Evidence for a Natural Limit to Electron Space Radiation: An Application of Benford's Law

Recent research has highlighted observational evidence for a natural limit to the severity of energetic electron differential fluxes in the Van Allen radiation belts. Here, we analyze the occurrence distributions of electron differential fluxes from the entire Van Allen Probes mission (2012–2019) to further investigate the energy dependence of electron flux distributions under the action of the flux-capping mechanism proposed by Kennel and Petschek (1966, https://doi.org/10.1029/jz071i001p00001). Specifically, we further examine the characteristics of the ensemble of flux values for at least weak geomagnetic activity (Dst30 nT) in the context of Benford's Law. Benford's Law proposes a logarithmic distribution of the first significant digit of ensembles of numerical values of various parameters, and has been found to be obeyed across a wide range of scientific, socioeconomic, and even financial data sets. We show that Benford's Law can be used to distinguish between the energies of electron flux distributions that are either strongly affected or largely unaffected by flux-capping Kennel-Petschek-like processes. In this paper, we present a representative numerical model of ensemble distributions formed through a large number of sequential multiplicative operations (such as those expected from repeated wave-particle interactions in the Van Allen belts). The model demonstrates that in the absence of capping processes, these distributions naturally evolve into log-normal forms. Furthermore, their first-digit occurrence distributions closely follow Benford's Law.