Comparison of Formulas for Resonant Interactions between Energetic Electrons and Oblique Whistler-mode Waves Jinxing Li, Jacob Bortnik, Lun Xie, Zuyin Pu, Lunjin Chen, Binbin Ni, Xin Tao, Richard M. Thorne, Suiyan Fu, Zhonghua Yao, and Ruilong Guo
Test particle simulation is a useful method for studying both linear and nolinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell, and the most recent relativistic form was given by Ginet and Albert and Bortnik. However, recently we found there was a (-1)^{l-1} term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggest a check of the signs for self-consistency which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.
We acknowledge Cluster Active Archive Web sites for provision of data from STAFF instrument on Cluster. This research is supported by the NSFC grants 41374166, 41274167, 41204120, and 40831061 and the Chinese Key Research Project 2011CB811404. UCLA authors would like to gratefully acknowledge the support of NSF’s Geospace Environment Modeling grant AGS-1103064 in performing this work. Binbin Ni also acknowledges the support from the Fundamental Research Funds for the Central Universities grant 2042014kf0251.
Li, J., et al. (2014), Interactions between magnetosonic waves and radiation belt electrons: Comparisons of quasi-linear calculations with test particle simulations, Geophys. Res. Lett., 41, doi:10.1002/2014GL060461.