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  1. Abstract

    We present Magnetospheric Multiscale observations of electrostatic double layers in quasi‐perpendicular Earth's bow shock. These double layers have predominantly parallel electric field with amplitudes up to 100 mV/m, spatial widths of 50–700 m, and plasma frame speeds within 100 km/s. The potential drop across a single double layer is 2%–7% of the cross‐shock potential in the de Hoffmann‐Teller frame and occurs over the spatial scale of 10 Debye lengths or one tenth of electron inertial length. Some double layers can have spatial width of 70 Debye lengths and potential drop up to 30% of the cross‐shock potential. The electron temperature variation observed across double layers is roughly consistent with their potential drop. While electron heating in the Earth's bow shock occurs predominantly due to the quasi‐static electric field in the de Hoffmann‐Teller frame, these observations show that electron temperature can also increase across Debye‐scale electrostatic structures.

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  2. Abstract

    Plasma sheet electron precipitation into the diffuse aurora is critical for magnetosphere‐ionosphere coupling. Recent studies have shown that electron phase space holes can pitch‐angle scatter electrons and may produce plasma sheet electron precipitation. These studies have assumed identical electron hole parameters to estimate electron scattering rates (Vasko et al., 2018, In this study, we have re‐evaluated the efficiency of this scattering by incorporating realistic electron hole properties from direct spacecraft observations into computing electron diffusion rates and lifetimes. The most important electron hole properties in this evaluation are their distributions in velocity and spatial scale and electric field root‐mean‐square intensity (). Using direct measurements of electron holes during a plasma injection event observed by the Van Allen Probe at, we find that when4 mV/m electron lifetimes can drop below 1 h and are mostly within strong diffusion limits at energies below10 keV. During an injection observed by the THEMIS spacecraft at, electron holes with even typical intensities (1 mV/m) can deplete low‐energy (a few keV) plasma sheet electrons within tens of minutes following injections and convection from the tail. Our results confirm that electron holes are a significant contributor to plasma sheet electron precipitation during injections.

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  3. Abstract

    We present analysis of electrostatic waves around the ramp of a quasi‐perpendicular Earth's bow shock observed by the Magnetospheric Multiscale spacecraft. The electrostatic waves have amplitudes up to 800 mV/m, which is the largest value ever reported in the Earth's bow shock. In contrast to previous studies, the electrostatic waves have large amplitudes of the electrostatic potential, up to 20 V or 20% of local electron temperature. The wavelengths are from 150 m to 3 km, that is from 15 to 300 Debye lengths and typically from 0.4 to 1.5 thermal electron gyroradii. Importantly, these waves can propagate not only quasi‐parallel or oblique, but also almost perpendicular to local magnetic field. The electrostatic waves are interpreted in terms of ion‐acoustic waves, although the presence of electron cyclotron harmonic waves cannot be entirely ruled out. These results suggest that electrostatic waves may strongly affect the dynamics of electrons in collisionless shocks.

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  4. Abstract

    We present the first observations of electrostatic solitary waves with electrostatic potential of negative polarity around a fast plasma flow in the Earth's plasma sheet. The solitary waves are observed aboard four Magnetospheric Multiscale spacecraft, which allowed accurately estimating solitary wave properties. Based on a data set of 153 solitary waves, we show that they are locally one‐dimensional Debye‐scale structures with amplitudes up to 20% of local electron temperature and they propagate at plasma frame speeds ranging from a tenth to a few ion‐acoustic speeds at arbitrary angles to the local magnetic field. The solitary waves are associated with multi‐component proton distributions and their velocities are around those of a beam‐like proton population. We argue that the solitary waves are ion holes, nonlinear structures produced by ion‐streaming instabilities, and conclude that once ions are not magnetized, ion holes can propagate oblique to local magnetic field.

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  5. Abstract

    Nonlinear ion-acoustic waves, ion holes, and electron holes have been observed on the Parker Solar Probe at a heliocentric distance of 35 solar radii. These time domain structures contain millisecond duration electric field spikes of several mV m−1. They are observed inside or at boundaries of switchbacks in the background magnetic field. Their presence in switchbacks indicates that both electron- and ion-streaming electrostatic instabilities occur there to thermalize electron and ion beams.

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  6. Abstract

    We present analysis of 17,043 proton kinetic-scale current sheets (CSs) collected over 124 days of Wind spacecraft measurements in the solar wind at 11 samples s−1magnetic field resolution. The CSs have thickness,λ,from a few tens to one thousand kilometers with typical values around 100 km, or within about 0.1–10λpin terms of local proton inertial length,λp. We found that the current density is larger for smaller-scale CSs,J0≈ 6 nAm−2· (λ/100 km)−0.56, but does not statistically exceed a critical value,JA,corresponding to the drift between ions and electrons of local Alvén speed. The observed trend holds in normalized units:J0/JA0.17·(λ/λp)0.51. The CSs are statistically force-free with magnetic shear angle correlated with CS spatial scale:Δθ19°·(λ/λp)0.5. The observed correlations are consistent with local turbulence being the source of proton kinetic-scale CSs in the solar wind, while the mechanisms limiting the current density remain to be understood.

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  7. Abstract

    We present a statistical analysis of >2,100 bipolar electrostatic solitary waves (ESWs) collected from 10 quasi‐perpendicular Earth's bow shock crossings by Magnetospheric Multiscale spacecraft. We developed and implemented a correction procedure for reconstruction of actual electric fields, velocities, and other properties of ESW, whose spatial scales are typically comparable with or smaller than spatial distance between voltage‐sensitive probes. We found that more than 95% of the ESW are of negative polarity with amplitudes typically below a few Volts and 0.1Te(5–30 V or 0.1–0.3Tefor a few percent of ESW), spatial scales of 10–100 m orλD–10λD, and velocities from a few tens to a few hundred km/s that is on the order of local ion‐acoustic speed. The spatial scales of ESW are correlated with local Debye lengthλD. The ESW have electric fields generally oblique to magnetic field and they propagate highly oblique to shock normalN; more than 80% of ESW propagate within 30° of the shock planeLM. In the shock plane, ESW typically propagates within a few tens of degrees of local magnetic field projectionBLMand preferentially opposite toN × BLM. We argue that the ESW of negative polarity are ion holes produced by ion‐ion streaming instabilities. We estimate ion hole lifetimes to be 10–100 ms, or 1–10 km in terms of traveling distance. The revealed statistical properties will be useful for quantitative studies of electron thermalization in the Earth's bow shock.

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  8. We present a statistical analysis of electrostatic solitary waves observed aboard Magnetospheric Multiscale spacecraft in the Earth's magnetosheath. Applying single‐spacecraft interferometry to several hundred solitary waves collected in about 2‐minute interval, we show that almost all of them have the electrostatic potential of positive polarity and propagate quasi‐parallel to the local magnetic field with plasma frame velocities of the order of 100 km/s. The solitary waves have typical parallel half‐widths from 10 to 100 m that is between 1 and 10 Debye lengths and typical amplitudes of the electrostatic potential from 10 to 200 mV that is between 0.01% and 1% of local electron temperature. The solitary waves are associated with quasi‐Maxwellian ion velocity distribution functions, and their plasma frame velocities are comparable with ion thermal speed and well below electron thermal speed. We argue that the solitary waves of positive polarity are slow electron holes and estimate the time scale of their acceleration, which occurs due to interaction with ions, to be of the order of one second. The observation of slow electron holes indicates that their lifetime was shorter than the acceleration time scale. We argue that multi‐spacecraft interferometry applied previously to these solitary waves is not applicable because of their too‐short spatial scales. The source of the slow electron holes and the role in electron‐ion energy exchange remain to be established. 
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    Free, publicly-accessible full text available March 1, 2025