the four predominant GCR nuclei (protons, helium, oxygen, and iron ions) during the Earth-to-Mars transit from December 2011 to June 2012. Next, using Equation 5, we combine the differential flux j ( r , E , t ) with the absorbed-FDCCs d T , R ( E ) from ICRP Publication 123 [4,14,15], where Ω = 4 π , E ranges from 1 MeV/nucleon to 100 GeV/nucleon, R ∈ H, He, O, Fe, and n t = 15 , to obtain the time-dependent simulated absorbed dose rates for the four main GCR nuclei ( ∼ 73.5 % ) during the transit, D t m a i n . To save computing resources and improve efficiency, as done by [10], we use the calculated heavy ion oxygen ( ∼ 8.5%) as a reference and incorporate the radiation doses from the remaining 22 particles ( ∼ 26.5%) into the results for the four main GCR nuclei, yielding the radiation absorbed dose rates for all 26 GCR nuclei (H to Fe), D t m o d . Finally, based on the results in Figure 7 of [10] that reveal a ∼ 24.3% underestimation in our 2012 GCR absorbed dose model, we corrected for this underestimation proportionally to obtain the final modeling charged GCR absorbed dose rates (in silicon) for free space during the Mars transit, D t c o r r with Equation 6. Our simulation results are similar to those of BON11 without pions, both being slightly lower than the observed data from MSL-RAD/B during the flight. However, the results from BON11 with pions in the simulation, align well with the observed central values from MSL-RAD/B. Furthermore, considering that the MSL-RAD was placed inside the spacecraft during the Mars transit, it was exposed to a complex shielding environment, which resulted in significant secondary charged particle effects, such as those from pions, that contributed substantially to the radiation levels. To quantitatively account for the net effect of these unmodeled processes, we empirically determined a scaling factor ( α ) through an average fitting procedure that minimizes the discrepancy between our model results and the MSL-RAD observations. This empirically-derived factor α = 1.286 was optimized to bring the total radiation dose rate for the 26 particles into closer alignment with the measured data, with Equation 7. This approach allowed us to quantify the aggregate radiation contribution from secondary charged particles generated by GCRs within the spacecraft’s shielding. This suggests that the radiation effects of secondary charged particles (e.g., from pions) generated by GCRs inside the spacecraft during the Mars flight should be carefully considered as well.

The scaling factor α introduced in this study aims to correct discrepancies between model results and measurements from the MSL-RAD silicon detector B. It is important to note that silicon detector B is primarily sensitive to charged particles and insensitive to neutral particles such as neutrons and γ rays. Therefore, factor α primarily quantifies dose discrepancies attributable to unmodeled charged secondary particles (e.g., pions) and other potential systematic model errors, rather than representing the total contribution from all secondary particles. To accurately assess the total absorbed dose within spacecraft shielding (encompassing all charged particles and neutral components), data from MSL-RAD plastic scintillator detector E is both necessary and more appropriate. Detector E’s tissue-equivalent properties and sensitivity to neutral particles (neutrons, γ rays) enable it to provide dosimetric data more directly relevant to human radiation effects. Consequently, in future work, we will employ detector E measurements as a key benchmark for developing and validating advanced models capable of fully simulating the radiation fields of primary and all secondary particles within shielded environments. It should be noted that the MSL-RAD dose rates include particles from the spacecraft’s RTG power supply, which emits a steady background of neutrons and γ rays. The RTG background contributions require correction for the data from detector B. In contrast, the influence on the dose measured by detector E is negligible because its energy threshold is high enough to exclude this background.

The discrepancies between our simulation results and observational data primarily stem from the following sources: First, inaccuracies in the GCR modulation model arise due to an oversimplified representation of magnetic turbulence and the heliospheric structure, along with insufficient consideration of localized and transient solar variations. These limitations diminish the model’s ability to fully reproduce the observed particle fluxes. Second, uncertainty is introduced in the estimation of contributions from less abundant particle species. Rather than performing explicit numerical simulations for these minor components, we relied on widely accepted abundance ratios from established literature, which may not capture the specific environmental conditions during the observation period. Third, the calculation of dose averages across 15 organs/tissues specified by the ICRP reference phantoms [4] –while providing a representative whole-body value–may overlook anatomical variations and tissue–specific energy deposition patterns, potentially introducing inaccuracies in biological dose estimation. Fourth, the use of a constant conversion coefficient between water and silicon-based dose measurements neglects energy-dependent and material-specific effects in radiation energy deposition. This simplification fails to fully represent the complex particle interactions within different detector and tissue materials. Finally, methodological differences between computational dose assessments and physical measurements contribute to the discrepancies. While our simulation follows ICRP guidelines for radiation protection quantities, the MSL-RAD measurements were obtained using a silicon detector located inside the MSL spacecraft during its journey to Mars, positioned directly beneath the descent stage and above the heat shield. This difference in phantom geometry, material composition, and shielding configuration between computational models and physical detectors introduces inherent inconsistencies in dose comparisons. Our model is currently primarily used for calculating GCR radiation doses in free space and does not yet account for secondary particle effects under different shielding conditions. Therefore, future work will require the use of a dedicated simulation model, such as GEANT4, to evaluate radiation doses under various shielding conditions. For such validation, measurements from the MSL-RAD scintillator detector E will be prioritized, as its tissue-equivalent composition and heightened sensitivity to low-energy secondary particles (e.g., electrons, gammas, and neutrons) provide a more relevant benchmark for assessing the total absorbed dose inside a spacecraft.