Radial diffusion in Saturn's radiation belts: A modeling analysis assuming satellite and ring E absorption

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Abstract
Phase space density profiles derived by Pioneer 11 and Voyager 1 investigators for Saturnian radiation‐belt protons with zero second adiabatic invariants and first invariants μ of 600, 1100, 2500, 5000, 10,000, and 20,000 MeV/G have been analyzed for the purpose of inferring the amplitude and L dependence of the time‐averaged radial diffusion coefficient D(L) in the inner magnetosphere. Three models for solid‐body absorption outside of L = 3 were considered. The first included satellite absorption only with satellites represented as simple geometric absorbers in an axially symmetric planetary magnetic field. The remaining two models included additional absorption by Ring E using a representative optical depth profile derived from ground‐based telescopic measurements and two possible characteristic latitudinal ring thicknesses. Minimum Ring E encounter times were estimated by assuming that the mirror latitude appropriate for the sampled protons is less than the maximum magnetic latitude of Ring E. The Ring E encounter times are generally longer than the estimated satellite absorption times for protons of these energies. Additional Ring E loss processes such as charge exchange in a possible associated torus could significantly reduce the effective loss times but are not considered in the present work. A low‐order L dependence (D(L) ∝ L², L³, or L4) was selected via a minimum‐variance criterion for five of the six data profiles studied for either of the three assumed absorption models. The cumulative number of selection occurrences for given assumed L dependences suggests a diffusion coefficient proportional to L3±1. The preferred amplitude D0 obtained for a given set of experimental phase space densities varies by a factor of 2 or 3 depending on which solid‐body absorption model was assumed. For μ ≤ 2500 MeV/G, forms for D(L) ranging from 0.5×10−9 L3±1 to 1.5×10−9 L3±1 s−1 were obtained. For μ > 2500 MeV/G the inferred amplitudes increased approximately monotonically with increasing μ reaching a maximum near 10−8 L3±1 s−1 at μ = 20,000 MeV/G. The latter increase may be an artificial consequence either of inappropriateness of the higher‐energy proton data profiles for analysis assuming simple diffusive transport or of underestimating the satellite absorption times at the highest proton energies. The inferred form for D(L) is least consistent with ‘terrestrial‐type’ diffusion mechanisms including magnetic impulses (D(L) ∝ L10) and electrostatic impulses of magnetospheric origin (D(L) ∝ L6 for μ ≪ 20 L² MeV/G and D(L) ∼ L10/μ² for μ ≫ 20 L² MeV/G). Theoretical models for ‘Jovian‐type’ diffusion via the ionospheric dynamo mechanism or the centrifugal interchange instability in regions of strong negative radial plasma density gradients predict lower‐order L dependences that appear to be more consistent with the inferred form.