A theoretical model of the inner proton radiation belt

A theoretical calculation provides inner radiation belt proton intensities as a function of time and of the three adiabatic invariants, M , K , and L , in the kinetic energy range from ∼10 MeV to ∼4 GeV and the L range from 1.1 to 2.4. Long residence times for trapped protons of up to several thousand years require similarly long input time series for the geomagnetic field, solar activity, and solar proton fluences. Additional inputs include galactic cosmic ray spectra, nuclear scattering cross sections, and the neutral and plasma densities in the atmosphere, ionosphere, and plasmasphere. Trapped proton sources are cosmic ray albedo neutron decay (CRAND), calculated from a Monte Carlo particle transport simulation, and solar proton injection using a derived empirical injection efficiency that is ∼10 −4 at 10 MeV. Radial diffusion provides inward transport of injected solar protons. Calculated intensities at energies ≲100 MeV and for L ≳ 1.3 are dominated by solar protons, CRAND being the dominant source otherwise. Losses are by ionization of the neutral atmosphere, energy transfer to plasma electrons, and inelastic nuclear scattering. Numerical trajectory tracing determines trapping limits and drift shell averages of the albedo neutron intensity and of neutral and plasma densities for loss rate calculations. Geomagnetic secular variations cause adiabatic energy and drift shell changes. Intensities are greater than they would be in a constant geomagnetic field by factors up to ∼10, a result of long proton residence times and the presently decreasing geomagnetic dipole moment.