Radiation belt phase space density: Calculation analysis and model dependence

The reprocessing of radiation belt electron flux measurements into phase space density (PSD) as a function of the adiabatic invariants is a widely-used method to address major questions regarding electron energization and loss in the outer radiation belt. In this reprocessing, flux measurements j (alpha, E) at local pitch angles alpha, energies E, and optionally magnetometer measurements B, are combined with a global magnetic field model to express the phase space density f (L) in terms of the third invariant Phi proportional to 1/L at fixed first and second invariants M and K. While the general framework of the calculation is agreed upon, implementation details vary amongst the literature, and the issue of magnetic field model dependence is rarely addressed. This work reviews the steps of the calculation with lists of commonly used implementation options. For the first time, analysis is presented to display the effect of doing the calculation with different implementation options and with different backing models (including both empirical and MHD-driven models). The results are summarized to inform evaluation of existing results and future efforts calculating and analyzing radiation belt electron phase space density. Three events are analyzed, and while differences are found, the primary structural interpretations of the phase space density analysis exhibit model independence.