Simplified solar modulation model of inner trapped belt proton flux as a function of atmospheric density

Abstract

No simple algorithm seems to exist for calculating proton fluxes and lifetimes in the Earth's inner, trapped radiation belt throughout the solar cycle. Most models of the inner trapped belt in use depend upon AP8 which only describes the radiation environment at solar maximum and solar minimum in Cycle 20. One exception is NOAAPRO which incorporates flight data from the TIROS/NOAA polar orbiting spacecraft. The present study discloses yet another, simple formulation for approximating proton fluxes at any time in a given solar cycle, in particular between solar maximum and solar minimum. It is derived from AP8 using a regression algorithm technique from nuclear physics. From flux and its time integral fluence, one can then approximate dose rate and its time integral dose. It has already been published in this journal that the absorbed dose rate, D , in the trapped belts exhibits a power law relationship, D = A ρ - n , where A is a constant, ρ is the atmospheric density, and the index n is weakly dependent upon shielding. However, that method does not work for flux and fluence. Instead, we extend this idea by showing that the power law approximation for flux J is actually bivariant in energy E as well as density ρ . The resulting relation is J ( E , ρ ) ∼ ∑ A ( E n ) ρ - n , with A itself a power law in E . This provides another method for calculating approximate proton flux and lifetime at any time in the solar cycle. These in turn can be used to predict the associated dose and dose rate.