Improvement of the Equivalent Sphere Model for Space Radiation Environments

In space radiation calculations it is often useful to calculate the dose or dose equivalent in blood-forming organs (BFOs), the eye, or the skin. Sometimes, an equivalent sphere is used to represent the organ for a fast estimate of the organ dose. It has been found that the equivalent sphere model (ESM) can approximate organ dose or dose equivalent values in galactic cosmic-ray environments. In solar particle event (SPE) environments, the model works marginally for BFOs, but it does not work for the eye or the skin. Here, we study the improvement of the ESM. Motivated by the two-component thickness distributions of the eye and the skin, we use two spheres with proper weights to represent the eye or the skin, and this drastically improves the accuracy. For example, in SPE environments, the average error for the skin dose equivalent using two spheres to represent the skin is [approximately]8%, while the average error using a single sphere is [approximately]100%.