Probability model for peak fluxes of solar proton events

A predictive model of worst case, > 10 MeV solar proton event peak fluxes is presented that fully accounts for the length of the space mission and the corresponding risk. Furthermore, the model predicts there is an upper limit which the peak flux can attain that is approximately twice the size of the largest observed peak flux to date. This is more restrictive than previous estimates of upper limits of solar proton event sizes that are based on historical evidence. It leads to a well-defined guideline for designing a space system that is radiation-hard against failures due to solar proton event peak flux effects. The model is based on a description of the solar proton event peak flux distribution obtained through application of the maximum entropy principle. This principle provides a mathematical basis for selecting the least biased distribution compatible with known information, and is especially useful for sets of data that are incomplete. The principle leads to a probability distribution that is a "truncated" power law. It behaves as a power law with an index of about -0.4 for 5-minute averaged peak fluxes less than about 10(3) cm(-2) s(-1) sr(-1). The distribution decreases more rapidly than this for larger peak flux values, and goes to zero at a maximum value of 1.78 x 10(5) cm(-2) s(-1) sr(-1). The theoretical distribution is in good agreement with satellite data dating back to 1967, which spans about 4 orders of magnitude in peak fluxes.