A statistical analysis of the Kappa-type energy spectrum distribution of radiation belt electrons observed by Van Allen Probes

The energy spectrum of energetic electrons is a key factor representing the dynamic variations of Earth’s Van Allen radiation belts. Increased measurements have indicated that the commonly used Maxwellian and Kappa distributions are inadequate for capturing the realistic spectral distributions of radiation belt electrons. Here we adopt the Kappa-type (KT) distribution as the fitting function and perform a statistical analysis to investigate the radiation belt electron flux spectra observed by the Van Allen Probes. By calculating the optimal values of the key KT distribution parameters (i.e., κ and θ²) from the observed spectral shapes, we fit the radiation belt electron fluxes at different L-shells under different geomagnetic conditions. In this manner, we obtain typical values of the KT distribution parameters, which are statistically feasible for modeling the radiation belt electron flux profiles during either geomagnetically quiet or active periods. A comparison of the KT distribution model results with those using the Maxwellian or Kappa distribution reveals the advantage of the KT distribution for studying the overall properties of the radiation belt electron spectral distribution, which has important implications for deepening the current understanding of the radiation belt electron dynamics under evolving geomagnetic conditions.