A Pc4 ultralow frequency 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 Alfvén velocity. In addition, the observed wave was in a drift resonance with energetic 80-keV protons and could be generated by an unstable bump on tail 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, that is, it is a westward propagating azimuthally small-scale wave. Plain Language SummaryThe study presented in this paper can be considered as the first direct experimental confirmation of the existence of the transverse Alfvénic resonators on the plasmapause exited by the kinetic instabilities in the hot plasma component. An Alfvén wave was detected by the Radiation Belt Storm Probes spacecraft B spacecraft on 23 October 2012 at the outer edge of the plasmapause where Alfvén velocity has a local maximum. The wave had strong amplitude modulation of the magnetic and electric fields. This amplitude modulation was the result of the superposition of (at least) two harmonics with close frequencies 15.3 and 13.6 mHz. We suppose that these harmonics are eigenmodes of the transverse Alfvénic resonator at the plasmapause. Moreover, the energetic proton fluxes were strongly modulated by the wave at energies near 80 keV. Assuming the drift wave-particle resonance, we found that the wave was azimuthally small-scale westward propagating wave with the azimuthal wavelength at the geomagnetic equator about 0.3 Earth's radius. The wave was probably generated by the instability caused by the inverted (bump on tail) proton distribution for energies below 84.4 keV.

Magnetic azimuthally small-scale (azimuthal wave numbers m ≫ 1) pulsations in Pc4-5 bands (45-600 s periods; Jacobs et al., 1964) on the dayside of the Earth's magnetosphere are intensively studied in recent years. The high-m waves are observed by satellites, high-frequency radars (Shi et al., 2018, and references therein), and optical manifestations of auroral undulations (Motoba et al., 2015). Generally, these waves propagate westward (m < 0; see Chelpanov et al., 2018), but some authors reported eastward propagating waves (e.g., Chelpanov et al., 2019;Yamamoto et al., 2019). These waves are believed to be excited through drift or drift-bounce resonance with ∼1-100 keV protons (Min et al., 2017;Takahashi et al., 2018). Electron flux oscillations in a wide energy range were found to correlate with Pc4-5 waves as well (Ren et al., 2017(Ren et al., , 2018. The energy transfer from particles to the wave going through internal instabilities caused by non-Maxwellian proton distribution or phase space density radial gradient (Southwood et al., 1969). Usually, Pc4-5 waves are associated with the MHD Alfvén waves (e.g., Dai et al., 2013), although sometimes they can be identified with the drift-compressional modes (Mager et al., 2019;Rubtsov et al., 2018). According to previous studies, the dayside high-m Pc4-5 waves usually appear as a consequence of magnetic storms (

This paper is concerned with the structure of ion-ion hybrid (IIH) waves in multicomponent magnetospheric plasma in the dipole geomagnetic field model. Like Alfvén waves, in IIH waves the field line can oscillate in different directions: in the azimuthal direction (the toroidal modes) and in the radial direction (the poloidal modes). Contrary to Alfvén waves, in IIH waves only the equatorial part of the field line can oscillate, since due to the heavy ions admixture the IIH waves are trapped in the resonator in the vicinity of the geomagnetic equator. The equatorial localization of the waves allow the calculation of the parallel structure of the toroidal and poloidal IIH modes analytically. It was found that the toroidal and poloidal modes have slightly different structures and that their frequencies are also slightly different. The difference between toroidal and poloidal frequencies (the polarization splitting) is small with respect to the basic harmonics of each mode. It was found that IIH modes have a considerable compressional component of the wave's magnetic field.

Ultra-low frequency (ULF) waves are regularly observed in the Earth's magnetosphere. They are a convenient magnetospheric diagnosing tool because they interact with energetic charged particles. ULF waves of the Pc4-5 (40-600 s period) ranges most often are Alfvén waves standing along the magnetic field line between magnetically conjugated points in the ionosphere. Besides, the observed Alfvén waves differ in polarization (Anderson et al., 1990): if the radial component of the wave's magnetic field is much larger than the azimuthal component, then such a wave is called a poloidal Alfvén wave, and in the opposite case a wave is called a toroidal one. Poloidal Alfvén waves can interact with charged particles via the drift or drift-bounce resonances (Klimushkin et al., 2021), since they have significant azimuthal component of the wave electric field coinciding with particle drift direction, which leads to acceleration or deceleration of the particles. These resonant interactions are important for the dynamics of the ring current (Southwood et al., 1969) and radiation belt (Schulz & Lanzerotti, 1974) particles. Moreover, through these types of resonances poloidal Alfvén waves can be generated by two types of instabilities: the gradient instability caused by a steep earthward particle density gradient at a resonant energy, and the bump-on-tail instability, when a velocity distribution of the particles is inverted around the resonant energy, that is there is a bump at the energetic part of the distribution (Chen & Hasegawa, 1988;Karpman et al., 1977;Southwood, 1976). Most of the observed poloidal waves are the second harmonic of the Alfvén wave. They are asymmetric in the electric field relative to the equator and are generated by the drift-bounce resonance (

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