Electron Two-stream Instability Research Articles

Electrostatic Solitary Waves and Electron-beam Instabilities in the Separatrix Region of Magnetic Reconnection

Using 2D particle-in-cell (PIC) simulations, the generation of electrostatic solitary waves (ESWs) and the associated plasma waves in symmetric magnetic reconnection are studied, and multiple kinds of ESWs with different propagating speeds are identified. Near the current sheet in the outflow region, there are two kinds of ESWs propagating away from the X line: their propagating speeds are about 0.73V Te0 and 1.2V Te0 (where V Te0 is the initial electron thermal velocity), and their generation is associated with the Buneman instability and the electron two-stream instability, respectively. In the separatrix region, there is one kind of ESW propagating toward the X line with a propagating speed of about 1.2 V Te0, which is formed during the nonlinear evolution of the electron two-stream instability. We also run a case with a guide field, and there exist two kinds of ESWs: the ESWs propagating away from the X line can be generated near the separatrices with electron outflow, while the ESWs propagating toward the X line can be generated near the separatrices with electron inflow. The two kinds of ESWs are associated with the electron two-stream instability and the Buneman instability, respectively.

Electrostatic Waves and Electron Heating Observed Over Lunar Crustal Magnetic Anomalies

AbstractAbove lunar crustal magnetic anomalies, large fractions of solar wind electrons and ions can be scattered and stream back toward the solar wind flow, leading to a number of interesting effects such as electrostatic instabilities and waves. These electrostatic structures can also interact with the background plasma, resulting in electron heating and scattering. We study the electrostatic waves and electron heating observed over the lunar magnetic anomalies by analyzing data from the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft. Based on the analysis of two lunar flybys in 2011 and 2013, we find that the electron two‐stream instability (ETSI) and electron cyclotron drift instability (ECDI) may play an important role in driving the electrostatic waves. We also find that ECDI, along with the modified two‐stream instability (MTSI), may provide the mechanisms responsible for substantial isotropic electron heating over the lunar magnetic anomalies.

Non-monotonic double layers and electron two-stream instabilities resulting from intermittent ion acoustic wave growth

Transient characteristics of a current-carrying plasma subjected to ion acoustic instability are studied via Vlasov–Poisson simulations. After saturation of the ion acoustic instability, when a sufficient range of long-wavelength ion acoustic modes is considered, ion acoustic wave packets form and give rise to ion phase space holes. These ion holes grow in magnitude until asymmetric electron reflection, due to the current carrying plasma, results in a potential gradient across the hole known as a non-monotonic double layer. Downstream of the double layer, an electron two-stream instability is generated due to a depletion of forward-streaming electrons by reflection. This secondary instability initiates a plasma wave whose phase velocity is determined by the magnitude of the double layer potential. While the double layer potential depends on the ion mass for a given domain length, the phase velocity of the secondary wave is consistently observed to be greater than the ion acoustic speed. Implications for the presence of these transient phenomena are discussed in the context of experimental plume measurements of hollow cathode devices.

The Solar Wind Electron Halo as Produced by Electron Beams Originating in the Lower Corona: Beam Density Dependence

Abstract It has been suggested that the isotropic electron halo observed in the solar wind electron velocity distribution function may originate from nanoflare-accelerated electron beams below 1.1 R ⊙ from the solar surface through the nonlinear electron two-stream instability (ETSI). This model unifies the origins of kinetic waves, the electron halo, and the coronal weak Type III bursts, and establishes a link between the solar wind observables and the electron dynamics in nanoflares. One of the important predictions of this model is that the halo-core temperature ratio is anticorrelated with the density ratio, and the minimum ratio is ∼4, a relic of the ETSI heating and has been found to be consistent with solar wind observations. However, how the density and relative drift of the electron beams determine the thermal properties of solar wind electrons is unclear. In this paper, using a set of particle-in-cell simulations and kinetic theory, we show that a necessary condition for an isotropic halo to develop is that the ratio of beam density n b and the background n 0 be lower than a critical value N c ∼ 0.3. Heating of the core electrons becomes weaker with decreasing beam density, while the heating of halo electrons becomes stronger. As a result, the temperature ratio of the halo and core electrons increases with the decrease of the beam density, explaining the physical meaning of the predicted anticorrelated relation. We apply these results to the current observations and discuss the possible electron beam density produced in the nanoflares.

Photoemission driven electron two-stream instability (ETSI) and evolution of plasma sheath

Analysis related to the onset and evolution of the electron two-stream instability (ETSI) near a surface with a continuous photoemission flux is presented. With the help of a particle-in-cell simulation code, it is shown that when a surface emits photoelectrons due to exposure to ultraviolet photons (or due to similar mechanisms), it may lead to the onset of the ETSI due to the relative bulk velocity difference between the photoelectrons and the plasma electrons. It is shown that the ETSI thus developed is sustained through the lifetime of the plasma and prevents thermalization of the electrons, which leads to a distortion in the electron velocity distribution function (EVDF) resulting a high energy tail, at least near the surface. We have shown that the resultant EVDF can be highly Lorentzian with a spectral index of ∼1.5. The simulation results are supported with the corresponding theory, which are found to be in good agreement.

Nonlinear radiation generation processes in the auroral acceleration region

Abstract. It is known from laboratory plasma experiments that double layers (DLs) radiate in the electromagnetic spectrum; but this is only known qualitatively. In these experiments, it was shown that the electron beam created on the high-potential side of a DL generates nonlinear structures which couple to electromagnetic waves and act as a sender antenna. In the Earth auroral region, observations performed by auroral spacecraft have shown that DLs occur naturally in the source region of intense radio emissions called auroral kilometric radiation (AKR). Very high time-, spatial-, and temporal-resolution measurements are needed in order to characterize waves and particle distributions in the vicinity of DLs, which are moving transient structures. We report observations from the FAST satellite of a localized large-amplitude parallel electric field (∼ 300 mV m−1) recorded at the edges of the auroral density cavity. In agreement with laboratory experiments, on the high-potential side of the DL, elementary radiation events are detected. They occur substantially above the local electron gyrofrequency and are associated with the presence of electron holes. The velocity of these nonlinear structures can be derived from the measurement of the Doppler-shifted AKR frequency spectrum above the electron gyrofrequency. The generated electron holes appear as the nonlinear evolution of electrostatic waves generated by the electron–electron two-stream instability because they propagate at about half the beam velocity. It is pointed out that, in the vicinity of a DL, the shape of the electron distribution gives rise to a significant power recorded in the left-hand polarized ordinary (LO) mode.

How electron two-stream instability drives cyclic Langmuir collapse and continuous coherent emission

Continuous plasma coherent emission is maintained by repetitive Langmuir collapse driven by the nonlinear evolution of a strong electron two-stream instability. The Langmuir waves are modulated by solitary waves in the linear stage and electrostatic whistler waves in the nonlinear stage. Modulational instability leads to Langmuir collapse and electron heating that fills in cavitons. The high pressure is released via excitation of a short-wavelength ion acoustic mode that is damped by electrons and reexcites small-scale Langmuir waves; this process closes a feedback loop that maintains the continuous coherent emission.

Electrostatic Structure of the Electron Phase-space Holes Generated by the Electron Two-stream Instability with a Finite Width

Space satellite observations in an electron phase-space hole (electron hole) have shown that bipolar structures are discovered at the parallel cut of parallel electric field, while unipolar structures spring from the parallel cut of perpendicular electric field. Particle-in-cell (PIC) simulations have demonstrated that the electron bi-stream instability induces several electron holes during its nonlinear evolution. However, how the unipolar structure of the parallel cut of the perpendicular electric field formed in these electron holes is still an unsolved problem, especially in a strongly magnetized plasma (<i>Ω</i>_e &gt; <i>ω</i>_pe, where <i>Ω</i>_e is defined as electron gyrofrequency and <i>ω</i>_pe is defined as plasma frequency, respectively). In this paper, with two-dimensional (2D) electrostatic PIC simulations, the evolution of the electron two-stream instability with a finite width in strongly magnetized plasma is investigated. Initially, those conditions lead to monochromatic electrostatic waves, and these waves coalesce with each other during their nonlinear evolution. At last, a solitary electrostatic structure is formed. In such an electron hole, a bipolar structure is formed in the parallel cut of parallel electric field, while a unipolar structure presents in the parallel cut of perpendicular electric field.

Electron–electron two-stream instability in embedded assembly of nanoparticle (NP) cluster in n-GaAs

The electron–electron two-stream instability has been studied in two-valley n-GaAs embedded with nanoparticle (NP) cluster. We considered polar optical phonon as the dominant intravalley scattering mechanism and drifted Maxwellian to approximate the distribution of carriers between each valley. We derived the dispersion relation for electrostatic wave using hydrodynamic model of plasmas. While investigating temporal behaviour, we found two novel modes of propagation. These two novel modes are found to be evanescent by nature and propagate with equal phase velocities, but in opposite directions. The pre-existing modes retained their profile structures even in the presence of NP cluster. On the other hand, in the case of convective instability, no new modes are obtained but the propagation and gain profiles of the preexisting modes are significantly modified by the presence of NP cluster in the host medium.

Electron two-stream instability and its application in solar and heliophysics

It is well known that electron beams accelerated in solar flares can drive two-stream instability and produce radio bursts in the solar corona as well as in the interplanetary medium. Recent observations show that the solar wind likely originates from nanoflare-like events near the surface of the Sun where locally heated plasma escapes along open field lines into space. Recent numerical simulations and theoretical studies show that electron two-stream instability (ETSI) driven by nanoflare-accelerated electron beams can produce the observed nanoflare-type radio bursts, the non-Maxwellian electron velocity distribution function of the solar wind, and the kinetic scale turbulence in solar wind. This brief review focus on the basic theoretical framework and recent progress in the nonlinear evolution of ETSI driven by electron beams, including the formation of electron holes, Langmuir wave generation in warm plasma, and the nonlinear modulation instability and Langmuir collapse. Potential applications in heliophysics and astrophysics are discussed.

Development and Test of 2.5-Dimensional Electromagnetic PIC Simulation Code

We have developed a 2.5-dimensional electromagnetic particle simulation code using the particle-in-cell (PIC) method to investigate electromagnetic phenomena that occur in space plasmas. Our code is based on the leap-frog method and the centered difference method for integration and differentiation of the governing equations. We adopted the relativistic Buneman-Boris method to solve the Lorentz force equation and the Esirkepov method to calculate the current density while maintaining charge conservation. Using the developed code, we performed test simulations for electron two-stream instability and electron temperature anisotropy induced instability with the same initial parameters as used in previously reported studies. The test simulation results are almost identical with those of the previous papers.

Electron heating during discharges driven by thermionic emission

The heating of plasma electrons during discharges driven by thermionic emission is studied using one-dimensional particle-in-cell Monte Carlo collisions modeling that self-consistently takes the dependence of the thermionic current on the plasma parameters into account. It is found that at a gas pressure of 102 Pa the electron two-stream instability is excited. As a consequence, the electrostatic plasma wave propagates from the cathode to the anode. The trapping of electrons by this wave contributes noticeably to the heating of the plasma. At a larger gas pressure, this instability is not excited. As a consequence, plasma electrons are heated only because of the generation of energetic electrons in ionization events and the scattering of emitted electrons.

THE ORIGIN OF NON-MAXWELLIAN SOLAR WIND ELECTRON VELOCITY DISTRIBUTION FUNCTION: CONNECTION TO NANOFLARES IN THE SOLAR CORONA

The formation of the observed core-halo feature in the solar wind electron velocity distribution function is a long-time puzzle. In this letter based on the current knowledge of nanoflares we show that the nanoflare-accelerated electron beams are likely to trigger a strong electron two-stream instability that generates kinetic Alfv\'en wave and whistler wave turbulence, as we demonstrated in a previous paper. We further show that the core-halo feature produced during the origin of kinetic turbulence is likely to originate in the inner corona and can be preserved as the solar wind escapes to space along open field lines. We formulate a set of equations to describe the heating processes observed in the simulation and show that the core-halo temperature ratio of the solar wind is insensitive to the initial conditions in the corona and is related to the core-halo density ratio of the solar wind and to the quasi-saturation property of the two-stream instability at the time when the exponential decay ends. This relation can be extended to the more general core-halo-strahl feature in the solar wind. The temperature ratio between the core and hot components is nearly independent of the heliospheric distance to the sun. We show that the core-halo relative drift previously reported is a relic of the fully saturated two stream instability. Our theoretical results are consistent with the observations while new tests for this model are provided.

Wave activities in separatrix regions of magnetic reconnection

Two‐dimensional particle‐in‐cell simulations have reproduced the waves consistent with those observed frequently in the separatrix regions of magnetic reconnection in the Earth's magnetotail. The key process generating the waves is intense parallel acceleration of the electrons due to an electrostatic potential hump formed in the inflow side of the separatrices. The intense electron beams trigger the electron two‐stream instability (ETSI) and the beam‐driven whistler instability (WI). The Buneman instability (BI) is also excited by moderate electron beams arising upstream the potential hump. The ETSI generates the Langmuir waves, while the BI gives lower hybrid waves. Both modes evolve the electrostatic solitary waves in the nonlinear phases. The ETSI traps the electrons in the parallel direction and forms a flat‐top distribution with high‐energy cutoff. On the other hand, the WI scatters the electrons in the perpendicular direction, producing isotropic distribution with nonthermal high‐energy tail.

Bidirectional Energy Cascades and the Origin of Kinetic Alfvénic and Whistler Turbulence in the Solar Wind

The observed steep kinetic scale turbulence spectrum in the solar wind raises the question of how that turbulence originates. Observations of keV energetic electrons during solar quiet time suggest them as a possible source of free energy to drive kinetic turbulence. Using particle-in-cell simulations, we explore how the free energy released by an electron two-stream instability drives Weibel-like electromagnetic waves that excite wave-wave interactions. Consequently, both kinetic Alfvénic and whistler turbulence are excited that evolve through inverse and forward magnetic energy cascades.

Electromagnetic Particle-in-Cell Simulations of Electron Holes Formed During the Electron Two-Stream Instability

Previous electrostatic particle-in-cell (PIC) simulations have pointed out that electron phase-space holes (electron holes) can be formed during the nonlinear evolution of the electron two-stream instability. The parallel cuts of the parallel and perpendicular electric field have bipolar and unipolar structures in these electron holes, respectively. In this study, two-dimensional (2D) electromagnetic PIC simulations are performed in the x − y plane to investigate the evolution of the electron two-stream instability, with the emphasis on the magnetic structures associated with these electron holes in different plasma conditions. In the simulations, the background magnetic field is along the x direction. In weakly magnetized plasma (Ωe < ωpe, where Ωe and ωpe are the electron gyrofrequency and electron plasma frequency, respectively), several 2D electron holes are formed. In these 2D electron holes, the parallel cut of the fluctuating magnetic field δBx and δBz has unipolar structures, while the fluctuating magnetic field δBy has bipolar structures. In strongly magnetized plasma (Ωe > ωpe), several quasi-1D electron holes are formed. The electrostatic whistler waves with streaked structures of Ey are excited. The fluctuating magnetic field δBx and δBz also have streaked structures. The fluctuating magnetic field δBx and δBy are produced by the current in the z direction due to the electric field drift of the trapped electrons, while the fluctuating magnetic field δBz can be explained by the Lorentz transformation of a moving quasielectrostatic structure. The influences of the initial temperature anisotropy on the magnetic structures of the electron holes are also analyzed. The electromagnetic whistler waves are found to be excited in weakly magnetized plasma. However, they do not have any significant effects on the electrostatic structures of the electron holes.

The magnetic structures of electron phase-space holes formed in the electron two-stream instability

It is well known that the parallel cuts of the parallel and perpendicular electric field in electron phase-space holes (electron holes) have bipolar and unipolar structures, respectively. Recently, electron holes in the Earth's plasma sheet have been observed by THEMIS satellites to have detectable fluctuating magnetic field with regular structures. Du et al. (2011) investigated the evolution of a one-dimensional (1D) electron hole with two-dimensional (2D) electromagnetic particle-in-cell (PIC) simulations in weakly magnetized plasma (Omega(epsilon) (x)) is along the x direction. Several 2D electron holes are formed during the nonlinear evolution, where the parallel cuts of E-x and E-y have bipolar and unipolar structures, respectively. Consistent with the results of Du et al. (2011), we found that the current along the z direction is generated by the electric field drift motion of the trapped electrons in the electron holes due to the existence of E-y, which produces the fluctuating magnetic field delta B-x and delta B-y in the electron holes. The parallel cuts of delta Bx and delta B-y in the electron holes have unipolar and bipolar structures, respectively.

Generation of low-frequency electrostatic and electromagnetic waves as nonlinear consequences of beam–plasma interactions

Nonlinear evolution of the electron two-stream instability in a current-carrying plasma is examined by using a two-dimensional electromagnetic particle-in-cell simulation. Formation of electron phase-space holes is observed as an early nonlinear consequence of electron–beam–plasma interactions. Lower-hybrid waves, electrostatic, and electromagnetic whistler mode waves are also excited by different mechanisms during the ensuing nonlinear wave–particle interactions. It is shown by the present computer simulation with a large simulation domain and a long simulation time that these low-frequency waves can disturb the electrostatic equilibrium of electron phase-space holes, suggesting that the lifetime of electron phase-space holes sometimes becomes shorter in a current-carrying plasma.

Electron surfing acceleration by the electron two-stream instability in a weak magnetic field

The thermalization of relativistically flowing colliding plasmas is not well understood. The transition layer, in which both plasmas interact and thermalize, is wide and highly structured and the instabilities in this layer may yield non-thermal particle distributions and shock-less energy dissipation. The objective in this work is to explore the ability of an electron two-stream instability for thermalizing a plasma beam that moves at the mildly relativistic speed 0.3c through weakly magnetized plasma and to identify the resulting particle distributions. It is demonstrated here with particle-in-cell simulations that the electron two-stream instability leads to waves that propagate within a wide angular range relative to the flow velocity. The waves are thus not planar, as required for efficient electron surfing acceleration (ESA). The short lifetime of the waves implies, however, only weak modifications of the ESA by the oblique modes, since the waves are sufficiently homogeneous. The ion (proton) beams are not modulated, which would be required to extract some of their energy. The instability can thus heat the electrons significantly, but it fails to accelerate them to relativistic energies and it cannot form a shock layer by thermalizing the protons, at least not for the system and the resolved timescales considered here.

A coupled two-step plasma instability in PW laser plasma interactions

A possible new mechanism for anomalous ion heating in ultra-intense laser plasmas is considered here. This mechanism is based on the excitation of an electron two-stream instability that is driven by the fast electron beam and resonantly decays into ion-acoustic waves. These low frequency waves are then strongly damped by the ion collisions in the dense plasma. The model gives a simple explanation for the preferential heating of the bulk ion population observed in recent laser experiments in the petawatt (PW) regime.