Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons

Lunjin Chen, Armando Maldonado, Jacob Bortnik, Richard M. Thorne, Jinxing Li, Lei Dai, Xiaoya Zhan

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90 down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude à and normalized wave number k≈z. The threshold for higher harmonic resonance is more strict, favoring higher à and k≈z, and the change in equatorial pitch angle is strongly controlled by k≈z. We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90.

Original languageEnglish (US)
Pages (from-to)6514-6527
Number of pages14
JournalJournal of Geophysical Research: Space Physics
Issue number8
StatePublished - Aug 1 2015

Bibliographical note

Publisher Copyright:
©2015. American Geophysical Union. All Rights Reserved.


  • bounce resonance
  • equatorial noise
  • magnetosonic waves
  • nonlinear
  • radiation belt
  • wave-particle interaction


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