Acceleration of trapped electrons and protons through bimodal diffusion in the Earth's radiation belts

Trapped particles can be accelerated or decelerated by diffusing in L by means of either of two competing diffusion modes, of which one conserves the first adiabatic invariant μ and the other conserves the particle energy E. Acceleration through such ‘bimodal diffusion’ is most efficient when the two diffusion modes are about equally probable. A computer model is used to study the effect of bimodal diffusion on particle intensity profiles and energy spectra under a variety of conditions. Through the action of bimodal diffusion, an outer belt of energetic electrons can be created, with detailed spatial features governed by the L dependence of the particle transition probabilities for undergoing one or the other diffusion mode. If we simulate magnetic storms by enhancing constant-μ diffusion over constant-E diffusion and displacing the trapping boundary inward, then low-energy electron intensities in the outer belt rise, while high-energy intensities decrease at the start of the storm but subsequently increase. At infrequent intervals, unusually strong magnetic storms may push electrons into the inner-belt region. Once there, these electrons may remain trapped for a long time owing to the absence of strong perturbing mechanisms. Acceleration of trapped protons through bimodal diffusion can account for high-energy trapped protons in the inner-belt region. The effects of bimodal diffusion are less obvious for low-energy proton intensity profiles, and are of consequence mostly at higher L shells; generally speaking, low-energy protons can be accounted for by constant-μ diffusion acting alone. The widely different spatial patterns and temporal behavior displayed by the proton and electron belts can be understood as resulting primarily from different ratios of constant-E to constant-μ diffusion rates for the two particle species. A typical L-dependence pattern of trapped-particle energy spectra in the presence of bimodal diffusion consists of a domain at low L's where spectra become softer with increasing L and a domain at higher L's where spectra are independent of L. The point of transition between the two domains and the absolute values of the spectral parameter E0 (approximate e-folding energy of the integral particle intensity) depend primarily upon the energy spectrum and the location of the particle source and the ratio of constant-E to constant-μ diffusion rates. Sequences simulating geomagnetic events produce various spatial and temporal patterns of trapped-particle energy spectra very similar to those actually observed in the radiation belts.