Section 5 presents discussion, and section 6 concludes the study. Section 4 presents analyses of the properties of the waves. Section 3 presents an overview of the observations on 10 April 2013. Section 2 describes experiments and data. The remainder of the paper is organized as follows. Accordingly, we term them compressional Pc3 waves. The waves had perturbations in the magnetic field magnitude mostly in the Pc3 band with a center frequency of ∼30 mHz. This paper presents the first evidence of the day-to-night propagation in spacecraft data. presented magnetometer and HF radar observations in support of the propagation. suggested that 5 to 20 mHz magnetic pulsations observed on the nightside originated from upstream waves. Previous studies using ground-based experiments provided possible evidence of the propagation. Ī remaining question on fast-mode waves of upstream origin is whether they propagate to the nightside. Equation 1 is close to empirical formulas obtained from ground observations and is in good agreement with spacecraft observations. (1) where B μ is the magnetic field magnitude. As for the frequency of the upstream waves, f UW, a theoretical formula has been derived by Takahashi et al. When the cone angle is small, upstream waves develop in a large volume in front of the bow shock and the resulting fast-mode waves in the magnetosphere become stronger. Evidence of the upstream source mechanism includes the following: (1) dependence of Pc3-Pc4 wave amplitude on the angle between the interplanetary magnetic field (IMF) and the Sun-Earth line, denoted θ x B and referred to as the IMF cone angle, and (2) dependence of Pc3-Pc4 wave frequency on the magnitude of the IMF. At times the frequency of the compressional waves may become low and falls into the Pc4 band (7–22 mHz). The waves are believed to propagate to the ground and produce Pc3 geomagnetic pulsations on the dayside. Spacecraft in the dayside magnetosphere routinely detect the fast-mode waves as compressional magnetic field oscillations in the Pc3 band (22–100 mHz). Once generated, the waves are convected toward the Earth in the superAlfvénic solar wind flow, are transmitted through the bow shock and magnetopause, and propagate into the magnetosphere as magnetohydrodynamic (MHD) fast-mode waves according to MHD theory, although wave propagation through the boundaries is more complicated when ion cyclotron waves and mirror-mode waves are taken into account. The waves are generated in the ion foreshock region by an ion beam cyclotron instability. Upstream ultralow frequency (ULF) waves are a well-known source of fast-mode waves observed in the magnetosphere. There is no evidence that the oscillations propagated to the ground in the midnight sector. The magnitude of the azimuthal wave number is estimated to be ∼30. The oscillations are attributed to magnetohydrodynamic fast-mode waves based on their propagation velocity of ∼300 km/s and the relationship between the electric and magnetic field perturbations. Upstream origin of the oscillations is concluded from the wave frequency that matches a theoretical model, globally coherent amplitude modulation, and duskward propagation that is consistent with expected entry of the upstream wave energy through the dawnside flank under the observed interplanetary magnetic field. At 1130–1730 UT on the selected day, the two Van Allen Probes spacecraft and the geostationary ETS-VIII satellite detected compressional 20 to 40 mHz magnetic field oscillations between L ∼ 4 and L ∼ 7 in the midnight sector, along with other spacecraft located closer to noon. We use data acquired on 10 April 2013 by multiple spacecraft to demonstrate that ULF waves of upstream origin can propagate to the midnight sector of the inner magnetosphere. Ultralow frequency (ULF) waves generated in the ion foreshock are a well-known source of Pc3-Pc4 waves (7–100 mHz) observed in the dayside magnetosphere.
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