Radial Diffusion of Planetary Radiation Belts’ Particles by Fluctuations with Finite Correlation Time

Abstract

Abstract Radial diffusion in planetary radiation belts is a dominant transport mechanism resulting in the energization and losses of charged particles by large-scale electromagnetic fluctuations. In this study, we revisit the radial diffusion formalism by relaxing the assumption of zero correlation time in the spectrum of fluctuations responsible for the transport of charged particles. We derive a diffusion coefficient by assuming fluctuations that (1) are time homogeneous, (2) too small to trap the particles, and (3) can decorrelate on timescales comparable to the transit time of the particles. We demonstrate through self-similar solutions of the Fokker–Planck equation that autocorrelation time τ c much larger than the linear transit time/particle drift period τ L = Ω D − 1 results in characteristic time for transport independent of the drift frequency and faster than for short correlation time. In both instances, that is for short (τ L ≫ τ c ) and long (τ L ≪ τ c ) autocorrelation time, the diffusion of particles is subdiffusive since the variance of increments along the magnetic drift shells L*, scales as 〈ΔL*2〉 ∼ t s , with s < 1. However, in the absence of sources and sinks, particle transport for both short and long autocorrelation times result in equilibrium distribution along L* with differences of less than 10% across lower magnetic drift shells. The main consequence of incorporating finite correlation time appears in intermediate times much longer than the drift period but before the distribution function reaches equilibrium and indicates the importance of quantifying observationally the spectral properties of fluctuations for the modeling of planetary radiation belts.