Quasi‐Monochromatic Ultra‐Low‐Frequency Waves: A New Challenge for Wave‐Particle Interaction Models

Abstract Wave‐particle resonant interactions are the main driver of radiation belt dynamics. The electron motion in the strong dipole field consists of three types of essentially periodic components and possesses three corresponding adiabatic invariants. Consequently, three different types of waves contribute to violation of these invariants and associated electron acceleration, scattering, and radial transport. For the two fastest types of periodic motion, gyromotion and bounce motion, theoretical models of adiabatic invariant violation have covered two main regimes—the quasi‐linear regime of invariant diffusion and the nonlinear regime, characterized by large‐amplitude jumps of invariants. Until very recently, the slowest type of particle motion, the azimuthal drift, was included in the global simulations of the radiation belt dynamics only through quasi‐linear models of electron diffusion by ultra‐low‐frequency (ULF) waves. However, the growing number of spacecraft observations of narrow‐band intense ULF waves requires a formulation of a new theoretical framework accounting for the electron nonlinear resonant interactions with such waves. In this commentary, we review the recent progress in the development of this framework, most of which was originally reported in four recent papers (Li et al., 2018, 2020, 2021, 2024, https://doi.org/10.1029/2018gl079038 , https://doi.org/10.1029/2020ja027787 , https://doi.org/10.1029/2020ja028842 , https://doi.org/10.1029/2024ja032742 ). We also discuss the potential importance of nonlinear electron resonances with ULF waves for explaining observational features in electron flux dynamics.