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

Li Li, Xu Zhi Zhou, Yoshiharu Omura, Zi Han Wang, Qiu Gang Zong, Ying Liu, Yi Xin Hao, Sui Yan Fu, Margaret G. Kivelson, Robert Rankin, Seth G. Claudepierre, John R. Wygant

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)8773-8782
Number of pages10
JournalGeophysical Research Letters
Issue number17
StatePublished - Sep 16 2018

Bibliographical note

Funding Information:
This study was supported by NSFC grants 41774168, 414221003, and 41474140. Y. O. acknowledges support from JSPS KAKENHI grant 17H06140, and R. R. acknowledges support from Canadian Space Agency and NSERC. The Van Allen Probes data used in this study can be accessed from NASA’s Space Physics Data Facility at


  • ULF waves
  • drift resonance
  • nonlinear process
  • particle acceleration
  • radiation belts
  • wave-particle interactions

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