Using diffusion theory, the first results for a phase space three‐dimensional model of the electron radiation belt are presented. The model is based on the numerical solution of a diffusion equation which takes into account the deceleration of electrons by free and bounded thermospheric and ionospheric electrons, pitch angle diffusion by Coulomb and wave‐particle interactions and radial diffusion by magnetic and electric field perturbations. Sources of two types are included. Alone, the cosmic ray albedo neutron decay (CRAND) internal source gives results much lower than measured values, though with the addition of an external source, the orders of magnitude for the fluxes are reasonable, suggesting that the belt is created and maintained by the injections occuring during storms and substorms.

The Salammbô code, which solves the three‐dimensional phase‐space diffusion equation for the electron radiation belt, was used to explain the dynamic conditions present during a geomagnetic storm. With a simple injection model, we have characterized the dynamic behavior for relativistic electrons in the outer belt. The particles in the range 100 keV – 500 keV are diffused throughout the belt, with a shape essentially dependent on the radial diffusion coefficients. Particles with higher energies are “created” by acceleration of slower particles near the plasmapause location. The calculated shape of the fluxes in an L versus time grid for the 1 MeV electrons looks globally like those measured aboard the CRRES satellite.

Using diffusion theory, we give the first results for a three-dimensional model of the proton radiation belt. This is based on the numerical solution of a diffusion equation which takes into account the cosmic ray albedo neutron decay source, deceleration of protons by the free and bounded electrons of the medium, the charge exchange loss process, and radial diffusion by magnetic and electric field perturbations. This model used in static conditions gives results which are in a good agreement with those of NASA's AP8 model. However, a better knowledge of thermospheric densities, radial diffusion, and improved measurements of proton flux near synchronous orbit altitudes may be necessary to improve future model results. We prove that an external boundary condition, which plays the part of an injection source, is essential to radiation belt existence and explains the effect of solar activity and magnetotail dynamics on radiation belt dynamics. 17,181 ß i.

Abstract. Using a convection-diffusion theory, we give the first results from a four-dimensional model of electron and proton radiation belts. This work is based on the numerical solution of a convection-diffusion equation taking into account (1) for protons, the deceleration of protons by the free and bounded thermospheric and ionospheric electrons, the charge exchange loss process, radial and azimuthal transports, and (2) for electrons, the deceleration of electrons by the free and bounded electrons of the medium, pitch angle diffusion by Coulomb and wave-particle interactions, radial and azimuthal transport. This model allows for simulation of a magnetic storm effects by increasing convective electric field and injecting particles with keV range energies in the nightside region. Particles in the energy range 50 -100 keV are "created" by acceleration of slower particles in the L = 4 region. Four hours are needed for ring current formation. The calculated particle distribution at 6.6 Earth radii as well as at low altitude are in good agreement with those deduced from ATS 6 measurements (the drift echo is well reproduced at this altitude) and from statistical studies of the precipitation by the DMSP satellites, respectively.

No abstract