Modeling the Proton Radiation Belt With Van Allen Probes Relativistic Electron-Proton Telescope Data

An empirical model of the proton radiation belt is constructed from data taken during 2013\textendash2017 by the Relativistic Electron-Proton Telescopes on the Van Allen Probes satellites. The model intensity is a function of time, kinetic energy in the range 18\textendash600 MeV, equatorial pitch angle, and L shell of proton guiding centers. Data are selected, on the basis of energy deposits in each of the nine silicon detectors, to reduce background caused by hard proton energy spectra at low L. Instrument response functions are computed by Monte Carlo integration, using simulated proton paths through a simplified structural model, to account for energy loss in shielding material for protons outside the nominal field of view. Overlap of energy channels, their wide angular response, and changing satellite orientation require the model dependencies on all three independent variables be determined simultaneously. This is done by least squares minimization with a customized steepest descent algorithm. Model uncertainty accounts for statistical data error and systematic error in the simulated instrument response. A proton energy spectrum is also computed from data taken during the 8 January 2014 solar event, to illustrate methods for the simpler case of an isotropic and homogeneous model distribution. Radiation belt and solar proton results are compared to intensities computed with a simplified, on-axis response that can provide a good approximation under limited circumstances.