Depth-Dose Equivalent Relationship for Cosmic Rays at Various Solar Minima

Galactic cosmic rays (GCR) pose a serious radiation hazard for long-duration missions. In designing a lunar habitat or a Mars transfer vehicle, the radiation exposure determines the shielding thickness, and hence the weight of spacecraft. In designing a habitat one has to focus on the worst-case radiation flux and its uncertainties. Using the spherically symmetric diffusion theory of the solar modulation of GCR, and data on the differential energy spectra of hydrogen, helium, oxygen, and iron from 1965 to 1989, it has been shown that the flux is determined by the diffusion parameter which is a function of the time in the solar cycle. This analysis also showed that the fluxes in the 1954 and 1976-1977 solar minima were similar and higher than those in 1965. In this paper, we have extended the spherical solar modulation theory back to 1954. These results show that the 1954-1955 GCR flux was nearly the same as that from 1976 to 1977 and that the 1965 flux values were nearly the same as those in 1986. Using this theory we have obtained the GCR spectra for all the nuclei and calculated the depth dose as a function of aluminum thickness. Using the ICRP 26 value for the quality factor, and the 1976-1977 spectra, it is shown that the shielding required to stay below 0.5 Sv is$17.5_{-3}^{+8}\ {\rm g}\ {\rm cm}^{-2}$ of aluminum, and$9_{-1.5}^{+5}\ {\rm g}\ {\rm cm}^{-2}$ to stay below 0.6 Sv. The calculated dose equivalent using the ICRP 60 values for quality factors is about 15% higher than that calculated using the ICRP 26 value. However, the errors on the quality factor itself may be substantial and are not taken into account.