Nonlinear Drift Resonance Between Charged Particles and Ultralow Frequency Waves: Theory and Observations

In Earth's inner magnetosphere, electromagnetic waves in the ultralow frequency (ULF) range play an important role in accelerating and diffusing charged particles via drift resonance. In conventional drift resonance theory, linearization is applied under the assumption of weak wave-particle energy exchange so particle trajectories are unperturbed. For ULF waves with larger amplitudes and/or durations, however, the conventional theory becomes inaccurate since particle trajectories are strongly perturbed. Here we extend the drift resonance theory into a nonlinear regime, to formulate nonlinear trapping of particles in a wave-carried potential well, and predict the corresponding observable signatures such as rolled-up structures in particle energy spectrum. After considering how this manifests in particle data with finite energy resolution, we compare the predicted signatures with Van Allen Probes observations. Their good agreement provides the first observational evidence for the occurrence of nonlinear drift resonance, highlighting the importance of nonlinear effects in magnetospheric particle dynamics under ULF waves. Plain Language Summary In Earth's Van Allen radiation belts, ultralow frequency (ULF) waves in the frequency range between 2 and 22 mHz play a crucial role in accelerating charged particles via a resonant process named drift resonance. When such a resonance occurs, a resonant particle observes a constant phase of the wave electric field, and it experiences a net energy excursion. In previous studies of drift resonance, a linearization approach is often applied with assumption of a weak wave-particle energy exchange. In this study, we extend the linear theory into the nonlinear regime to formulate the particle behavior in the ULF wave field, and predict characteristic signatures of the nonlinear process observable from a virtual magnetospheric spacecraft. Such newly predicted signatures are found to agree with observations from the National Aeronautics and Space Administration's Van Allen Probes, which provides the first identification of nonlinear drift resonance and highlights the importance of nonlinear effects in ULF wave-particle interactions in the Van Allen radiation belts.