Eigenmodes of the transverse Alfv\ enic resonator at the plasmapause: a Van Allen Probes case study

A Pc4 ULF wave was detected at spacecraft B of the Van Allen Probes at the plasmapause. A distinctive feature of this wave is the strong periodical modulation of the wave. It is assumed that this modulation is a beating of oscillations close in frequency: at least two harmonics with frequencies of 15.3 and 13.6 MHz are found. It is shown that these harmonics can be the eigenmodes of the transverse resonator at the local maximum of the Alfv\ en velocity. In addition, the observed wave was in a drift resonance with energetic 80 keV protons and could be generated by an unstable \textquotedblleftbump on tail\textquotedblright distribution of protons simultaneously observed with the wave. The estimate of the azimuthal wave number m made from the drift resonance condition gives a value of about -100, i.e., it is a westward propagating azimuthally small-scale wave.