Test Particle Simulations of the Butterfly Distribution of Relativistic Electrons in Magnetic Dips

Magnetic dips are the localized depression of magnetic field in the inner magnetosphere and are suggested to play an important role in the formation of the butterfly distribution of relativistic electrons in the radiation belts. In this study, we conduct test-particle simulations to trace the electrons' trajectory within a magnetic dip and evaluate the response of PAD based on the long-term averaged flux of electrons between $L$ = 3–6 from Van Allen Probes. Our results show that the electron dynamics are significantly changed by magnetic dips, especially at the dip center. In a magnetic dip, the electrons' energy, $L$-shell, and pitch angle decrease, and the variation in $L$-shell is more significant than the pitch angle and energy. Based on the observational electron fluxes, the electron butterfly-like distributions are well reproduced by the simulation. Moreover, the parameterizations reveal that the butterfly distribution of electrons is closely related to the electron's energy, location, and depth of the magnetic dip. A negative radial gradient of electron flux also plays a potentially crucial role in the formation of the electron butterfly distribution. Our study provides deep insights into the evolution of the butterfly distribution of relativistic electrons within magnetic dips.