ULF waves in the active magnetosphere

We have carried out a detailed case study of ULF waves in near-Earth space during the passage of a magnetic cloud which caused a moderate geomagnetic storm on 20 July 2016, published in the Journal of Geophysical Research [Takahashi et al., 2021]. The exceptionally good coverage of spacecraft and ground-based observations during this event, including measurements in the foreshock, the magnetosheath, the outer magnetosphere, the nightside magnetosphere and on the ground in the morning sector, provided us with a unique opportunity to study the transmission of foreshock waves from the upstream region of the bow shock to the ground, and how their properties vary from one region to another.Our observational study was complemented by the analysis of a numerical simulation performed with the Vlasiator model, which provided a global view of near-Earth space during this event.

Because of the extreme solar wind conditions caused by the magnetic clouds, the foreshock waves were characterized by higher frequencies and more complex signatures than during quiet times [Turc et al., 2019, GRL]. This allowed us to study for the first time how the wave activity inside the magnetosphere is affected by these different foreshock wave signatures.

Our main findings are that

• The spatial scale lengths of the waves is much shorter than usual during this magnetic cloud event, both in the foreshock (consistent with the findings of Turc et al., 2019) and in the magnetosphere, where the coherence of the waves between different observation points is low.
• The wave power inside the magnetosphere is strongly attenuated away from local noon, resulting in a very low wave power being observed in the nightside magnetosphere in this frequency range, whereas previous studies have reported significant wave power on the nightside associated with transmitted foreshock waves during quiet solar wind conditions [Takahashi et al., 2016]. We note that the wave power in the foreshock is stronger than usual during the 2016-07-20 magnetic cloud event, suggesting that the strong decrease in magnetospheric wave power may be due to the shorter spatial scale lengths of the waves rather than a weaker wave source.
• Ground magnetometers located near local noon did not detect oscillations at frequencies matching the foreshock waves, nor fundamental field-line resonances. This is likely due to the fact that the frequency of the foreshock waves was too high to couple with the local field-line resonances. The absence of field
  line resonance driven by foreshock waves is a feature unique to times of high interplanetary magnetic field magnitudes.

Transmission of foreshock waves through Earth’s bow shock

One of the main goals of our ISSI team’s work was to tackle the long-standing open question of the transmission of foreshock waves through a shock and into the downstream magnetosheath. Our results are presented in two articles, one published in the Journal of Geophysical Research [Kajdič et al., 2021], and the other in Nature Physics [Turc et al., 2023]. We give here a brief summary of both studies.

In Kajdič et al. [2021], we investigated ULF wave properties upstream and downstream of collisionless shocks, as well as some of the characteristics of the shock itself, using a set of 11 local hybrid-Particle-in-Cell simulations with different parameters. The simulations are conducted at two different Alfvénic Mach numbers, and four different values of the θ_Bn angle between the shock normal direction and the upstream magnetic field, both parameters which are known to strongly affect the shock properties.

The amplitude of the ULF waves in the upstream is shown to increase with the product of the reflected ion density and velocity, which depends on both the Alfvénic Mach number and the θ_Bn angle. As these waves reach the shock front, they cause large-scale shock ripples with similar wavelengths. The larger the upstream wave amplitude, the more pronounced those ripples are. Consequently, the local shock properties show much larger variability when the upstream ULF waves have larger amplitudes. This in turn can strongly impact the transmission of waves and structures through the shock, as different portions of a given structure or wave front will effectively interact with a shock with different local properties.

We also searched for possible evidence of the upstream wave transmission through the shock in these local simulations. Fourier analysis downstream of the shock revealed a bump or a flattening of the spectrum of the compressive waves at the same wavelengths as the upstream waves, suggesting that wave transmission may be occurring. However, these features are much less prominent than in the upstream spectra. Overall, the properties of the downstream fluctuations differ strongly from those in the upstream. In the light of our results with global simulations, described in Turc et al. [2023] and briefly summarised below, this could be due to the transmitted waves not being the dominant mode in the shock’s downstream.

As presented in Turc et al. [2023], using a global numerical simulation performed with the Vlasiator model, we were able to identify fast-mode waves at the same frequency as the foreshock waves traversing the magnetosheath. Contrary to the findings of previous theoretical works, their wavevector was oriented earthward. Their properties were thus incompatible with the “direct transmission” scenario invoked in previous studies. A detailed investigation of the interaction of the foreshock waves with the shock revealed that the foreshock waves modulate the shock parameters, and in particular the shock compression ratio, at the same frequency. This results in periodic variations of the plasma parameters just downstream of the shock, creating pressure imbalance. This leads to the generation of fast-mode pulses just downstream of the shock, at the same frequency as the foreshock waves, which propagate towards the magnetosphere.

The simulation also provided us with clues as to why these earthward-propagating fast-mode waves had not been observed previously: these waves are not the dominant mode in the magnetosheath, except very near the subsolar point. They appear clearly when performing analyses over space and time, which is possible in a numerical simulation, while identifying them from time series alone was more challenging. Guided by our numerical results, we were able to identify intervals during which the MMS spacecraft were located in the subsolar magnetosheath, downstream of the foreshock. Analysis of the spacecraft data revealed signatures of earthward-propagating waves at the foreshock wave frequency, thereby confirming our numerical results. Our study therefore provided a convincing scenario explaining the transmission of foreshock waves through the magnetosheath and eventually into the magnetosphere.