Analytic Expressions for Radial Diffusion

I briefly review, compare and contrast two theoretical works that have significantly influenced radial diffusion research thus far, namely, the works of Fälthammar (1965, https://doi.org/10.1029/JZ070i011p02503) and the works of Fei et al. (2006, https://doi.org/10.1029/2005JA011211). Leveraging Fälthammar's model for magnetic field disturbances, I demonstrate that Fei et al's formulas are incorrect: they underestimate radial diffusion by a factor two in the presence of magnetic field disturbances. This underestimation comes from the erroneous assumption that radial displacements driven by magnetic field disturbances are statistically independent from radial displacements driven by induced electric fields while in fact both displacements are proportional to each other. Fei et al.'s approach is similar to Fälthammar's approach in that they both analyze radial diffusion by pieces, depending on the nature of the driver. Yet, the Fokker-Planck equation requires only one radial diffusion coefficient to characterize statistically a trapped radiation belt population cross drift shell motion. Thus, it is worth questioning the practice that consists of defining the coefficient as a sum of independent contributions. In addition, both theoretical models rely on the assumption that the background magnetic field is primarily dipolar, leading to flawed estimates. To overcome these limitations and to improve radial diffusion quantification, I use a general formulation for the variation of the third adiabatic invariant (1) to describe how to compute a radial diffusion coefficient in the most general way and (2) to highlight the assumptions that need to be questioned.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV-even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp.

KEY POINTS

Analytic expressions for the radial diffusion coefficients are presentedThe coefficients do not dependent on energy or wave m valueThe electric field diffusion coefficient dominates over the magnetic.