LAUSR

Abstract. We present multi-period modulation of energetic electron flux observed by the BeiDa Imaging Electron Spectrometer (BD-IES) on board a Chinese navigation satellite on 13 October 2015. Electron flux oscillations were observed at a dominant period of ∼190  s in consecutive energy channels from ∼50 to ∼200  keV. Interestingly, flux modulations at a secondary period of ∼400  s were also unambiguously observed. The oscillating signals at different energy channels were observed in sequence, with a time delay of up to ∼900  s. This time delay far exceeds the oscillating periods, by which we speculate that the modulations were caused by localized ultra-low-frequency (ULF) waves. To verify the wave–particle interaction scenario, we revisit the classic drift-resonance theory. We adopt the calculation method therein to derive the electron energy change in a multi-period ULF wave field. Then, based on the modeled energy change, we construct the flux variations to be observed by a virtual spacecraft. The predicted particle signatures well agree with the BD-IES observations. We demonstrate that the particle energy change might be underestimated in the conventional theories, as the Betatron acceleration induced by the curl of the wave electric field was often omitted. In addition, we show that azimuthally localized waves would notably extend the energy width of the resonance peak, whereas the drift-resonance interaction is only efficient for particles at the resonant energy in the original theory.