Naoko Takahashi

Ultra-low frequency waves, with periods between 1-1000 s, are ubiquitous in the near-Earth plasma environment and play an important role in magnetospheric dynamics and in the transfer of electromagnetic energy from the solar wind to the magnetosphere. A class of those waves, often referred to as Pc3 waves when they are recorded from the ground, with periods between 10 and 45 s, are routinely observed in the dayside magnetosphere. They originate from the ion foreshock, a region of geospace extending upstream of the quasi-parallel portion of Earth’s bow shock. There, the interaction between shock-reflected ions and the incoming solar wind gives rise to a variety of waves, and predominantly fast-magnetosonic waves with a period typically around 30 s. The connection between these waves upstream of the shock and their counterparts observed inside the magnetosphere and on the ground was inferred already early on in space observations due to similar properties, thereby implying the transmission of the waves across near-Earth space, through the shock and the magnetopause. This review provides an overview of foreshock 30-second/Pc3 waves research from the early observations in the 1960s to the present day, covering the entire propagation pathway of these waves, from the foreshock to the ground. We describe the processes at play in the different regions of geospace, and review observational, theoretical and numerical works pertaining to the study of these waves. We conclude this review with unresolved questions and upcoming opportunities in both observations and simulations to further our understanding of these waves.

Internally driven Pc4‐5 waves are excited in the plasmaspheric drainage plume (PDP) and near the plasmapause. The excitation of ultralow frequency (ULF) waves was investigated by using the magnetosphere‐ionosphere coupled model between Geospace Environment Modeling System for Integrated Studies‐Ring Current (GEMSIS‐RC) and GEMSIS‐POTential solver (GEMSIS‐POT). In order to investigate the effects of cold plasma on the wave excitation, the simulation code to describe the dynamics of cold plasma was included in the model. The model can reproduce the shrink of the plasmasphere on the nightside and the formation of the PDP on the dayside. First, fundamental Pc5 waves are excited through the drift resonance on the dayside. The waves are caused by positive energy gradient of ion phase space density (PSD) at 50–130 keV. Second harmonic waves (drift‐bounce resonance) are generated outside the plasmapause. These two types of ULF waves are also seen in the case of constant density. Unlike the case of constant density, localized eastward propagating Pc4 waves (drift resonance) are seen on the dawnside associated with the azimuthal density gradient. The azimuthal wave number of Pc4 waves is about 70 and anti‐earthward gradient of PSD about 10 keV contributes to wave growth. We also detect fundamental Pc4‐5 waves near the plasmapause on the nightside in the drift resonance with 100–150 keV ions. Simulation results suggest that the plasmapause has an effect to sustain the excitation of Pc4‐5 ULF wave through the drift resonance.

Two types of storm‐time Pc5 waves are excited in the magnetosphere–ionosphere coupled model. We conduct magnetosphere–ionosphere (M–I) coupling between geospace environment modeling system for integrated studies‐ring current (GEMSIS‐RC) and GEMSIS‐POTential solver (GEMSIS‐POT) models in order to investigate the excitation of storm‐time Pc5 waves under more realistic conditions. The coupled model enables us to simulate ion transport from the plasma sheet by the convection electric field. First, we find the excitation of fundamental mode Pc5 waves on the dayside. These waves are generated by the drift resonance and driven by positive energy gradient of ion phase space density (PSD). The wave excitation is similar with the case without M–I coupling. Second, we detect second harmonic mode Pc5 waves with high azimuthal wave number in the dusk and premidnight region. The PSD oscillates associated with the waves, and the drift‐bounce resonance occurs at 50–80 keV ions. We find that these ions drift around the Earth and reach the nightside again at t ∼ 4,500 s, whose time scale is comparable to the drift period of these ions. At that time, inward gradient of the PSD is created, which contributes to the wave growth. This effect does not happen in the case without dawn‐to‐dusk convection electric field driven by Region 1 field aligned current (FAC). We find that the shielding by Region 2 FAC suppresses the flux of newly injected ions at the nightside, inward gradient of the PSD, and power spectra of second harmonic mode waves.

We present observations of an equatorward detachment of the auroral arc from the main oval and magnetically conjugate measurements made by the Arase satellite in the inner magnetosphere. The all‐sky imager at Gakona (magnetic latitude = 63.6°N), Alaska, shows the detachment of the auroral arc in both red and green lines at local midnight (∼0130–0230 MLT) on 30 March 2017. The electron density derived from the Arase in‐situ observations shows that this arc occurred outside the plasmapause. At the arc crossing, the electron flux of energies ∼0.1–2 keV is found to be locally enhanced at L∼4.3–4.5. We estimated auroral intensities for both red and green lines by using the Arase low‐energy (0.1–19 keV) electron flux data. The peak latitude of the estimated intensity shows reasonably good correspondence with the observed intensity mapped at the ionospheric footprints of the Arase satellite. These findings indicate that the observed arc detachment at Gakona was associated with the localized enhancement of low‐energy electrons (∼0.1–2 keV) at the inner edge of the electron plasma sheet. Further, we employ the simulation results of the Community Coordinated Modeling Center (CCMC), the BATS‐R‐US–CIMI 3‐D MHD code to understand the conditions in the inner magnetosphere around the time of detachment. Although the simulation could not reproduce the lower‐energy component responsible for the arc detachment, it successfully reproduced two earthward convection events at the lower radial distance (R) (R ≤ ∼4) around the time of arc detachment and the features of enhanced convection in similarity with the observations.

We study the interaction of upstream ultralow frequency (ULF) waves with collisionless shocks by analyzing the outputs of 11 2D local hybrid simulation runs. Our simulated shocks have Alfvénic Mach numbers between 4.29 and 7.42 and their angles are , , , and . The ULF wave foreshocks develop upstream of all of them. The wavelength and the amplitude of the upstream waves exhibit a complex dependence on the shock's and . The wavelength positively correlates with both parameters, with the dependence on being much stronger. The amplitude of the ULF waves is proportional to the product of the reflected beam velocity and density, which also depend on and . The interaction of the ULF waves with the shock causes large‐scale (several tens of upstream ion inertial lengths) shock rippling. The properties of the shock ripples are related to the ULF wave properties, namely their wavelength and amplitude. In turn, the ripples have a large impact on the ULF wave transmission across the shock because they change local shock properties (, strength), so that different sections of the same ULF wavefront encounter shock with different characteristics. Downstream fluctuations do not resemble the upstream waves in terms the wavefront extension, orientation or their wavelength. However, some features are conserved in the Fourier spectra of downstream compressive waves that present a bump or flattening at wavelengths approximately corresponding to those of the upstream ULF waves. In the transverse downstream spectra, these features are weaker.

We investigate the time and location where ULF waves and whistler‐mode chorus contributed to the net flux enhancement of relativistic electrons during the magnetic storm of May 2017. During the early recovery phase, both ULF and chorus waves contribute to the enhancement of relativistic electron fluxes, but ULF waves play roles of the inward diffusion. During the late recovery phase, both Van Allen Probe‐B and Arase show that whistler‐mode chorus contributes to the flux enhancement confined in the L‐value. The CRCM coupled with BATS‐R‐US simulation qualitatively reproduces the global evolution of ULF waves. Although the electron flux is underestimated by the simulation, this study reveals a large anisotropy of hot electrons in the region where whistler‐mode chorus waves were actually observed by satellites. In addition, the estimated magnetic field curvature on the dayside is small during the recovery phase. Furthermore, we investigate the control of wave evolution. Both observations and the simulation suggest that the observed ULF waves in the frequency range of ∼2–5 mHz are excited by the enhancement of the solar wind dynamic pressure. Observations also indicate that whistler‐mode chorus on the nightside is predominantly excited by hot electrons with temperature anisotropy, whereas the dayside chorus is enhanced by the change of the magnetic field line configuration. The estimated spatial distributions of electron anisotropy and magnetic field curvature provide an explanation for the presence of enhanced whistler‐mode chorus in the dusk sector, which is far from the usual location of wave generation.

We have examined the properties of ultralow‐frequency (ULF) waves in space (the ion foreshock, magnetosheath, and magnetosphere) and at dayside magnetometer stations (L = 1.6–6.5) during Earth's encounter with a magnetic cloud in the solar wind, which is characterized by magnetic fields with large magnitudes (∼14 nT) and small cone angles (∼30°). In the foreshock, waves were excited at ∼90 m Hz as expected from theory, but there were oscillations at other frequencies as well. Oscillations near 90 mHz were detected at the other locations in space, but they were not in general the most dominant oscillations. On the ground, pulsations in the approximate Pc2–Pc4 band (5 mHz–120 mHz) were continuously detected at all stations, with no outstanding spectral peaks near 90 mHz in the H component except at stations where the frequency of the third harmonic of standing Alfvén waves had this frequency. The fundamental toroidal wave frequency was below 90 mHz at all stations. In the D component spectra, a minor spectral peak is found near 90 mHz at stations located at L < 3, and the power dropped abruptly above this frequency. Magnetospheric compressional wave power was much weaker on the nightside. A hybrid‐Vlasov simulation indicates that foreshock ULF waves have short spatial scale lengths and waves transmitted into the magnetosphere are strongly attenuated away from noon.

We investigated the excitation mechanism and global distribution of internally driven Pc3‐Pc5 ultralow‐frequency waves in the inner magnetosphere using a kinetic and self‐consistent simulation (Geospace Environment Modeling System for Integrated Studies‐Ring Current model). These waves can be excited through the drift‐bounce resonance with ring current ions injected into the inner magnetosphere during substorms. Initial phase space density of ring current ions is the butterfly‐like distribution with the asymmetry in pitch angle direction. We find two kinds of internally driven ultralow‐frequency waves. First, the dynamic power spectra of the field fluctuations show the excitation of poloidal, toroidal, and compressional Pc5 waves. We find that the excited waves are fundamental modes propagating westward with the azimuthal wave number of m ~ − 50. These waves are excited by the drift resonance with ions having the energy of 50–150 keV. Second, we can reproduce the excitation of poloidal Pc3 waves in the dusk region with m ~ − 30, which are driven by the bounce resonance with ions having energies of 20–50 keV for the first time. We investigate the energy transfer between ions and waves and find that poloidal Pc5 and Pc3 waves are excited mainly by positive energy gradient of the phase space density, while we find the inward gradient of the phase space density at L > 6. The velocity distribution of the growth rate suggests that Pc5 waves are driven by ions with pitch angle of around 90°, while Pc3 waves are excited by ions at oblique pitch angle.

Storm time Pc5 waves are considered to be excited through the drift‐bounce resonance by ring current ions associated with the injection from the magnetotail. Using the Geospace Environment Modeling System for Integrated Studies–Ring Current simulation, a drift‐kinetic and self‐consistent model for ring current particles, we investigate the excitation mechanism of these waves in the inner magnetosphere. The power spectra of electromagnetic field fluctuations show the excitation of both poloidal and toroidal mode waves in Pc5 frequency range. It is found that these waves are fundamental mode waves with the azimuthal wave number m~ − 20 and excited through the drift resonance with the drifting ions with energies of 80–120 keV. The simulation indicates that global distribution of wave power coincides with the positive local growth rate mainly contributed by the positive phase space density gradient in energy.