Buneman Instability Research Articles

Stimulated emission–based model of fast radio bursts

ABSTRACT Fast radio bursts (FRBs) are bright, short-duration radio transients with very high brightness temperatures implying highly coherent emission. We suggest that the FRBs are caused by the self-focusing of an electron beam interacting with an ambient plasma right beyond the light cylinder radius of a neutron star. The magnetic field at the light cylinder radius is relatively high that can accommodate both young Crab-like systems and old millisecond pulsars addressing the diverse environments of FRBs. At the first stage, the intense pulsed-beam passing through the background plasma causes instabilities such that the trapped particles in local Buneman-type cavitons saturate the local field. The beam is then radially self-focused due to the circular electric field developed by the two-stream instability that leads to Weibel instability in the transverse direction. Finally, the non-linear saturation of the Weibel instability results in the self-modulational formation of solitons due to plasmoid instability. The resonant solitary waves are the breather-type solitons hosting relativistic particles with self-excited oscillations. The analytical solutions obtained for non-linear dispersion and solitons suggest that, near the current sheets, the relativistic bunches are accelerated/amplified by klystron-like structures due to self-excited oscillations by the induced local electric field. Boosted coherent radio emission propagates through a narrow cone with strong focusing due to radial electric field and magnetic pinching. The non-linear evolution of solitons and the stimulated emission are associated with the Buneman instability and the possibility of the presence of nanosecond shots in FRBs are investigated.

Particle acceleration in coalescent and squashed magnetic islands

Aims.Particles are known to have efficient acceleration in reconnecting current sheets with multiple magnetic islands that are formed during a reconnection process. Using the test-particle approach, the recent investigation of particle dynamics in 3D magnetic islands, or current sheets with multiple X- and O-null points revealed that the particle energy gains are higher in squashed magnetic islands than in coalescent ones. However, this approach did not factor in the ambient plasma feedback to the presence of accelerated particles, which affects their distributions within the acceleration region.Methods.In the current paper, we use the particle-in-cell (PIC) approach to investigate further particle acceleration in 3D Harris-type reconnecting current sheets with coalescent (merging) and squashed (contracting) magnetic islands with different magnetic field topologies, ambient densities ranging between 108 − 1012m−3, proton-to-electron mass ratios, and island aspect ratios.Results.In current sheets with single or multiple X-nullpoints, accelerated particles of opposite charges are separated and ejected into the opposite semiplanes from the current sheet midplane, generating a strong polarisation electric field across a current sheet. Particles of the same charge form two populations: transit and bounced particles, each with very different energy and asymmetric pitch-angle distributions, which can be distinguished from observations. In some cases, the difference in energy gains by transit and bounced particles leads to turbulence generated by Buneman instability. In magnetic island topology, the different reconnection electric fields in squashed and coalescent islands impose different particle drift motions. This makes particle acceleration more efficient in squashed magnetic islands than in coalescent ones. The spectral indices of electron energy spectra are ∼ − 4.2 for coalescent and ∼ − 4.0 for squashed islands, which are lower than reported from the test-particle approach. The particles accelerated in magnetic islands are found trapped in the midplane of squashed islands, and shifted as clouds towards the X-nullpoints in coalescent ones.Conclusions.In reconnecting current sheets with multiple X- and O-nullpoints, particles are found accelerated on a much shorter spatial scale and gaining higher energies than near a single X-nullpoint. The distinct density and pitch-angle distributions of particles with high and low energy detected with the PIC approach can help to distinguish the observational features of accelerated particles.

Solar Radio Bursts Associated with Standing Shock Waves

A number of phenomena with radio bursts in the decimeter and centimeter wavelength ranges similar to type-II bursts in the meter range have been considered. In all phenomena, the radio bursts are characterized by the cessation of frequency drift and its reversal. Analysis of all of the available data on relevant bursts provides evidence of termination shocks with particle accelerations in their fronts. This is confirmed by the generation of new sources of hard X-ray radiation and the radio emission of fast bursts (spikes), fibers, and zebra structures. The sources of drift stripes with a drift turn are located either between the burst loop and the lower shock wave or between the lower and upper shock waves. Estimates of the critical Mach number for common parameters of the burst plasma indicated that the values (Mcr = 1.1–1.3) can easily be observed in the given phenomena and that the radiation can be associated with the Buneman instability. The conditions necessary for the generation of observed electromagnetic radiation bursts can be provided in helmet-shaped magnetic structures in the solar corona.

Instabilities and turbulence in low-β guide field reconnection exhausts with kinetic Riemann simulations

The role of turbulence in low-β, guide-field reconnection exhausts is explored in 2D reconnection and 2D and 3D Riemann simulations. The structure of the exhaust and associated turbulence is controlled by a pair of rotational discontinuities (RDs) at the exhaust boundary and a pair of slow shocks (SSs) that are generated by counterstreaming ions beams. In 2D, the exhaust develops large-amplitude striations at the ion Larmor radius scale that are produced by electron-beam-driven ion cyclotron waves. The electron beams driving the instability are injected into the exhaust from one of the RDs. However, in 3D Riemann simulations, the additional dimension (in the out-of-plane direction) results in strong Buneman and electron-electron streaming instabilities at the RD which suppress the electron beam formation and therefore the striations in the exhaust. The strength of the streaming instabilities at the RD is controlled by the ratio of the electron thermal speed to Alfvén speed, with the lower thermal speed being more unstable. In the 3D simulations, an ion-ion streaming instability acts to partially thermalize the counterstreaming ion beams at the SSs. This instability is controlled by the ratio of the sound speed to Alfvén speed and is expected to be stable in the low β solar corona. The results suggest that in a guide field reconnection exhaust with 1≫β>me/mi, the kinetic-scale turbulence that develops will be too weak to play a significant role in energy conversion and particle acceleration. Therefore, the energy conversion will be mostly controlled by laminar physics or multi-x-line reconnection.

Ion kinetics and nonlinear saturation of current-driven instabilities relevant to hollow cathode plasmas

Ion kinetics and time evolution of bulk plasma properties in the nonlinear saturation regime of a collisionless current-driven instability are studied using a 1D Vlasov–Poisson simulation. In the simulations, the ratio of initial electron bulk velocity to initial electron thermal velocity, called the electron Mach number, ranges from 0.5 to 2.5, and electron-to-ion temperature ratio is 10. A significant population of backstreaming high-energy ions is observed when the initial electron Mach number is larger than or equal to 1.3, which agrees with previous literature indicating transition to the Buneman instability. The simulations suggest that the electrons trapped in large-amplitude waves result in a bi-directional ion acoustic wave, which generates a backward-propagating high-energy ion distribution. A concise formula that describes the high-energy ion distribution and potential fluctuation amplitude are obtained as a function of initial electron Mach numbers. Sputtering rate calculations using the non-Maxwellian distributions for ions obtained from the simulation and Maxwellian ion distributions of temperatures ranging from 0.5 to 4.0 eV are compared, illustrating the potential contribution of kinetic effects on cathode erosion.

On the dispersion relation for the Buneman instability in spherically confined plasmas

In this paper an analytically derived dispersion relation for the Buneman instability in spherically confined plasmas is presented. The calculations are based on plasmas with spherical symmetry in which the dependence of the dispersion relation is, thus, only radial. This article is supposed to give a solution for said dispersion relation as this has not been done for such a peculiar geometry. On the other hand, new research on electrostatic confinement fusion schemes shows that there are physical effects that are strongly connected with such instabilities in spherical plasma devices and have, hence, to be taken into account in order to get a proper scientific understanding of the underlying mechanisms.

Dynamics of a slow electron hole coupled to an ion-acoustic soliton

This paper demonstrates stable embedding of an electron phase-space hole into an ion-acoustic soliton simulated using one-dimensional Particle-In-Cell simulation, forming a stable Coupled Hole-Soliton pair, which is a coupled state of a fluid soliton and a Bernstein-Green-Kruskal mode electron phase-space hole. Collision tests reveal that its collisional dynamics are a hybrid of soliton collision and electron hole merging. This hybrid state is separated from the classical free electron hole branch by a gap in their ion-frame velocities. Transition is possible from the coupled state to the free state by ion Landau damping and in the opposite direction by hole growth. Buneman instability simulation is performed, showing generation of both types of electron holes depending on the ion temperature. The results from our work can be readily applied to better understand the electrostatic solitary wave observations in space plasmas.

Electron shock-surfing acceleration in the presence of magnetic field

The effect of perpendicular (to the direction of shock propagation) magnetic fields on electron shock-surfing acceleration (ESSA) is investigated. Two-dimensional particle-in-cell simulations show that the strength of background magnetic fields can significantly affect the shock formation process and the electrostatic field structure near the leading edge of the shock. It is found that ESSA is most efficient when the ratio of electron cyclotron frequency to plasma frequency is about 0.1. In this case, there are two types of electrostatic field structures near the shock edge, namely, small-scale filamentary and large-scale dipole electric fields, induced by the Buneman instability and fluid compression, respectively. In such a mixed field structure, the affected electrons can undergo multiple accelerations and gain much higher energies than that under weaker or stronger background magnetic fields.

Impact of the electron to ion mass ratio on unstable systems in particle-in-cell simulations

The evolution of the Buneman and two-stream instabilities driven by a cold dilute mildly relativistic electron beam is studied as a function of the ion-to-electron mass ratio. The growth rates of both instabilities are comparable for the selected parameters if the realistic ion-to-electron mass ratio is used and the Buneman instability outgrows the two-stream instability for an artificially reduced mass ratio. Particle-in-cell simulations show that both instabilities grow independently during their linear growth phase. The much lower saturation amplitude of the Buneman instability implies that it saturates first even if the linear growth rates of both instabilities are equal. The electron phase space holes it drives coalesce. Their spatial size increases in time and they start interacting with the two-stream mode, which results in the growth of electrostatic waves over a broad range of wave numbers. A reduced ion-to-electron mass ratio results in increased ion heating and in an increased energy loss of the relativistic electron beam compared to that in a simulation with the correct mass ratio.

Harnessing the relativistic Buneman instability for laser-ion acceleration in the transparency regime

We examine the relativistic Buneman instability in systems relevant to high-intensity laser-plasma interactions under conditions of relativistically-induced transparency, as this instability can generate large-amplitude electrostatic waves at low frequencies that are pertinent to ion dynamics in these systems. Ion flows are shown to significantly alter the range of unstable wave numbers and to increase the phase velocities of the unstable modes; we particularly highlight the relativistic effects from both the ion and electron (with transverse motion) populations. These findings are related to the mode structure seen in particle-in-cell simulation results of a short-pulse laser breaking through an initially opaque target with the onset of relativistic transparency. Additionally, driving mechanisms from free energy present in density and velocity gradients are shown to be capable of significantly enhancing the growth rates, and these instabilities furthermore extend the breadth of the unstable wave number range. Lastly, we discuss how the transverse self-generated magnetic fields characteristic of short-pulse interactions can potentially constrain the unstable wave numbers in a non-trivial manner.

Effects of Ion Magnetization on the Farley–Buneman Instability in the Solar Chromosphere

Abstract Intense heating in the quiet-Sun chromosphere raises the temperature from 4000 to 6500 K but, despite decades of study, the underlying mechanism remains a mystery. This study continues to explore the possibility that the Farley–Buneman instability contributes to chromospheric heating. This instability occurs in weakly ionized collisional plasmas in which electrons are magnetized, but ions are not. A mixture of metal ions generate the plasma density in the coolest parts of the chromosphere; while some ions are weakly magnetized, others are demagnetized by neutral collisions. This paper incorporates the effects of multiple, arbitrarily magnetized species of ions to the theory of the Farley–Buneman instability and examines the ramifications on instability in the chromosphere. The inclusion of magnetized ions introduces new restrictions on the regions in which the instability can occur in the chromosphere—in fact, it confines the instability to the regions in which heating is observed. For a magnetic field of 30 G, the minimum ambient electric field capable of driving the instability is 13.5 V/m at the temperature minimum.

A detailed examination of laser-ion acceleration mechanisms in the relativistic transparency regime using tracers

We present a particle-in-cell study of linearly polarized laser-ion acceleration systems, in which we use both two-dimensional (2D) and three-dimensional (3D) simulations to characterize the ion acceleration mechanisms in targets which become transparent to the laser pulse during irradiation. First, we perform a target length scan to optimize the peak ion energies in both 2D and 3D, and the predictive capabilities of 2D simulations are discussed. Tracer analysis allows us to isolate the acceleration into stages of target normal sheath acceleration (TNSA), hole boring (HB), and break-out afterburner (BOA) acceleration, which vary in effectiveness based on the simulation parameters. The thinnest targets reveal that enhanced TNSA is responsible for accelerating the most energetic ions, whereas the thickest targets have ions undergoing successive phases of HB and TNSA (in 2D) or BOA and TNSA (in 3D); HB is not observed to be a dominant acceleration mechanism in the 3D simulations. It is in the intermediate optimal regime, both when the laser breaks through the target with appreciable amplitude and when there is enough plasma to form a sustained high density flow, that BOA is most effective and is responsible for the most energetic ions. Eliminating the transverse laser spot size effects by performing a plane wave simulation, we can isolate with greater confidence the underlying physics behind the ion dynamics we observe. Specifically, supplemented by wavelet and FFT analyses, we match the post-transparency BOA acceleration with a wave-particle resonance with a high-amplitude low-frequency electrostatic wave of increasing phase velocity, consistent with that predicted by the Buneman instability.

Particle-in-cell simulation of Buneman instability beyond quasilinear saturation

Spatio-temporal evolution of Buneman instability has been followed numerically till its quasilinear quenching and beyond, using an in-house developed electrostatic 1D particle-in-cell (PIC) simulation code. For different initial drift velocities and for a wide range of electron to ion mass ratios, the growth rate obtained from simulation agrees well with the numerical solution of the fourth order dispersion relation. Quasi-linear saturation of Buneman instability occurs when the ratio of electrostatic field energy density to initial electron drift kinetic energy density reaches up to a constant value, which, as predicted by Hirose [Plasma Phys. 20, 481 (1978)], is independent of initial electron drift velocity but varies with the electron to ion mass ratio (m/M) as ≈(m/M)1/3. This result stands verified in our simulations. The growth of the instability beyond the first saturation (quasilinear saturation) till its final saturation [Ishihara et al., PRL 44, 1404 (1980)] follows an algebraic scaling with time. In contrast to the quasilinear saturation, the ratio of final saturated electrostatic field energy density to initial kinetic energy density is relatively independent of the electron to ion mass ratio and is found from simulation to depend only on the initial drift velocity. Beyond the final saturation, electron phase space holes coupled to large amplitude ion solitary waves, a state known as coupled hole-soliton, have been identified in our simulations. The propagation characteristics (amplitude–speed relation) of these coherent modes, as measured from present simulation, are found to be consistent with the theory of Saeki et al. [PRL 80, 1224 (1998)]. Our studies thus represent the first extensive quantitative comparison between PIC simulation and the fluid/kinetic model of Buneman instability.

Numerical Simulation of Plasma Near the Cathode Spot of Vacuum Arc

Kinetic numerical simulation of plasma near the cathode spot (CS) was performed. Two types of possible solutions for the self-sustained CS on copper cathode were found. The firs type of solutions is valid for quasi-stationary spot with radius of about $100~\mu \text{m}$ . Stationary solution in this case is possible with cathode temperature 4.2–4.5 kK, current density $\sim 10^{6}$ A/cm2, and applied voltage 20–25 V. The second type of solution is obtained for the spot with radius of $1~\mu \text{m}$ and spherical geometry of plasma expansion. Possible solutions were obtained for the cathode temperature of above 6.2 kK, current density of about $10^{8}$ A/cm2 and applied voltage of 15–25 V. Transient simulations of the near-cathode plasma expansion have shown that if current density remains less than $10^{9}$ A/cm2 then the plasma expansion has a “quiet” self-similar character. At higher current density the plasma expansion has an essentially nonstationary character. The high-density current leads first to the development of Buneman instability and second to the plasma rupture with the creation of conditions for collective acceleration of ions toward the cathode and toward the anode. The accelerated ions create an additional powerful heat flux to the cathode, which should facilitate the reproduction of the CSs in the spark stage of vacuum discharge.

The asymptotic behavior of Buneman instability in dissipative plasma

The problem of time evolution of initial perturbation excited at the development of the Buneman instability (BI) in plasma with dissipation is solved. Developing fields are presented in the form of a wave train with slowly varying amplitude. It is shown that the evolution of the initial pulse in space and time is given by the differential equation of third order. The equation is solved and the expression for the asymptotic pulse shape is obtained. The expression gives the most complete information on the instability: the space-time distribution of the fields, growth rates, velocities of unstable perturbations, the influence of the collisions/dissipation on the instability, its character, (absolute/convective), etc. All these characteristics of the BI are carried out by analyzing the expression for the shape. The obtained results may be applied to any system in which the red-shifted electron stream oscillations resonantly interact with ions. Asymptotic shapes of the BI are presented for various levels of d...

Triggering of Buneman instability and existence of multiple double layers in laboratory plasma

We report experimentally observed triggering criteria for Buneman instability and boundary conditions for existence of multiple double layers (MADL) in glow discharge plasma. The MADLs are generated by accelerating plasma electrons towards a positively biased electrode submerged in it. The boundary conditions for the formation and existence of MADL are obtained from the experiment in terms of electron drift velocity (νd) and electron thermal velocity (νte). The MADL is found to exist within the range 3νte≥νd≥1.3νte. For the condition νd≥1.3νte, rise of an instability and simultaneous formation of MADL is observed in the experiment. The analysis of fluctuations in floating potential showed that the instability has all the characteristics of Buneman instability.

How anomalous resistivity accelerates magnetic reconnection

Whether turbulence induced anomalous resistivity (AR) can facilitate a fast magnetic reconnection in collisionless plasma is a subject of active debate for decades. Recent space observations suggest that the reconnection rate can be higher than the Hall-reconnection rate and turbulent dissipation is required. In this paper, using particle-in-cell simulations, we present a case study of how AR produced by Buneman instability accelerates magnetic reconnection. We first show that the AR/drag produced by Buneman instability in a thin electron current layer (1) can dissipate magnetic energy stored in the current layer through dissipation of the kinetic energy of electron beams; (2) the inhomogeneous drag caused by wave couplings spontaneously breaks the magnetic field lines and causes impulsive fast non-Hall magnetic reconnection on electron-scales with a mean rate reaching of 0.6 VA. We then show that a Buneman instability driven by intense electron beams around the x-point in a 3D magnetic reconnection significantly enhances the dissipation of the magnetic energy. Electron-scale magnetic reconnections driven by the inhomogeneous drag around the x-line enhance the reconnection electric field and the in-plane perpendicular magnetic field. About 40% of the released magnetic energy is converted into electron thermal energy by AR while 50% is converted into kinetic energy of the electron beams through the acceleration by the reconnection electric field. The enhanced magnetic energy dissipation is balanced by a net Poynting flux in-flow. About 10% of the released magnetic energy is brought out by an enhanced Poynting flux out-flow. These results suggest that AR with sufficient intensity and electron-scale inhomogeneity can significantly accelerate magnetic reconnection.

Lorentzian characteristics of the Buneman space-charge wave in a kappa plasma-filled waveguide

The nonthermal and harmonic-mode effects on the Buneman space charge wave are investigated in a kappa dusty plasma-filled waveguide by employing the normal mode analysis and the method of separation of variables. The growth rate and the real frequency of the Buneman space charge wave are obtained as functions of the harmonic roots of the Bessel function and the spectral index of the kappa plasma. It is shown that the growth rate of Buneman instability and the real frequency with higher-harmonic modes are smaller than those with lower-harmonic modes. It is also shown that the nonthermal effect suppresses the growth rate as well as the real frequency of the Buneman space-charge wave. The variations of the growth rate and the real frequency of the space charge wave are also discussed.

Energy exchange via multi-species streaming in laser-driven ion acceleration

Due to the complex electron dynamics and multiple ion acceleration mechanisms that can take place in the interaction of an ultra-intense laser pulse with a thin foil, it is possible for multiple charged particle populations to overlap in space with varying momentum distributions. In certain scenarios this can drive streaming instabilities such as the relativistic Buneman instability and the ion–ion acoustic instability. The potential for such instabilities to occur are demonstrated using particle-in-cell simulations. It is shown that if a population of ions can be accelerated such that it can propagate through other slowly expanding ion populations, energy exchange can occur via the ion–ion acoustic instability.

Influence of electron-ion collisions on Buneman instability in fully ionized plasma

The stability of a fully ionized plasma with a relative electron-ion (e-i) motion is considered taking into account the e-i collisions of high level. The relative e-i drift speed is assumed to be much higher than the thermal spread of electrons, and in the absence of collisions the system is subject to the low frequency and strongly growing Buneman instability. The transport equation with the Landau collision integral is solved taking into account the dependence of the collision frequency on the velocity of colliding particles. The effective frequency of e-i collisions is determined as a function of the system parameters. It is shown that with an increase in the level of e-i collisions the Buneman instability gradually transforms to the instability of dissipative type. This transition is traced in detail. The dependence of the growth rate on collision frequency upon this transformation is obtained.