Numerical investigation of solar energetic particle transport between the Sun, Earth, and Mars

Abstract

Solar energetic particles pose a danger to spacecraft electronics, and even more significantly, to a future spacecraft crew beyond the Earth’s magnetosphere. Given the current NASA and SpaceX interest in interplanetary space travel, solar energetic particles have therefore become the focus of much space physics and space weather research. Noting the frequent use of the Hohmann transfer (Hohmann, 1925) in interplanetary space travel, this study, assuming the Hohmann-Parker effect (Posner et al., 2013) addresses the propagation of potentially harmful 4 and 32 MeV protons along a Hohmann transfer trajectory between Earth and Mars. This is done using a one-dimensional finitedifference solar energetic particle transport model based on the Roelof (1969) equation. Different finite-difference numerical schemes/techniques are investigated, whereafter the model is compared to various contemporary models to establish its validity. An investigation into the spatial (z coordinate) and radial (r coordinate) dependence of the solar energetic particle peak intensities, anisotropies, and the so-called time of maximum, is presented. It is shown that the peak intensities and anisotropies along the Hohmann transfer display a power-law decrease, and that the peak intensities have an average functional form of z−1.06, which is found to decrease if smaller radial mean free path values are used. The peak anisotropies are found to have a functional form of z−0.18. The corresponding radial dependence of the solar energetic particle peak intensities is shown to have an average functional form of r−1.74, which is in consensus with the numerical studies of Lario et al. (2007) and He et al. (2017), and encouragingly, with the observational study of Lario et al. (2013). Assuming 4 MeV protons and varying scattering conditions, it is shown that a spacecraft crew halfway to Mars, along the Hohmann transfer trajectory, will have a “warning time” of approximately one hour once an SEP event peaks at Earth.