A note on vector flux models for radiation dose calculations.

This paper reviews and extends modelling of anisotropic fluxes for radiation belt protons to provide closed-form equations for vector proton fluxes and proton flux anisotropy in terms of standard omnidirectional flux models. These equations provide a flexible alternative to the data-based vector flux models currently available. At higher energies, anisotropy of trapped proton flux in the upper atmosphere depends strongly on the variation of atmospheric density with altitude. Calculations of proton flux anisotropies using present models require specification of the average atmospheric density along trapped particle trajectories and its variation with mirror point altitude. For an isothermal atmosphere, calculations show that in a dipole magnetic field, the scale height of this trajectory-averaged density closely approximates the scale height of the atmosphere at the mirror point of the trapped particle. However, for the earth's magnetic field, the altitudes of mirror points vary for protons drifting in longitude. This results in a small increase in longitude-averaged scale heights compared to the atmospheric scale heights at minimum mirror point altitudes. The trajectory-averaged scale heights are increased by about 10-20% over scale heights from standard atmosphere models for protons mirroring at altitudes less than 500 km in the South Atlantic Anomaly. Atmospheric losses of protons in the geomagnetic field minimum in the South Atlantic Anomaly control proton flux anisotropies of interest for radiation studies in low earth orbit. Standard atmosphere models provide corrections for diurnal, seasonal and solar activity-driven variations. Thus, determination of an "equilibrium" model of trapped proton fluxes of a given energy requires using a scale height that is time-averaged over the lifetime of the protons. The trajectory-averaged atmospheric densities calculated here lead to estimates for trapped proton lifetimes. These lifetimes provide appropriate time-averaging intervals for equilibrium models of trapped proton fluxes.