A compressional Pc5 wave associated with localized hot proton injection was observed by the five THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft in the dusk sector of the Earth's magnetosphere at L ∼ 10R E on 21 May 2007. The wave magnetic field perturbation transverse to the background magnetic field was primarily poloidal, in agreement with the predominately azimuthal wave vector direction (with westward phase velocity). The observation followed two consecutive substorms, when the cloud of energetic particles comprised of the lower-energy protons from the earlier substorm was mixed with higher-energy protons from the subsequent one. The clear signatures of the wave-particle drift resonance of protons modulated by the wave were observed. The wave period was found to be about 2 times longer than the corresponding Alfvén wave eigenmode period on the same L-shells calculated with the THEMIS data. The increase of the particle energy with the distance from the Earth and the observed strong dependence of the wave frequency on the azimuthal wave number constitutes conditions for the gradient instability of the drift compressional mode (for the Alfvén mode one supposes the particle energy decrease with radial distance). Based on these results, we conclude that the observed wave was the drift compressional mode generated by the gradient instability.
This paper investigates the conditions of the ballooning instability of the coupled Alfvén and slow magnetoacoustic modes in the dipole model of Earth's magnetosphere taking into account plasma and magnetic field inhomogeneity in the direction along the magnetic field lines. The diamagnetic condition (meaning vanishing perturbation of the total pressure) is satisfied. It was shown that the instability develops on the slow magnetoacoustic oscillation branch, but the instability threshold is determined by the coupling with the Alfvén mode. The symmetric (with respect to the magnetic equator) modes were found to be more unstable than antisymmetric ones. In this case, the instability threshold depends on plasma compressibility: the finite sound velocity raises the instability threshold. For all other equal conditions, the instability threshold decreases with the decrease in the field line curvature radius on the equator.
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 (
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