Effects of Fine Spectral Structure of Chorus Emissions on Nonlinear Scattering and Acceleration of Radiation Belt Electrons

Whistler-mode chorus waves play a crucial role in accelerating electrons in Earth's outer radiation belt to relativistic and ultrarelativistic energies. While this electron evolution is typically modeled using a diffusion approximation for scattering, high-amplitude chorus waves induce nonlinear resonant effects that challenge this approach on short time scales. The long-term influence of these nonlinear interactions on radiation belt dynamics remains an unresolved issue. Recent simplified models suggest rapid nonlinear acceleration to ultrarelativistic energies, with formation of butterfly distributions during parallel wave propagation. In this study, we introduce a novel numerical approach based on Liouville phase space density mapping to investigate nonlinear scattering by high-amplitude waves over extended periods (minutes and beyond). We use a numerical wave field model of lower-band chorus risers that includes realistic fine-spectral features including subpacket modulations, phase decoherence, and jumps in wave normal angle. By incorporating these detailed spectral characteristics of the waves, we demonstrate that the rapid acceleration occurs across a broader pitch-angle range, forming a flat-top distribution. Similar effect is observed as the repetition period of chorus elements becomes shorter, with the additional effect of increased electron precipitation due to transition from bursty to continuous flux profiles in the loss cone. These findings highlight the importance of incorporating nonlinear effects and fine-scale wave properties in the future development of high-energy electron models for the outer radiation belt.