Nonlinear drift resonance between charged particles and ultra-low frequency waves: Theory and Observations

In Earth\textquoterights inner magnetosphere, electromagnetic waves in the ultra-low 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.