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

Anton V. Artemyev; Michael D. Hartinger; Dmitri L. Vainchtein; Robert Rankin

doi:10.1029/2025JA034043

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. Plain Language Summary Understanding of complex space plasma systems starts with the revealing of peculiarities of individual charged particle dynamics in electromagnetic fields characterized such systems. There is no analytical solution of equations of motion of charged particles experiencing Lorentz force in and arbitrary electromagnetic field. Therefore different problems require different approximate/perturbative approaches within the discipline of classical mechanics, that can quantify charged particle motion. One of the most powerful approximations is the theory of adiabatic invariants, that found distinct applications in many space and laboratory plasma problems. Different aspects of this theory provided us with a quite comprehensive description of charged particle motion in near‐Earth plasma environments, such as the inner Earth's magnetosphere. In this commentary paper, we aim to review a recent development of the application of the theory of adiabatic invariants to electron dynamics in quasi‐monochromatic electromagnetic fields, that oscillate on time scales similar to those of the electron drifts in Earth's dipole. We argue that basic ideas of this development can be important for different space plasma systems. Key Points We provide an overview of recent investigations of nonlinear electron interactions with ultra‐low‐frequency (ULF) waves We discuss criteria for the application of theory of nonlinear resonant interactions for ULF waves We discuss the relevance of nonlinear interactions for radiation belt dynamics

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

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

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