Phase relationship between ULF waves and drift-bounce resonant ions: A statistical study

We explore the phase relationship between the poloidal mode ULF wave electric field oscillations and drift-bounce resonant oxygen ions under the resonant condition of N = 2 at the magnetic equator. Using Cluster data from 2001 to 2004, we identify 55 fundamental poloidal mode wave events, among which 42 show "negative slope" pitch angle dispersion signatures in the southern hemisphere, 11 show "positive slope" dispersion in the northern hemisphere, and two near-equatorial events are associated with in-phase field-aligned signatures. For each event, the off-equatorial resonant ions are traced along their bouncing trajectories to determine the last time they moved across the equator. The resulting time series of the resonant oxygen ion fluxes at the equator are found to be statistically in antiphase with the wave electric fields. The resonant ion flux variation depends on both ion energy change and radial transportation. This antiphase relationship in statistics suggests two possibilities: (1) the fundamental poloidal mode wave electric fields are generally characterized by electric field intensity peaking near the magnetic equator if the flux variation is mainly caused by energy change and (2) the radial gradient of phase space density is positive if the flux variation caused by radial transportation is dominant.National Natural Science Foundation of China [41421003]; Major Project of Chinese National Programs for Fundamental Research and Development [2012CB825603]; NSERC; Canadian Space AgencySCI(E)ARTICLE77087-709612