Effect of shell splitting on radial diffusion in the magnetosphere

The radial diffusion coefficient DL attributable to pitch-angle scattering in the presence of magnetic shell splitting is calculated analytically to lowest order in µ0 and L, where µ0 is the cosine of the equatorial pitch angle at the midnight meridian and L is the McIlwain parameter. The result is that DL, ∼ Rs−8L10(µ0²/τ), where Rs is the stand-off distance to the magnetopause (in earth radii) and τ is the lifetime against pitch-angle scattering. For electrons (E > 0.5 Mev) having µ0 ≲ 0.5 this diffusion coefficient falls an order of magnitude below the coefficient of diffusion that is customarily extracted from observational data under the assumption that the first two adiabatic invariants are conserved.