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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 two minute intervals, 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.

High resolution electron and ion velocity distributions, f(v), which consist of N effectively disjoint beams, have been measured by NASA's Magnetospheric Multi-Scale Mission (MMS) observatories and in reconnection simulations. Commonly used standard velocity moments generally assume a single mean-flow-velocity for the entire distribution, which can lead to counterintuitive results for a multibeam f(v). An example is the (false) standard thermal energy moment of a pair of equal and opposite cold particle beams, which is nonzero even though each beam has zero thermal energy. By contrast, a multibeam moment of two or more beams has no false thermal energy. A multibeam moment is obtained by taking a standard moment of each beam and then summing over beams. In this paper we will generalize these notions, explore their consequences and apply them to an f(v) which is sum of tri-Maxwellians. Both standard and multibeam energy moments have coherent and incoherent forms. Examples of incoherent moments are the thermal energy density, the pressure and the thermal energy flux (enthalpy flux plus heat flux). Corresponding coherent moments are the bulk kinetic energy density, the RAM pressure and the bulk kinetic energy flux. The false part of an incoherent moment is defined as the difference between the standard incoherent moment and the corresponding multibeam moment. The sum of a pair of corresponding coherent and incoherent moments will be called the undecomposed moment. Undecomposed moments are independent of whether the sum is standard or multibeam and therefore have advantages when studying moments of measured f(v)., Comment: 27 single-spaced pages. Three Figures

The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a diagnostics to study the spectrum of fluctuations in the various regions around a reconnection site. We define the regions in terms of the local value of the flux function that determines the distance form the reconnection site, with positive values in the outflow and negative values in the inflow. We find that fluctuations belong to two very different regimes depending on the local plasma beta (defined as the ratio of plasma and magnetic pressure). The first regime develops in the reconnection outflows where beta is high and is characterized by a strong link between plasma and electromagnetic fluctuations leading to momentum and energy exchanges via anomalous viscosity and resistivity. But there is a second, low beta regime: it develops in the inflow and in the region around the separatrix surfaces, including the reconnection electron diffusion region itself. It is remarkable that this low beta plasma, where the magnetic pressure dominates, remain laminar even though the electromagnetic fields are turbulent., Comment: arXiv admin note: substantial text overlap with arXiv:1904.02094

The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a new diagnostics, the topographical fluctuations analysis (TFA) to study the spectrum of fluctuations in the various regions around a reconnection site. We find that fluctuations belong to two very different regimes. The first regime is better known, it develops in the reconnection outflows and is characterized by a strong link between plasma and electromagnetic fluctuations leading to momentum and energy exchanges via anomalous viscosity and resistivity. But there is a second, new, regime: it develops in the inflow and in the region around the separatrix surfaces, including the reconnection diffusion region itself. In this new regime the plasma remains laminar but the electromagnetic fields fluctuates strongly. We present an analogy with the smooth continuous motion of the bow of a violin producing the vibrations of the strings to emit music., Comment: 4 figures, submitted, 3 april 2019

The properties of the turbulence which develops in the outflows of magnetic reconnection have been investigated using self-consistent plasma simulations, in three dimensions. As commonly observed in space plasmas, magnetic reconnection is characterized by the presence of turbulence. Here we provide a direct comparison of our simulations with reported observations of reconnection events in the magnetotail investigating the properties of the electromagnetic field and the energy conversion mechanisms. In particular, simulations show the development of a turbulent cascade consistent with spacecraft observations, statistics of the the dissipation mechanisms in the turbulent outflows similar to the one observed in reconnection jets in the magnetotail, and that the properties of turbulence vary as a function of the distance from the reconnecting X-line., Comment: 7 pages, 5 figures

The collision of magnetic reconnection jets is studied by means of a three dimensional numerical simulation at kinetic scale, in the presence of a strong guide field. We show that turbulence develops due to the jets collision producing several current sheets in reconnection outflows, aligned with the guide field direction. The turbulence is mainly two-dimensional, with stronger gradients in the plane perpendicular to the guide field and a low wave-like activity in the parallel direction. First, we provide a numerical method to isolate the central turbulent region. Second, we analyze spatial second-order structure function and prove that turbulence is confined in this region. Finally, we compute local magnetic and electric frequency spectra, finding a trend in the sub-ion range that differs from typical cases for which the Taylor hypothesis is valid, as well as wave activity in the range between ion and electron cyclotron frequencies. Our results are relevant to understand observations of reconnection jets collisions in space plasmas., Comment: 16 pages, 10 figures

Data from the NASA Magnetospheric Multiscale (MMS) mission are used to investigate asymmetric magnetic reconnection at the dayside boundary between the Earth's magnetosphere and the solar wind (the magnetopause). High-resolution measurements of plasmas, electric and magnetic fields, and waves are used to identify highly localized (~15 electron Debye lengths) standing wave structures with large electric-field amplitudes (up to 100 mV/m). These wave structures are associated with spatially oscillatory dissipation, which appears as alternatingly positive and negative values of J dot E (dissipation). For small guide magnetic fields the wave structures occur in the electron stagnation region at the magnetosphere edge of the EDR. For larger guide fields the structures also occur near the reconnection x-line. This difference is explained in terms of channels for the out-of-plane current (agyrotropic electrons at the stagnation point and guide-field-aligned electrons at the x-line).

The kinetic features of secondary magnetic reconnection in a single flux rope undergoing internal kink instability are studied by means of three-dimensional Particle-in-Cell simulations. Several signatures of secondary magnetic reconnection are identified in the plane perpendicular to the flux rope: a quadrupolar electron and ion density structure and a bipolar Hall magnetic field develop in proximity of the reconnection region. The most intense electric fields form perpendicularly to the local magnetic field, and a reconnection electric field is identified in the plane perpendicular to the flux rope. An electron current develops along the reconnection line in the opposite direction of the electron current supporting the flux rope magnetic field structure. Along the reconnection line, several bipolar structures of the electric field parallel to the magnetic field occur making the magnetic reconnection region turbulent. The reported signatures of secondary magnetic reconnection can help to localize magnetic reconnection events in space, astrophysical and fusion plasmas.

Buneman instability is often driven in magnetic reconnection. Understanding how velocity shear in the beams driving the Buneman instability affects the growth and saturation of waves is relevant to turbulence, heating, and diffusion in magnetic reconnection. Using a Mathieu-equation analysis for weak cosine velocity shear together with Vlasov simulations, the effects of shear on the kinetic Buneman instability are studied in a plasma consisting of strongly magnetized electrons and cold unmagnetized ions. In the linearly unstable phase, shear enhances the coupling between oblique waves and the sheared electron beam, resulting in a wider range of unstable eigenmodes with common lower growth rates. The wave couplings generate new features of the electric fields in space, which can persist into the nonlinear phase when electron holes form. Lower hybrid instabilities simultaneously occur at $k_{\shortparallel}/k_{\perp} \sim \sqrt{m_e/m_i}$ with a much lower growth rate, and are not affected by the velocity shear., Comment: Accepted by Physics of Plasma

On 8 September 2015, the four Magnetospheric Multiscale spacecraft encountered a Kelvin-Helmholtz unstable magnetopause near the dusk flank. The spacecraft observed periodic compressed current sheets, between which the plasma was turbulent. We present observations of large-amplitude (up to 100 mVm) oscillations in the electric field. Because these oscillations are purely parallel to the background magnetic field, electrostatic, and below the ion plasma frequency, they are likely to be ion acoustic-like waves. These waves are observed in a turbulent plasma where multiple particle populations are intermittently mixed, including cold electrons with energies less than 10 eV. Stability analysis suggests a cold electron component is necessary for wave growth.

We report observations from the Magnetospheric Multiscale satellites of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the Earth's magnetopause. The observed waves have parallel electric fields (E(sub parallel)) with amplitudes on the order of 100 mV/m and display nonlinear characteristics that suggest a possible net E(sub parallel). These waves are observed within the ion diffusion region and adjacent to (within several electron skin depths) the electron diffusion region. They are in or near the magnetosphere side current layer. Simulation results support that the strong electrostatic linear and nonlinear wave activities appear to be driven by a two stream instability, which is a consequence of mixing cold (less than 10eV) plasma in the magnetosphere with warm (approximately 100eV) plasma from the magnetosheath on a freshly reconnected magnetic field line. The frequent observation of these waves suggests that cold plasma is often present near the magnetopause.

We report observations from the Magnetospheric Multiscale satellites of parallel electric fields (E (sub parallel)) associated with magnetic reconnection in the subsolar region of the Earth's magnetopause. E (sub parallel) events near the electron diffusion region have amplitudes on the order of 100 millivolts per meter, which are significantly larger than those predicted for an antiparallel reconnection electric field. This Letter addresses specific types of E (sub parallel) events, which appear as large-amplitude, near unipolar spikes that are associated with tangled, reconnected magnetic fields. These E (sub parallel) events are primarily in or near a current layer near the separatrix and are interpreted to be double layers that may be responsible for secondary reconnection in tangled magnetic fields or flux ropes. These results are telling of the three-dimensional nature of magnetopause reconnection and indicate that magnetopause reconnection may be often patchy and/or drive turbulence along the separatrix that results in flux ropes and/or tangled magnetic fields.

A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (less than or equal to 500 mV/m) driven by a stream of 20 eV to 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 microseconds sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam-driven Langmuir turbulence in the presence of a moderate magnetic field (OMEGA (sub e) approximately equals Omega (sub pe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream-driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.

Intense bursts of Langmuir waves with electric fields of 50 to 500 mV / m have been frequently observed at altitudes greater than 500 km in the auroral ionosphere. These bursts are driven by 20 eV to 4 keV field-aligned electrons, which are embedded in an approximately isotropic nonthermal tail of scattered electrons. The Langmuir bursts are often observed at altitudes where the ionosphere is moderately magnetized (OMEGA (sub e) approximately equals omega (sub pe)). Both the moderate magnetization and the scattered electrons have a major influence on the linear dispersion and damping of Langmuir waves. In particular, the linear dispersion is topologically different depending on whether the magnetic field is subcritical (OMEGA (sub e) less than omega (sub pe)) or supercritical (OMEGA (sub e) greater than omega (sub pe)). The correct dispersion and damping can account for the observed polarization of the Langmuir waves, which is very nearly parallel to the geomagnetic field. Inferred properties of the linear instability driven by the field-aligned electrons are discussed. The linear dispersion and damping derived here provide the basis for a nonlinear turbulence study described in a companion paper (Newman et al., this issue).

The effects of long-wavelength dissipation on beam-driven Langmuir turbulence are investigated using numerical simulations that include both weak and strong turbulence effects. Strong-turbulence wave collapses occur concurrently with weak-turbulence energy cascades if the long-wavelength damping is sufficiently small relative to the growth rate of the beam-unstable waves. Above a threshold damping level, only the weak-turbulence backscatter cascade is observed, and it becomes increasingly truncated as the damping increases, eventually consisting of only a single backscatter. A simple Lotka-Volterra model gives an excellent description of the periodic evolution observed in the weak-turbulence regime. Suppression of the usual backscatter cascade by long-wavelength damping enables intense beam-aligned density troughs to form, which trap and duct Langmuir waves.

A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.

A simple two-component model of strong turbulence that makes clear predictions for the scalings, spectra, and statistics of Langmuir waves is developed. Scalings of quantities such as energy density, power input, dissipation power wave collapse, and number density of collapsing objects are investigated in detail and found to agree well with model predictions. The nucleation model of wave-packet formation is strongly supported by the results. Nucleation proceeds with energy flowing from background to localized states even in the absence of a driver. Modulational instabilities play little or no role in maintaining the turbulent state when significant density nonuniformities are present.

Strong turbulence and transit-time scattering theory are applied here to calculate the statistical distribution of intense Langmuir fields and the consequent beam scattering in plasma turbulence driven by an electron beam. The experimentally observed electric-field distributions are compared with predictions of strong-turbulence theory, concentrating on the wave levels, the Gaussian tail of the high-field distribution observed in one experiment, the arrest scale of collapse, and the fractional volume occupied by the highest fields. The Guassian form of the tail is confirmed, and the results imply that the collapse is arrested at a scale where the peak electrostatic energy density is of the same order as the thermal energy density. The theory of transit-time interactions is generalized to include relativistic particle dynamics and is applied to predict the scattering of the beam electrons in energy and angle as they pass through strong Langmuir turbulence. The results support the validity of the recently developed scaling theory of strong turbulence.

A recently developed two-component model of strong Langmuir turbulence is applied to determine the scalings, spectra, and statistics of the associated density fluctuations. The predictions are found to be in excellent agreement with extensive results from numerical solution of the Zakharov equations in two and three dimensions.

Particle-in-cell (PIC) simulations and Zakharov's partial differential equations (PDEs) are used to investigate the collapse of isolated Langmuir wave packets in two dimensions. Collapse thresholds are determined numerically, and the roles of enhanced Langmuir wave damping and nonlinearities not included in the standard Zakharov equations are discussed. The Langmuir wave and ion dynamics in PIC simulations are compared with the predictions of PDE simulations incorporating enhanced Langmuir damping. Electron heating and coherent acceleration in the PIC simulations are discussed and compared with predictions of the transit-time theory.