“…MagEIS and REPT measure particle count rates and direction of arrival, which are then converted into particle fluxes and pitch angles using the known instrument characteristics such as geometry factors and the local direction of the geomagnetic field Blake et al, 2013]. In order to differentiate between the physical processes of radial transport and in situ energization, it is necessary to transform the flux and pitch angle measurements into phase space density (PSD), f , defined as f (W, , r) = j(W, , r)∕p 2 , where j is the measured differential directional flux and is a function of the particle energy W, pitch angle , spatial location r, and particle momentum p. In order to understand the physical process of electron energization, the electron PSD must be transformed and expressed in terms of the three adiabatic invariants of particle motion in the geomagnetic field, viz., , K, and L * [Schulz and Lanzerotti, 1974] which correspond to gyrational motion about the magnetic field, bounce motion along the field lines, and drift motion around the Earth, respectively.…”