Observational evidence of accelerating electron holes and their effects on passing ions

As a universal structure in space plasma, electron holes represent an obvious signature of nonlinear process. Although the theory has a 60-year history, whether electron hole can finally accelerate ambient electrons (or ions) is quite controversial. Previous theory for one-dimensional holes predicts that net velocity change of passing electrons (or ions) occurs only if the holes have non-zero acceleration. However, the prediction has not yet been demonstrated in observations. Here, we report four electron holes whose acceleration/deceleration is obtained by fitting the spatial separations and detection time delays between different Magnetospheric Multiscale spacecraft. We find that electron hole acceleration/deceleration is related to the ion velocity distribution gradient at the hole's velocity. We observe net velocity changes of ions passing through the accelerating/decelerating holes, in accordance with theoretical predictions. Therefore, we show that electron holes with non-zero acceleration can cause the velocity of passing ions to increase in the acceleration direction.

Properties and Acceleration Mechanisms of Electrons Up To 200 keV Associated With a Flux Rope Pair and Reconnection X-Lines Around It in Earth's Plasma Sheet

The properties and acceleration mechanisms of electrons (<200 keV) associated with a pair of tailward traveling flux ropes and accompanied reconnection X-lines in Earth's plasma sheet are investigated with MMS measurements. Energetic electrons are enhanced on both boundaries and core of the flux ropes. The power-law spectra of energetic electrons near the X-lines and in flux ropes are harder than those on flux rope boundaries. Theoretical calculations show that the highest energy of adiabatic electrons is a few keV around the X-lines, tens of keV immediately downstream of the X-lines, hundreds of keV on the flux rope boundaries, and a few MeV in the flux rope cores. The X-lines cause strong energy dissipation, which may generate the energetic electron beams around them. The enhanced electron parallel temperature can be caused by the curvature-driven Fermi acceleration and the parallel electric potential. Betatron acceleration due to the magnetic field compression is strong on flux rope boundaries, which enhances energetic electrons in the perpendicular direction. Electrons can be trapped between the flux rope pair due to mirror force and parallel electric potential. Electrostatic structures in the flux rope cores correspond to potential drops up to half of the electron temperature. The energetic electrons and the electron distribution functions in the flux rope cores are suggested to be transported from other dawn-dusk directions, which is a 3-dimensional effect. The acceleration and deceleration of the Betatron and Fermi processes appear alternately indicating that the magnetic field and plasma are turbulent around the flux ropes.

Physical regimes of electrostatic wave-wave nonlinear interactions generated by an electron beam propagating in a background plasma

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of the quasilinear and weak turbulence theories, their validities are limited by the requirements of a sufficiently dense mode spectrum and a small wave amplitude. In this paper, we extensively study the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing high-resolution two-dimensional particle-in-cell simulations and using analytical theories. We confirm that, during the initial stage of two-stream instability between the beam and background cold electrons, it is saturated due to the well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the regimes are analyzed in detail. We identify a new regime in the strong Langmuir turbulence featured by what we call electron modulational instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually, the beam-plasma wave interaction stops being resonant due to the strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a repetitive (intermittent) process. The beam electrons are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa (κ) distribution and a wave-energy spectrum E^{2}(k)∼k^{-5} are observed in the strong turbulent regime.

Electrostatic Solitary Structures in Space Plasmas: Soliton Perspective

Occurrence of electrostatic solitary waves (ESWs) is ubiquitous in space plasmas, e.g., solar wind, Lunar wake and the planetary magnetospheres. Several theoretical models have been proposed to interpret the observed characteristics of the ESWs. These models can broadly be put into two main categories, namely, Bernstein–Green–Kruskal (BGK) modes/phase space holes models, and ion- and electron- acoustic solitons models. There has been a tendency in the space community to favor the models based on BGK modes/phase space holes. Only recently, the potential of soliton models to explain the characteristics of ESWs is being realized. The idea of this review is to present current understanding of the ion- and electron-acoustic solitons and double layers models in multi-component space plasmas. In these models, all the plasma species are considered fluids except the energetic electron component, which is governed by either a kappa distribution or a Maxwellian distribution. Further, these models consider the nonlinear electrostatic waves propagating parallel to the ambient magnetic field. The relationship between the space observations of ESWs and theoretical models is highlighted. Some specific applications of ion- and electron-acoustic solitons/double layers will be discussed by comparing the theoretical predictions with the observations of ESWs in space plasmas. It is shown that the ion- and electron-acoustic solitons/double layers models provide a plausible interpretation for the ESWs observed in space plasmas.

Spacecraft Observations and Theoretical Understanding of Slow Electron Holes

We present Magnetospheric Multiscale observations showing large numbers of slow electron holes with speeds clustered near the local minimum of double-humped velocity distribution functions of background ions. Theoretical computations show that slow electron holes can avoid the acceleration that otherwise prevents their remaining slow only under these same circumstances. Although the origin of the slow electron holes is still elusive, the agreement between observation and theory about the conditions for their existence is remarkable.

First Measurements of Electrons and Waves inside an Electrostatic Solitary Wave

Electrostatic solitary wave (ESW)-a Debye-scale structure in space plasmas-was believed to accelerate electrons. However, such a belief is still unverified in spacecraft observations, because the ESW usually moves fast in spacecraft frame and its interior has never been directly explored. Here, we report the first measurements of an ESW's interior, by the Magnetospheric Multiscale mission located in a magnetotail reconnection jet. We find that this ESW has a parallel scale of 5λ_{De} (Debye length), a superslow speed (99  km/s) in spacecraft frame, a longtime duration (250 ms), and a potential drop eφ_{0}/kT_{e}∼5%. Inside the ESW, surprisingly, there is no electron acceleration, no clear change of electron distribution functions, but there exist strong electrostatic electron cyclotron waves. Our observations challenge the conventional belief that ESWs are efficient at particle acceleration.

Observations of Electromagnetic Electron Holes and Evidence of Cherenkov Whistler Emission

We report observations of electromagnetic electron holes (EHs). We use multispacecraft analysis to quantify the magnetic field contributions of three mechanisms: the Lorentz transform, electron drift within the EH, and Cherenkov emission of whistler waves. The first two mechanisms account for the observed magnetic fields for slower EHs, while for EHs with speeds approaching half the electron Alfvén speed, whistler waves excited via the Cherenkov mechanism dominate the perpendicular magnetic field. The excited whistler waves are kinetically damped and typically confined within the EHs.

Unified View of Nonlinear Wave Structures Associated with Whistler-Mode Chorus

A range of nonlinear wave structures, including Langmuir waves, unipolar electric fields, and bipolar electric fields, are often observed in association with whistler-mode chorus waves in near-Earth space. We demonstrate that the three seemingly different nonlinear wave structures originate from the same nonlinear electron trapping process by whistler-mode chorus waves. The ratio of the Landau resonant velocity to the electron thermal velocity controls the type of nonlinear wave structures that will be generated.

Direct Observation of Electron Distributions inside Millisecond Duration Electron Holes

Despite the importance of millisecond duration spatial structures [chorus wave nonlinearity or time domain structures (TDS)] to plasma dynamics, there have been no direct observations of the generation and interaction of these waves and TDS with electrons at the millisecond timescale required for their understanding. Through superposition of 0.195 ms Magnetospheric Multiscale Satellite electron measurements inside 37 superposed, millisecond duration electron holes, the first observations of electron spectra and pitch angle distributions on a submillisecond timescale have been obtained. They show that keV electrons inside the superposed electron hole are accelerated by several hundred volts and that the spectrum of electrons inside the electron hole contain several maxima and minima that are explained by a model of electron energy changes on entering the holes. We report the first observation of trapped electrons inside the TDS, in accordance with the theoretical requirement that such electrons must be present in order to form the phase space holes. Mechanisms of electron acceleration by electron holes (through perpendicular energy gain as the TDS moves into a converging magnetic field) and scattering (due to the perpendicular electric field) are discussed.

Electron Bulk Acceleration and Thermalization at Earth's Quasiperpendicular Bow Shock

Electron heating at Earth's quasiperpendicular bow shock has been surmised to be due to the combined effects of a quasistatic electric potential and scattering through wave-particle interaction. Here we report the observation of electron distribution functions indicating a new electron heating process occurring at the leading edge of the shock front. Incident solar wind electrons are accelerated parallel to the magnetic field toward downstream, reaching an electron-ion relative drift speed exceeding the electron thermal speed. The bulk acceleration is associated with an electric field pulse embedded in a whistler-mode wave. The high electron-ion relative drift is relaxed primarily through a nonlinear current-driven instability. The relaxed distributions contain a beam traveling toward the shock as a remnant of the accelerated electrons. Similar distribution functions prevail throughout the shock transition layer, suggesting that the observed acceleration and thermalization is essential to the cross-shock electron heating.

Electrostatic solitary waves and hole structures generated by bump-on-tail instability in electron-positron plasmas

Electrostatic solitary waves (ESWs) and solitons are widely present in the solar system plasma environment. Many theoretical and numerical studies have been carried out to address the formation and structure of ESWs and solitons in electron-ion plasmas. Due to the inertia symmetry, the issue of whether solitons can exist in pair plasmas has been raised and has been discussed in a number of papers. Recently, we have shown that interlacing electron and positron holes in phase space associated with periodic positive and negative potentials may be generated by current-free electron and positron beams streaming in stationary electron-positron background plasmas [Jao and Hau, Phys. Rev. E 86, 056401 (2012)]. The question remains of whether pure electron or positron holes with positive or negative polarity may exist in neutral electron-positron plasmas. In this paper, we show the formation of electron (positron) holes associated with ESWs of positive (negative) potential based on the particle-in-cell simulations of bump-on-tail streaming instability in pair plasmas. The fluid theory shows that the coexistence of two unstable modes with different wavelengths is the essential condition for the generation of electrostatic solitons and hole structures in an electron-positron plasma.

Formation of electrostatic solitons and hole structures in pair plasmas

In an electron-proton plasma, electrostatic solitary waves and hole structures can easily be generated by streaming instability due to the asymmetric inertia between ions and electrons. It has been argued theoretically whether electrostatic solitons and/or hole structures can form in a pair plasma. This paper presents results on the formation of pair electrostatic hole structure in an electron-positron plasma based on one-dimensional electrostatic particle-in-cell simulations. In particular, we show the feature of interlacing electron and positron holes in phase space generated by current-free electron and positron beams streaming in a stationary electron-positron background plasma. The coexistent electron and positron holes are associated with periodic interlacing of positive and negative potentials, respectively. Detailed comparisons between simulation results and linear theory of streaming instability in pair plasmas are made and the thermodynamic state is inferred.

A current filamentation mechanism for breaking magnetic field lines during reconnection

During magnetic reconnection, the field lines must break and reconnect to release the energy that drives solar and stellar flares and other explosive events in space and in the laboratory. Exactly how this happens has been unclear, because dissipation is needed to break magnetic field lines and classical collisions are typically weak. Ion-electron drag arising from turbulence, dubbed 'anomalous resistivity', and thermal momentum transport are two mechanisms that have been widely invoked. Measurements of enhanced turbulence near reconnection sites in space and in the laboratory support the anomalous resistivity idea but there has been no demonstration from measurements that this turbulence produces the necessary enhanced drag. Here we report computer simulations that show that neither of the two previously favoured mechanisms controls how magnetic field lines reconnect in the plasmas of greatest interest, those in which the magnetic field dominates the energy budget. Rather, we find that when the current layers that form during magnetic reconnection become too intense, they disintegrate and spread into a complex web of filaments that causes the rate of reconnection to increase abruptly. This filamentary web can be explored in the laboratory or in space with satellites that can measure the resulting electromagnetic turbulence.

Formation of electron holes and particle energization during magnetic reconnection

Three-dimensional particle simulations of magnetic reconnection reveal the development of turbulence driven by intense electron beams that form near the magnetic x-line and separatrices. The turbulence collapses into localized three-dimensional nonlinear structures in which the electron density is depleted. The predicted structure of these electron holes compares favorably with satellite observations at Earth's magnetopause. The birth and death of these electron holes and their associated intense electric fields lead to strong electron scattering and energization, whose understanding is critical to explaining why magnetic explosions in space release energy so quickly and produce such a large number of energetic electrons.

Electrostatic mode excitation in electron holes due to wave bounce resonances

A kinetic theory of resonant interaction between electrostatic waves and the bounce motion of electrostatically trapped electrons is developed. Precise criteria are derived for the stability of electrostatic potential structures which trap electrons in a highly magnetized plasma. The theory explains the energy transfer from electron phase space holes to waves observed in simulations. It may also account for the destabilization of electrostatic waves propagating obliquely to the geomagnetic field and some characteristics of the holes as observed in the auroral ionosphere.

Transverse instability of magnetized electron holes

We study a transverse instability of the nonlinear equilibria known as electron phase-space holes in the presence of a magnetic field. The instability is intrinsically two dimensional and is determined by the dynamics of the trapped electrons. It depends on hole amplitudes, ambient magnetic fields, and the perpendicular velocity spread. The long-standing hole stability problem in multiple dimensions can be characterized by the gyro-to-bounce frequency ratio. A low ratio associated with a small perpendicular velocity spread results in a disintegration of the positive potential spikes.

Generation of broadband electrostatic waves in Earth's magnetotail

The theory that broad-band electrostatic waves (BEN) in Earth's magnetotail are trapped-electron ("BGK") modes is reexamined. Electron/ion beams analyzed for a realistic magnetized-plasma source model with kappa distributions are found to drive an unstable spectrum of broad angular range over several orders of magnitude in f, up to (0.1-0.2)f(pe). Analysis indicates that trapping essential for the BGK paradigm is good only at the highest f, whereas most of the spectrum has minimal trapping and can be driven by electron/ion beam instabilities. A new model is proposed in which trapped-electron modes exist only at the highest f band, whereas electron/ion beam instabilities drive the bulk of the broad-band spectrum below that. BEN wave data from ISEE-1 and ISEE-3 show large angles of propagation with respect to the magnetic field for f<f(ce) as predicted by the new model but not the BGK model. However f>f(ce) is observed only in a narrow angular range around the magnetic field and may be BGK modes. This predicts that the BEN solitary waves in the source region are not in BEN well into the lobe.