Buneman Instability Research Articles

Wave dynamics of an electrojet: generalized Farley–Buneman instability

AbstractIn this paper we generalize the classical Farley–Buneman (FB) instability to include space-charge effects and finite electron inertia. The former effect makes the ion-acoustic wave dispersive with the usual resonance appearing at the ion plasma frequency, but other than that the structure of the FB instability remains intact. However, the inclusion of the latter, finite electron inertia, gives rise to the propagating electron-cyclotron mode, albeit modified by collisions. In the presence of differential electron streaming relative to the ions, the interaction between this mode, attempting to propagate against the stream, but convected forward by the stream, and a forward propagating ion-acoustic mode, gives rise to a new instability distinct from the FB instability. The process may be thought of in terms of the coupling between negative energy waves (electron-cyclotron waves attempting to propagate against the stream) and positive energy waves (forward propagating ion-acoustic waves). In principle, the instability simply requires super-ion acoustic streaming electrons and the corresponding growth rates are of the order of one half of the lower hybrid frequency, which are faster than the corresponding FB growth rates. For conditions appropriate to the middle day-side E-region this instability excites a narrow band of frequencies just below the ion plasma frequency. Its role in the generation of electrojet irregularities may be as important as the classical FB instability.

Relativistic Buneman instability in the laser breakout afterburner

A new laser-driven ion acceleration mechanism has been identified in particle-in-cell simulations of high-contrast-ratio ultraintense lasers with very thin (10s of nm) solid targets [Yin et al., Laser and Particle Beams 24, 291 (2006); Yin et al., Phys. Plasmas 13, 072701 (2007)]. After a brief period of target normal sheath acceleration (TNSA), “enhanced” TNSA follows. In this stage, the laser rapidly heats all the electrons in the target as the target thickness becomes comparable to the skin depth and enhanced acceleration of the ions results. Then, concomitant with the laser penetrating the target, a large accelerating longitudinal electric field is generated that co-moves with the ions. This last phase has been termed the laser “breakout afterburner” (BOA). Earlier work suggested that the BOA was associated with the Buneman instability that efficiently converts energy from the drift of the electrons into the ions. In this Brief Communication, this conjecture is found to be consistent with particle-in-cell simulation data and the analytic dispersion relation for the relativistic Buneman instability.

Absence of Electron Surfing Acceleration in a Two-dimensional Simulation

Electron acceleration in high Mach number perpendicular shocks is investigated through a two-dimensional electrostatic particle-in-cell (PIC) simulation. We simulate the shock-foot region by modeling particles that consist of three components—such as incident protons and electrons, and reflected protons in the initial state—which satisfies the Buneman instability condition. In contrast to previous one-dimensional simulations in which strong surfing acceleration is realized, we find that surfing acceleration does not occur in two-dimensional simulations. This is because excited electrostatic potentials have a two-dimensional structure that makes electron trapping impossible. Thus, the surfing acceleration does not work either in itself or as an injection mechanism for the diffusive shock acceleration. We briefly discuss implications of the present results on the electron heating and acceleration by shocks in supernova remnants.

Monoenergetic and GeV ion acceleration from the laser breakout afterburner using ultrathin targets

A new laser-driven ion acceleration mechanism using ultrathin targets has been identified from particle-in-cell simulations. After a brief period of target normal sheath acceleration (TNSA) [S. P. Hatchett et al., Phys. Plasmas 7, 2076 (2000)], two distinct stages follow: first, a period of enhanced TNSA during which the cold electron background converts entirely to hot electrons, and second, the “laser breakout afterburner” (BOA) when the laser penetrates to the rear of the target where a localized longitudinal electric field is generated with the location of the peak field co-moving with the ions. During this process, a relativistic electron beam is produced by the ponderomotive drive of the laser. This beam is unstable to a relativistic Buneman instability, which rapidly converts the electron energy into ion energy. This mechanism accelerates ions to much higher energies using laser intensities comparable to earlier TNSA experiments. At a laser intensity of 1021W∕cm2, the carbon ions accelerate as a quasimonoenergetic bunch to 100s of MeV in the early stages of the BOA with conversion efficiency of order a few percent. Both are an order of magnitude higher than those realized from TNSA in recent experiments [Hegelich et al., Nature 441, 439 (2006)]. The laser-plasma interaction then evolves to produce a quasithermal energy distribution with maximum energy of ∼2GeV.

Parallel and lower hybrid turbulence in low β plasmas driven by strong parallel currents and the resulting parallel electron and perpendicular ion energization

In plasmas with strong field aligned currents, the most unstable mode is not always at parallel propagation, but may be at intermediate and very oblique angles. 2D particle simulations are performed in order to examine the interaction between the plasma waves at various angles and the electron and ion distributions in low β collisionless plasmas with strong electron drifts. The parallel Buneman instability is known to arise in this situation, but the simulations demonstrate that the very oblique lower hybrid (LH) waves, until recently considered unimportant, may actually play a role just as significant as the waves at parallel propagation. The LH waves are energized by a current-driven linear instability, which may be seen as the oblique limit of the Buneman or ion-acoustic instability. The simulations resolve strong LH turbulence, substantial perpendicular ion tail heating and parallel electron heating. The combined action of parallel and oblique modes results in more complete electron relaxation than may be produced by the parallel Buneman instability alone.

Plasma particle simulations using a special-purpose computer system for gravitational N-body problems

Plasma particle simulations are performed using GRAPE-6, a special-purpose computer for calculating gravitational N-body systems. GRAPE-6 rapidly calculates the gravitational force between particles using specialized pipeline processors. The peak performance of a unit of GRAPE-6 reaches 985 GFLOPS. We investigated speeding up plasma simulations through the use of GRAPE-6 for the calculation of Coulomb interactions, which have the same form of central force as the gravitational force. As an example of plasma particle simulation using GRAPE-6, we simulated the Buneman instability. As another example of plasma particle simulation, we simulated a Coulomb crystal in a dusty plasma. The formation of a Coulomb crystal was observed under typical laboratory conditions. We found that GRAPE-6 can perform the entire operation of the simulation of a Coulomb crystal with 5 × 103 particles up to 210 times faster than a 1.6-GHz Pentium4 CPU.

Stabilisation of BGK modes by relativistic effects

We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. We observe the growth of these waves and their subsequent saturation via electron trapping for a range of proton beam velocities, from 0.15c to 0.9c. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ~160 plasma periods. Furthermore we observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW's which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma.

Lower hybrid turbulence driven by parallel currents and associated electron energization

Parallel currents are usually in the form of field-aligned electron drifts in collisionless plasmas. The field-aligned drifts often drive instabilities. For instance, Drake et al. [Science, 299, 873 (2003)] found growth of parallel propagating turbulence initially and strong levels of oblique lower hybrid (LH) waves at later times; substantial parallel electron acceleration was also found. We use collisionless linear theory and quasilinear simulations to study wave growth and parallel electron dynamics in similar systems. In low-β plasmas with intense parallel currents and both with or without parallel E fields, LH waves are shown to grow even for electron distributions stable to the parallel Buneman instability and to accelerate electrons parallel to B very rapidly. This instability may be seen as the oblique limit of the ion acoustic and Buneman instabilities. The quasilinear diffusion via LH waves may release almost all of the available drift energy, and produce stronger electron acceleration and heating than the parallel Buneman instability alone.

Cylindrical lower‐hybrid electron holes at the Earth's dayside magnetopause

The analytic model of lower‐hybrid electron holes (Jovanović and Shukla, 2004) is applied to analyze the strong coherent unipolar electric field signals perpendicular to the ambient magnetic field with a characteristic frequency in the lower‐hybrid frequency range, recorded at the dayside magnetopause by the Polar mission (Mozer et al., 2004). On the basis of a good agreement with theoretical predictions, these structures are identified as the oblique cylindrical electron holes. Their localization results from the balance of nonlinearity associated with the electrons that are trapped along the magnetic field direction and undergo the × drift in the perpendicular direction and the dispersion provided by the electron polarization drift. It is suggested that electron holes can be related to the nonlinear evolution of the Buneman instability of lower‐hybrid waves, driven by the parallel electric field that develops in the course of collisionless reconnection.

On reformation of quasi-perpendicular collisionless shocks

We review recent studies on mass ratio dependence of self-reformation of high Mach number, low β, highly oblique quasi-perpendicular shocks by Scholer et al. (Scholer, M., Shinohara, I., Matsukiyo, S. Quasi-perpendicular shocks: length scale of the cross-shock potential, shock reformation, and implication for shock surfing, J. Geophys. Res., 108, 1014, doi:10.1029/2002JA009515, 2003.), Matsukiyo and Scholer (Matsukiyo, S., Scholer, M. Modified two-stream instability in the foot of high Mach number quasi-perpendicular shocks, J. Geophys. Res., 108, 1459, doi:10.1029/2003JA10080, 2003.), and Scholer and Matsukiyo (Scholer, M., Matsukiyo, S. Nonstationarity of quasi-perpendicular shocks: a comparison of full particle simulations with different ion to electron mass ratio, Ann. Geophys., in press, 2004.). A one-dimensional full particle simulation code is utilized. In small ion to electron mass ratio runs, reformation is due to the accumulation of gyrating reflected ions at the upstream edge of the foot. Furthermore, at an extremely small mass ratio, the Buneman instability is generated in the foot. In the realistic mass ratio run, however, the modified two-stream instability excited in the foot plays an important role in a shock reformation process.

Coupling between upper-hybrid waves and electron holes in Earth’s magnetotail

An analytic theory of the nonlinear interaction between electrostatic high-frequency upper-hybrid waves and the low-frequency electron holes in a magnetized plasma is presented. It provides an explanation for the simultaneous occurrence of upper-hybrid bursts and electron holes, observed recently by the WIND and CLUSTER spacecrafts in the vicinity of the X point during the collisionless reconnection in Earth’s deep magnetotail. Using a fluid description for the high-frequency mode and a drift-kinetic description for the low-frequency mode, a Zakharov-type system of equations is obtained that describes the interaction between the upper-hybrid and lower-hybrid waves in the presence of an oblique Buneman instability and resonant electrons. The saturation of the linear and explosive parametric instabilities is shown to result from the electron trapping in the combined low-frequency and ponderomotive potentials, yielding an oblique lower-hybrid hole. The presence of an electron hole produces the localization of the upper-hybrid waves, yielding either a bright nonlinear Schrödinger soliton trapped inside the hole or a dark soliton driven by the defocusing nonlinear Schrödinger nonlinearity, which is trapped outside of the hole.

Nonlinear dynamic of low-frequency Buneman instability of a current-driven plasma

Theoretical investigation of the nonlinear dynamic of the low-frequency Buneman instability of a current-driven plasma is presented. In the nonlinear stage, this instability is described by the diffusion equation with a negative nonlinear diffusion coefficient. As a result, the plasma density profile reaches a sharp peak and is accompanied by the breakdown of quasineutrality and establishment of stationary self-focusing structures.

Onset and saturation of guide-field magnetic reconnection

The onset and saturation of collisionless magnetic reconnection in the presence of a guide field are investigated using two-dimensional particle-in-cell simulations in which the reconnection evolves out of the initial thermal noise in the current sheet and in which the resolution is sufficient to resolve the electron singular layer. The simulations show that reconnection does not abate when the island width exceeds either the electron singular layer or the initial current sheet width. Instead, reconnection proceeds through an explosive stage which appears to be limited only by the spatial size of the system. The guide-field reconnection dynamics is dominated by the formation of an asymmetric configuration with a deep density cavity along one pair of separatrix arms. In this cavity an electron beam feature is formed which excites the Buneman instability. Near the X line the reconnection electric field is supported by a combination of quasiviscous and bulk inertia effects for the electrons. Around the island perimeter, intense Debye-scale, predominantly perpendicular, electric field structures are formed.

Simulation study of surfing acceleration in magnetized space plasmas

We present a numerical study of the surfing mechanism in which electrons are trapped in Bernstein–Greene–Kruskal (BGK) modes, and are accelerated across the magnetic field direction by the Lorentz force in magnetized space plasmas. The BGK modes are the product of an ion-beam Buneman instability that excites large-amplitude electrostatic upper-hybrid waves in the plasma. Our study, which is performed with particle-in-cell (PIC) and Vlasov codes, reveals the stability of the BGK mode as a function of the magnetic field strength and the ion beam speed. It is found that the surfing acceleration is more effective for a weaker magnetic field owing to the longer lifetime of the BGK modes. The importance of our investigation to electron acceleration in astrophysical environments has been emphasized.

Linear theory for fast collisionless magnetic reconnection in the lower-hybrid frequency range

A linear theory is presented for the interplay between the fast collisionless magnetic reconnection and the lower-hybrid waves that has been observed in recent computer simulations [J. F. Drake, M. Swisdak, C. Cattell et al., Science 299, 873 (2003)]. In plasma configurations with a strong guide field and anisotropic electron temperature, the electron dynamics is described within the framework of standard electron magnetohydrodynamic equations, accounting also for the effects of the electron polarization and ion motions in the presence of perpendicular electric fields. In the linear phase, we find two types of instabilities of a thin current sheet with steep edges, corresponding to its filamentation (or tearing) and bending. Using a surface-wave formalism for the perturbations whose wavelength is larger than the thickness of the current sheet, the corresponding growth rates are calculated as the contributions of singularities in the plasma dispersion function. These are governed by the electron inertia and the linear coupling of the reconnecting magnetic field with local plasma modes propagating in the perpendicular direction that are subject to the Buneman instability. The linear surface wave instability may be particularly important as a secondary instability, dissipating the thin current sheets that develop in the course of the fast reconnection in the shear-Alfvén and kinetic-Alfvén regimes, and providing the anomalous resistivity for the growth of magnetic islands beyond the shear-Alfvén and kinetic-Alfvén scales.

Surfatron and stochastic acceleration of electrons in astrophysical plasmas

Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency $\omega_{\rm pe}$ by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If $\omega_{\rm pe}$ is much higher than the electron cyclotron frequency $\Omega_{\rm e}$, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both $\omega_{\rm pe}/\Omega_{\rm e}$ and the size of the simulation box $L$. If $L$ is equal to one wavelength, $\lambda_0$, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when $\omega_{\rm pe}/\Omega_{\rm e} \simeq 100$: in this case electrons are accelerated to speeds of up $c/2$ where $c$ is the speed of light. In a simulation with $L=4\lambda_0$ and $\omega_{\rm pe}/\Omega_{\rm e} = 100$, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if $\omega_{\rm pe}/\Omega_{\rm e}> 100$. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks.

On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath

Abstract. Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any distance from the bow shock and that this distance has no dependence on the time durations and amplitudes of the solitary waves. In addition we have found that these same two quantities show no dependence on either the ion velocity or the angle between the ion velocity and the local magnetic field direction. These results point to the conclusion that the solitary waves are probably created locally in the magnetosheath at multiple locations, and that the generation mechanism is most likely not solely related to ion dynamics, if at all. To gain insight into a possible local generation mechanism, we have examined the electron differential energy flux characteristics parallel and perpendicular to the magnetic field, as well as the local electron plasma and cyclotron frequencies and the type of bow shock that Cluster is behind, for several time intervals where solitary waves were observed in the magnetosheath. We have found that solitary waves are most likely to be observed when there are counterstreaming (~parallel and anti-parallel to the magnetic field) electrons at or below about 100eV. However, there are times when these counterstreaming electrons are present when solitary waves are not. During these times the background magnetic field strength is usually very low (<10nT), implying that the amplitudes of the solitary waves, if present, would be near or below those of other waves and electrostatic fluctuations in this region making it impossible to isolate or clearly distinguish them from these other emissions in the waveform data. Based on these results, we have concluded that some of the near-Earth magnetosheath solitary waves, perhaps in the form of electron phase-space holes, may be generated locally by a two-stream instability involving electrons based on the counterstreaming electrons that are often observed when solitary waves are present. We have not ruled out the possibility that the solitary waves could be generated as a result of the lower-hybrid Buneman instability in the presence of an electron beam, through the electron acoustic mode or through processes involving turbulence, which is almost always present in the magnetosheath, but these will be examined in a more comprehensive study in the future.

Filamentation Instability of Thin Current Sheets in Low-β Plasmas

An analytic theory is presented for the collisionless filamentation instability of thin current sheets in the frequency domain of lower-hybrid waves in low-β plasmas. In a configuration with a strong guide field, the plasma dynamics is studied in a fluid description, accounting for the effects of electron polarization and finite Larmor radii, as well as of the motion of unmagnetized ions in the presence of perpendicular electric fields. In the linear phase, two types of unstable perturbations of a thin current sheet with steep edges are identified that correspond to its filamentation or tearing and bending. Using a surface-wave formalism for the modes whose wavelength is larger than the current sheet thickness, the corresponding growth rates are calculated as the contributions of singularities in the dispersion function of surface waves. These are governed by the electron inertia and by linear coupling with local plasma modes propagating in the perpendicular direction that are subjected to the Buneman instability. This new linear instability provides a suitable channel for the dissipation of current sheets that evolve during the collisionless magnetic reconnection in shear- and kinetic-Alfvén regimes, and for the creation of anomaluos resistivity.

Formation of nonlinear magnetic islands via trapped electrons in the lower-hybrid range

Coherent nonlinear stationary state is studied in the frequency and spatial domain of electromagnetic lower-hybrid waves in a beam-plasma configuration that is subjected to the oblique linear Buneman instability. In the presence of magnetic shear, a solution is found in the form of a nonlinear chain of magnetic islands. Such equilibrium may represent the saturated state of fast collisionless magnetic reconnection that is reached after the reconnection has ended. It is demonstrated that the topological constraints that hamper the reconnection of magnetic field lines in the fluid representation are efficiently removed by the nonlinear currents and space charges of trapped electrons. Two distinct trapping mechanisms are distinguished. Besides the electrostatic trapping of particles in the self-consistent minima of potential energy, a different type of magnetic trapping is identified that is responsible for the creation of thin current sheets at the separatrices between open and closed magnetic field lines. Combined effects of the resulting two types of nonlinear phase-space vortices provide for a topological transformation of a sheared magnetic field into a single chain of magnetic islands coupled with a double chain of hydrodynamic vortices.

Ion thermal effects on E-region instabilities: 2D kinetic simulations

Radars frequently receive strong returns from naturally occurring plasma density irregularities centered around 100 km altitude in the atmosphere. These E-region ionospheric irregularities occur when electrojet polarization electric fields drive plasma instabilities, most commonly the Farley–Buneman (FB) and gradient drift instabilities. This paper presents results from two fully kinetic, 2D simulations of field driven instabilities in the E-region. These simulations show the important impact of ion thermal effects on wave growth and turbulence. The first simulation applies parameters meant to replicate a strongly driven high-latitude FB instability where the polarization electric field exceeds the FB threshold by a factor of 4. In this case, waves grow and saturate with characteristics dominated by ion thermal perturbations resulting from a balance between frictional ion heating and cooling. These characteristics differ substantially from those expected for FB waves. In the second simulation, the driving field exceeds the threshold by a factor of 2, causing FB waves to grow with distinct modifications by ion thermal effects. The thermal effects reproduced by these simulations may account for some of the previously unexplained observational characteristics of E-region irregularities, particularly at high latitude and in the upper E-region. They also explain the results seen in the simulations of Janhunen (J. Geophys. Res. 99 (1994b) 11461).