On Electron Adiabaticity in Collisionless Shocks

Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade that is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave–particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region exhibiting features of turbulent dissipation, like reconnecting current sheets. We used observations from magnetospheric multiscale (MMS) over four separate bow shock crossings of varying shock normal angle to characterize turbulence in the shock transition region and how it evolves toward the magnetosheath. These cases studies have been chosen to ensure validity of Taylor's hypothesis, which we discuss in depth. We observe the magnetic spectrum evolving by fitting power laws over many short intervals, finding that the power-law index in the shock transition region is separable from the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across the shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in solar wind; however, the opposite can occur for quasi-parallel shocks.

We present a statistical analysis of large-amplitude bipolar electrostatic structures measured by the Magnetospheric Multiscale spacecraft in the Earth's bow shock. The analysis is based on 371 large-amplitude bipolar structures collected in nine supercritical quasi-perpendicular Earth's bow shock crossings. We have found that 361 of the bipolar structures have negative electrostatic potentials, and only 10 structures (> 1, a parameter range typical of collisionless shocks in the heliosphere and various astrophysical environments. This analysis indicates that the original mechanism of electron surfing acceleration involving electron phase space holes is not likely to be efficient in realistic collisionless shocks.

Using test particle trajectories in a simplified model of a supercritical, oblique, collisionless shock, we investigate the interaction of solar wind thermal ions with the earth's bow shock. We present results for shocks with shock angle (θBn) between 35° and 60° and show that their velocity space signatures are consistent with observations of many upstream ion events, particularly gyrating ions and field‐aligned ion beams. The shock is modeled as a finite, planar discontinuity in the magnetic field and in the electrostatic potential, which is also given an overshoot at the shock. We find that the shock can produce backstreaming ions by reflecting a small fraction of the incident distribution. The reflected particle trajectories are of three types: specularly reflected, multiple traversal, and multiple bounce. All backstreaming reflected ions are found to suffer specular reflection on their first encounter with the shock surface; their subsequent behavior is determined by the angle θBn and their initial conditions.

The Earth's quasi-parallel bow shock: Review of observations and perspectives for Cluster

The Earth’s bow shock is the best-known collisionless shock in space. Although much is known about the bow shock, the mechanisms of heating and thermalization processes still remain poorly understood. Collisionless shocks are different from ordinary fluid shocks, because a fraction of the incident solar wind is reflected from the bow shock and the transmitted particles are not immediately thermalized. The reflected particles interact with the incident solar wind producing waves and instabilities that can heat and accelerate particles to high energies. Some of the waves can grow to large amplitudes such as Short Large Amplitude Magnetic Structures. Other upstream nonlinear structures include hot flow anomalies and density holes. The upstream nonlinear structures subsequently convect Earthward with the SW and could impact the structure and dynamics of the bow shock. These observations have clearly indicated that the upstream dynamics are an integral part of the bow shock system. Although much has been learned about the behavior of Earth’s bow shock dynamics from the existing data, many fundamental questions remain not answered. This article will review observations of ion dynamics of Earth’s bow shock system, what we have learned from recent and past observations. We provide new perspectives from multi-spacecraft Cluster observations about the spatial and temporal variations including the fundamental shock heating, acceleration, and entropy generation processes.

We investigate the dynamics of Earth's quasi-parallel terrestrial bow shock based on measurements from the Magnetospheric MultiScale (MMS) spacecraft constellation during a period of near-radial interplanetary magnetic conditions, when the interplanetary magnetic field and the solar wind (SW) velocity are nearly anti-parallel. High-speed earthward ion flows with properties that are similar to those of the pristine SW are observed to be embedded within the magnetosheath-like plasma. These flows are accompanied by Interplanetary Magnetic Field (IMF) intensity of less than about 10 nT, compared to nearby magnetosheath intensities of generally greater than 10 nT. The high-speed flow intervals are bounded at their leading and trailing edges by intense fluxes of more energetic ions and large amplitude quasi-sinusoidal magnetic oscillations, similar to ultra-low frequency waves known to steepen and pileup on approach toward Earth to form the quasi-parallel bow shock. The MMS string-of-pearls configuration is aligned with the outbound trajectory and provides inter-spacecraft separations of several hundred km along its near 103 length, allowing sequential observation of the plasma and magnetic field signatures during the event by the four spacecraft. The SW-like interval is most distinct at the outer-most MMS-2 and sequentially less distinct at each of the trailing MMS spacecraft. We discuss the interpretation of this event alternatively as MMS having observed a quasi-rigid bow shock contraction/expansion cycle, ripples or undulations propagating on the bow shock surface, or a more spatially local evolution in the context of either a deeply deformed shock surface or a porous shock surface, as in the three-dimensional patchwork concept of the quasi-parallel bow shock, under the extant near-radial IMF condition.

Abstract. Field-aligned beams are known to originate from the quasi-perpendicular side of the Earth's bow shock, while the diffuse ion population consists of accelerated ions at the quasi-parallel side of the bow shock. The two distinct ion populations show typical characteristics in their velocity space distributions. By using particle and magnetic field measurements from one Cluster spacecraft we present a case study when the two ion populations are observed simultaneously in the foreshock region during a high Mach number, high solar wind velocity event. We present the spatial-temporal evolution of the field-aligned beam ion distribution in front of the Earth's bow shock, focusing on the processes in the deep foreshock region, i.e. on the quasi-parallel side. Our analysis demonstrates that the scattering of field-aligned beam (FAB) ions combined with convection by the solar wind results in the presence of lower-energy, toroidal gyrating ions at positions deeper in the foreshock region which are magnetically connected to the quasi-parallel bow shock. The gyrating ions are superposed onto a higher energy diffuse ion population. It is suggested that the toroidal gyrating ion population observed deep in the foreshock region has its origins in the FAB and that its characteristics are correlated with its distance from the FAB, but is independent on distance to the bow shock along the magnetic field.

The electron heating at collisionless shocks in near‐Earth space is normally found to be relatively small. We report here on two sets of bow shock crossings observed by the ISEE 1 and ISEE 2 spacecraft in which very large electron temperature increases were found. The two sets of shocks are part of a larger set of 52 bow shock crossings compiled from the ISEE data set. When the shocks with the large electron heating are compared to the rest of the shocks in the compiled set, it is found that the only upstream parameter which is out of the ordinary is the upstream solar wind flow speed Vu. Indeed, for the entire shock set the only upstream parameters which correlate well with the electron heating are the solar wind speed and quantities derived from it. The best correlation among those tested is between the temperature increase (Ted ‐ Teu) and the difference in the square of the bulk flow speed (Vu² ‐ Vd²) across the shock, which is proportional to the total amount of bulk flow energy dissipated by the shock. A subsequent search for bow shock crossings which occur during intervals of high solar wind speed confirms that the electron heating is very large under high‐speed conditions. The first‐order dependence of the electron temperature increase on the available bulk flow energy is consistent with a heating process which is dominated by the macroscopic cross‐shock electrostatic potential jump. This study suggests that the temperature difference is the appropriate measure of electron heating at shocks (rather than the ratio Ted/Teu) and that the first‐order dependence on (Vu² ‐ Vd²) should be normalized out in future studies of electron heating at space shocks.

Adiabatic heating of solar wind electrons at the Earth's bow shock and its foreshock region produces transversely anisotropic hot electrons that, in turn, generate intense high-frequency whistler-mode waves. These waves are often detected by spacecraft as narrow-band, electromagnetic emissions in the frequency range of [0.1, 0.5] of the local electron gyrofrequency. Resonant interactions between these waves and electrons may cause electron acceleration and pitch-angle scattering, which can be important for creating the electron population that seeds shock drift acceleration. The high intensity and coherence of the observed whistler-mode waves prohibit the use of quasi-linear theory to describe their interaction with electrons. In this paper, we aim to develop a new theoretical approach to describe this interaction, which incorporates nonlinear resonant interactions, gradients of the background density and magnetic field, and the fine structure of the waveforms that usually consist of short, intense wave-packet trains. This is the first of two accompanying papers. It outlines a probabilistic approach to describe the wave–particle interaction. We demonstrate how the wave-packet size affects electron nonlinear resonance at the bow shock and foreshock regions, and how to evaluate electron distribution dynamics in such a system that is frequented by short, intense whistler-mode wave-packets. In the Paper II, this probabilistic approach is merged with a mapping technique, which allows us to model systems containing short and long wave-packets.

Experimental investigations of the fine plasma structure of interplanetary shocks are extremely difficult to conduct due to their small thickness and high speed relative to the spacecraft. We study the variations in the parameters of twice-ionized helium ions (4He++ ions or {\alpha}-particles) in the solar wind plasma during the passage of interplanetary shocks and Earth's bow shock. We use data with high time resolution gathered by the BMSW (Bright Monitor of Solar Wind) instrument installed on the SPEKTR-R satellite, which operated between August 2011 and 2019. The MHD parameters of He++ ions (the bulk velocity Va, temperature Ta, absolute density Na, and helium abundance Na/Np) are analyzed for 20 interplanetary shocks and compared with similar parameters for 25 Earth's bow shock crossings. Measurements from the WIND, Cluster and THEMIS satellites were also analyzed. The correlations in the changes in helium abundance Na/Np with the parameters {\beta}_{i}, {\theta}_{Bn} and M_{ms} were investigated. A correlation between Na/Np and the angle {\theta}_{Bn} was found: the lower the value of {\theta}_{Bn}, the greater the drop in helium abundance Na/Np falls behind the IP shock front. For Earth's bow shock crossings, we found a significant increase in the helium abundance Na/Np in quasi-perpendicular events.

Some model distributions based on recent observations and simulations of the plasma at the earth's bow shock are found to be unstable to obliquely propagating electrostatic instabilities. The model distributions consist of either an ion beam or an ion velocity ring accompanied by a bi‐Maxwellian background ion distribution and a flattop electron distribution. Ion anisotropies and nonthermal electrons are capable of significantly lowering the threshold of the ion beam instability. The generated waves share many properties in common with the ion acoustic waves that have been observed at the earth's bow shock. The results also indicate the importance of an anisotropy in the background ion velocity distribution in identifying sources of the ion‐acoustic‐like waves observed in the ion foreshock and the solar wind.

We report measurements of ∼150 keV proton intensity enhancements obtained at ACE and WIND when both spacecraft were upstream of the Earth's bow shock. We investigate differences in the onset times, the duration's, and the local magnetic field orientations for 4 events observed simultaneously at the two spacecraft. A simple statistical analysis shows only 2% of the simultaneous events could be random coincidences, which indicates that out of the 20 events observed at each spacecraft, the 4 simultaneous measurements are probably observations of the same events. Since these measurements were obtained when the two spacecraft were separated by distances >25 RE, these particles probably originate from a source region that possibly covers the scale size of the Earth's bow shock (∼10 RE), and this is substantially larger than the smaller source regions proposed by existing models.

A general technique is given for calculating the spectrum of plasma waves emitted upstream and downstream by a turbulent shock transition for a plane shock of arbitrary structure. The problem of identifying the waves of frequency ∼1 cps that sometimes appear to emanate from the earth's bow shock is discussed.

A kinetic entropy diagnostic was systematically developed for fully kinetic collisionless particle-in-cell (PIC) simulations in Liang et al., Phys. Plasmas 26, 082903 (2019). Here, we first show that kinetic entropy can be used to quantitatively evaluate numerical dissipation in the PIC simulation. Assuming numerical effects can be treated using a relaxation time approximation collision operator, the rate of increase of the kinetic entropy is related to the kinetic entropy. The effective collision frequency due to numerical effects is then easy to evaluate in a collisionless PIC simulation. We find an effective collision frequency of approximately a tenth of the ion cyclotron frequency. This could have important implications for collisionless PIC simulation studies of magnetic reconnection, plasma turbulence, and collisionless shocks. Then, we analyze the uncertainty of the local kinetic entropy density at different locations as a function of the chosen velocity space grid. We find that although the numerically obtained kinetic entropy density varies significantly for small or large velocity space grids, there is a range for which the kinetic entropy density is only weakly sensitive to the velocity space grid. Our analysis of the uncertainty suggests a velocity space grid close to the thermal velocity is optimal, and the uncertainty introduced is significantly less than the physical change in kinetic entropy density.

Abstract. Hot flow anomalies (HFAs) at Earth's bow shock were identified in Time History of Events and Macroscale Interactions During Substorms (THEMIS) satellite data from 2007 to 2009. The events were classified as young or mature and also as regular or spontaneous hot flow anomalies (SHFAs). The dataset has 17 young SHFAs, 49 mature SHFAs, 15 young HFAs, and 55 mature HFAs. They span a wide range of magnetic local times (MLTs) from approximately 7 to 16.5 MLT. The largest ratio of solar wind to HFA core density occurred near dusk and at larger distances from the bow shock. In this study, HFAs and SHFAs were observed up to 6.3 RE and 6.1 RE (Earth radii), respectively, upstream from the model bow shock. HFA–SHFA occurrence decreases with distance upstream from the bow shock. HFAs of the highest event core ion temperatures were not seen at the flanks. The ratio of HFA ion temperature increase to HFA electron temperature increase is highest around 12 MLT and slightly duskward. For SHFAs, (Tihfa∕Tisw)/(Tehfa∕Tesw) generally increased with distance from the bow shock. Both mature and young HFAs are more prevalent when there is an approximately radial interplanetary magnetic field. HFAs occur most preferentially for solar wind speeds from 550 to 600 km s−1. The correlation coefficient between the HFA increase in thermal energy density from solar wind values and the decrease in kinetic energy density from solar wind values is 0.62. SHFAs and HFAs do not show major differences in this study.