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Abstract Nonlinear interactions between electrons and whistler‐mode chorus waves play an important role in driving electron precipitation in Earth's radiation belts. In this letter, we employ the second fundamental model of the Hamiltonian approach to derive the inhomogeneity ratio, assessing nonlinear resonant interactions between nearly field‐aligned electrons and parallel propagating chorus waves. We perform test particle simulations by launching electrons from a high latitude to the equator, encountering counter‐streaming chorus waves. Our simulations reveal that anomalous scattering, encompassing anomalous trapping and positive bunching, extends the resonant location to the downstream of electrons. The comparison with test particle results demonstrates the efficacy of the inhomogeneity ratio in characterizing nonlinear interactions at small pitch angles. We emphasize the importance of applying this ratio specifically for small pitch angle electrons, as the previously provided inhomogeneity ratio significantly underestimates the impact of nonlinear interactions on electron precipitation. 

Abstract Last closed drift shell (LCDS) has been identified as a crucial parameter for investigating the magnetopause shadowing loss of radiation belt electrons. However, drift orbit bifurcation (DOB) effects have not been physically incorporated into the LCDS calculation. Here we calculate event‐specific LCDS using different approaches to dealing with the DOB effects, that is, tracing field lines ignoring DOB, tracing test particles rejecting field lines with DOB, and tracing particles including field lines with DOB, and then incorporate them into a radial diffusion model to simulate the fast electron dropout observed by Van Allen Probes in May 2017. The model effectively captures the fast dropout at highL*and exhibits the best agreement with data when LCDS is calculated by tracing test particles with DOB more physically included. This study represents the first quantitative modeling of the DOB effects on radiation belt magnetopause shadowing loss via a more physical specification of LCDS.