Two-stream Instability Research Articles

Study of two stream instabilities in Lorentzian dusty plasma

Two-stream instabilities in an unmagnetized Lorentzian dusty plasma have been investigated using a kinetic theory approach. The occurrence of this instability is discussed in the case of three different plasma wave modes. The first one is the instability of the Langmuir wave driven by streaming suprathermal electrons. The second one is the instability of the dust ion-acoustic wave driven by streaming suprathermal electrons, ions, and dust grains. The last one is concerned with the instability of the dust acoustic wave driven by streaming suprathermal dust grains. Using the Lorentzian kappa velocity distribution function, the real and imaginary frequencies of these waves have been derived analytically. The effect of the suprathermal particle density and the streaming particle density on the real and imaginary frequencies of the waves is examined numerically.

A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

A model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V0 ∝ kh(k, 0) that eventually decays in time as 1/kV0t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude hrms(k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of khrms for the initial spectrum is used to calculate a nonlinear factor FNL that reduces V0, as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝tθ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

Взаємодія хвиль і частинок при інжекції модульованого електронного пучка в іоносферну плазму. Теорія та експеримент

We present the results of the active space experiment with charged particle beam's injection (electrons and xenon ions) carried out onboard Intercosmos-25 station and daughter Magion-3 subsatellite. The ones are obtained under conditions when the particle beams were injected in opposite directions relative to the magnetic field B0 in such a way that the electron injection was directed towards the Earth. Mechanisms of beam-plasma instabilities relative to the excitation of electrostatic and electromagnetic waves are considered during the electron beam injection (~10 keV, 0.1 A) from the Intercosmos-25 station. Development of transverse instability on the first cyclotron resonance leads to the excitation of whistler mode waves backward-propagating relative to the injected electrons (from the Earth). The investigation object was the beam-excited differential fluxes of ionospheric electrons in a wide energetic range of 27 eV — 412 keV registered by the charged particle spectrometers onboard the Magion-3 subsatellite. Thereby, the interaction of whistler waves with ionospheric electron fluxes is stimulated by the energy transfer mechanisms such as 'particle-wave-particle'. Numerical results of beam-plasma instabilities are compared also with thermal plasma parameters registered at different space points on the station and subsatellite. Excitation of longitudinal and transverse beam-plasma instabilities will inevitably lead to their competition, which will affect the results of the experiment. The data of stimulated fluxes of ionospheric electrons allow us to investigate the various effects of the wave-particle interaction, taking into account the influence of the growth rate of longitudinal instability on the excitation angle of whistlers and their structure. This approach is based on the results of laboratory experiments to determine the pattern of excited whistlers for an electric dipole antenna and the analogy of the beam-plasma channel with the radiating system. The results of the active space experiment confirm the dependence of the growth rate of whistler mode waves on the development of longitudinal beam instability.

Ion-acoustic waves in non-isothermal electron distribution using particle-in-cell method

We consider the ion-acoustic waves mode in plasma where electrons are consisted of free and trapped by ion-acoustic waves. The electron distribution for free and trapped electrons are the Maxwellian distribution function with the different temperatures. The system is considered as a one dimensional and simulates a collisionless, unmagnetized plasma. The Particle-In-Cell (PIC) method is applied to show the ion-acoustic oscillation as well as two-stream instability of this system.

The Effect of Ion-to-Electron Mass Ratio on the Electron Beam-Plasma Interaction

Two-dimensional electromagnetic particle-in-cell simulations are carried out to investigate the effect of ion-to-electron mass ratio on the evolution of warm electron beam-plasma instability. Four cases are considered: A: mi/me = 0 (two-electron stream instability); B: mi/me = 1 (pair plasma); C: mi/me = 100; and D: mi/me = 1000. It is shown that the generation of Langmuir waves in the fundamental mode of electron plasma frequency and the subsequent dynamics of large-amplitude solitons are not affected by the ion species. However, it determines the decay process of solitons and the excitation of electromagnetic waves in the second harmonic. In the first two cases, mi/me = 0 and 1, there is no sign of emission in the second harmonic, while the strongest emission in the second harmonic is found for the case of largest mass ratio, mi/me = 1000. This confirms the two-step wave-wave coupling mechanism for the generation of second harmonic electromagnetic waves, which requires the excitation of ion-acoustic waves in the first step. Moreover, the dispersion diagrams of all excited waves are presented.

Beam-plasma instability, the features of HXR spectra and polarization in solar flares

A one-dimensional quasi-linear beam relaxation leads to the formation of a plateau-like electron distribution function. Of greatest practical interest is the case when the initial velocity of the beam v0 greatly exceeds the thermal velocity of the plasma electrons VT, and the initial velocity spread in the beam ∼Δv0 is small compared with v0. These conditions are usually met for solar flares. The article deals with the features of the energy spectra and polarization of hard x-ray radiation (HXR) in the energy range of 20 -150 keV generated by electrons with a plateau-like electron distribution function. Calculations in the framework of a thick target take into account not only the energy losses of electrons interacting with plasma particles, but also changes in their angular distribution. It is shown that the break down energy of the electron spectrum leads to changes in HXR spectra, as well as the degree of linear polarization. There is a characteristic softening of the spectrum near the break-down energy. HXR polarization increases with quanta energy and can reach tens of percent.

Simulation of Charged Electron Plasma Heating by an Additional Electron Beam

The interaction of an additional electron beam with a previously created charged electron plasma of the squeezed state of two counter-propagating superlimiting electron beams in a closed equipotential cavity was studied numerically. The onset of plasma–beam instability in the absence of ions and quasi-linear relaxation is demonstrated. A significant broadening of the EDF towards higher electron energies was established. The considered process can be useful, for example, in electronic traps operating in the electronic string mode and used for generating highly charged ions with their subsequent injection into ion accelerators.

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.

Contributions to the linear and nonlinear theory of the beam–plasma interaction

We focus our attention on some relevant aspects of the beam–plasma instability in order to refine some features of the linear and nonlinear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the background plasma in the form of a linear dielectric, we study the non-perturbative properties of the linear dispersion relation, showing the necessity for a better characterization of the mode growth rate in those flat regions of the distribution function where the Landau formula is no longer predictive. We then upgrade the original $N$ -body approach in O'Neil et al. (Phys. Fluids, vol. 14, 1971, pp. 1204–1212), in order to include a return current in the background plasma. This correction term is responsible for smaller saturation levels and growth rates of the Langmuir modes, as result of the energy density transferred to the plasma via the return current. Finally, we include friction effects, as those due to the collective influence of all the plasma charges on the motion of the beam particles. The resulting force induces a progressive resonance detuning, because particles are losing energy and decreasing their velocity. This friction phenomenon gives rise to a deformation of the distribution function, associated with a significant growth of the less energetic particle population. The merit of this work is to show how a fine analysis of the beam–plasma instability outlines a number of subtleties about the linear, intermediate and late dynamics which can be of relevance when such a system is addressed as a paradigm to describe relevant nonlinear wave–particle phenomena (Chen & Zonca, Rev. Mod. Phys., vol. 88, 2016, 015008).

Expansion of alternatively extracted ion–ion beam in a low pressure collisional medium

The aim of this paper is to investigate, through particle-in-cell with Monte Carlo collisions (PIC-MCC) simulations, the effects of collisions on the expansion of an ion–ion beam formed by the alternate extraction of oppositely charged ions. This beam is extracted from an ion–ion plasma, formed in the downstream of a radiofrequency magnetically filtered iodine electronegative plasma, by the mean of two extraction grids. In this grid system, the screen grid is biased with a square voltage waveform, in the low MHz range, while the acceleration grid is grounded. The collisionless interaction between the extracted ion packets involves and enhances electrostatic waves propagating at beam velocity. Our results show that in addition to these electrostatic waves, the presence of significant fraction of low energy ions, produced by charge exchange, beside extracted fast ions gives rise to two-stream instability. Furthermore, space and time dependent electric field might accelerate the slow ions, produced by charge exchange collision. This acceleration, involving Landau damping and its inverse mechanism, is mainly due to the interaction between ions and potential patterns inherent to two-stream instability.

Effect of plasma density gradients on generation of terahertz radiation in magnetized plasma column during relaxation of kiloampere REB inside it

Generation of terahertz radiation in the magnetized plasma column due to the two-stream instability developing in the relativistic electron beam (REB) with a current of 10 kA is studied at the GOL-PET facility. In the first series of the experiments, at the regular transverse plasma density gradients, power of the generated terahertz radiation increased thirty times. At a frequency of the upper-hybrid oscillations (0.2–0.3 THz) and pulse duration of few microseconds, it reached 4 MWs. In the next experiments, when the additional longitudinal density gradients were created in plasma, the radiation power exceeded 10 MWs. These results are described in this paper.

Growth of the modified two-stream instability in the plume of a magnetically shielded Hall thruster

The electrostatic dispersion relation for an unbounded homogeneous plasma in the presence of unmagnetized ions, magnetized electrons, and an applied magnetic field has been solved numerically in the near-plume of a magnetically shielded Hall thruster. The plasma conditions have been obtained by 2D (r-z) multifluid-particle-in-cell simulations. We find growth of the modified two-stream instability in most regions of the domain, with the fastest growth approaching the fluid-limit ωLH/2, radially away from the channel centerline downstream of the front magnetic poles where ωpe/ωce ∼ 1. In this region, the relative drift between magnetized electrons and beam ions perpendicular to the magnetic field is u ≳ 3 uTi, while that between the counterstreaming beam and cathode ions is ≳4 uTi. The latter suggests that the ion–ion cross field lower hybrid instability may also be active here. The presence of these instabilities can lead to anomalous heating of ions enhancing the average energy with which they impact nearby surfaces.

Collective Thomson scattering in non-equilibrium laser produced two-stream plasmas

We investigate collective Thomson scattering (CTS) in two-stream non-equilibrium plasmas analytically, numerically, and experimentally. In laboratory astrophysics, CTS is a unique tool to obtain local plasma diagnostics. While the standard CTS theory assumes plasmas to be linear, stationary, isotropic, and equilibrium, they are often nonlinear, non-stationary, anisotropic, and non-equilibrium in high energy phenomena relevant to laboratory astrophysics. We theoretically calculate and numerically simulate the CTS spectra in two-stream plasmas as a typical example of a non-equilibrium system in space and astrophysical plasmas. The simulation results show the feasibility to diagnose two-stream instability directly via CTS measurements. To confirm the non-equilibrium CTS analysis, we have developed an experimental system with a high repetition rate tabletop laser for laboratory astrophysics.

Pair Separation in Parallel Electric Field in Magnetar Magnetosphere and Narrow Spectra of Fast Radio Bursts

Abstract When the magnetosphere of a magnetar is perturbed by crustal deformation, an electric field E ∥ parallel to the magnetic field line would appear via Alfvén waves in the charge starvation region. The electron–positron pair bunches will be generated via two-stream instability in the magnetosphere, and these pairs will undergo charge separation in the E ∥ and in the meantime emit coherent curvature radiation. Following the approach of Yang & Zhang, we find that the superposed curvature radiation becomes narrower due to charge separation, with the width of spectrum depending on the separation between the electron and positron clumps. This mechanism can interpret the narrow spectra of fast radio bursts (FRBs), in particular, the spectrum of Galactic FRB 200428 recently detected in association with a hard X-ray burst from the Galactic magnetar SGR J1935+2154.

Pulsar radio emission mechanism − I. On the amplification of Langmuir waves in the linear regime

ABSTRACT Observations suggest that in normal period radio pulsars, coherent curvature radiation is excited within 10${{\ \rm per\ cent}}$ of the light cylinder. The coherence is attributed to Langmuir mode instability in a relativistically streaming one-dimensional plasma flow along the open magnetic field lines. In this work, we use a hot plasma treatment to solve the hydrodynamic dispersion relation of Langmuir mode for realistic pulsar parameters. The solution involves three scenarios of two-stream instability, viz. driven by high energy beams, due to longitudinal drift that leads to a separation of electron–positron distribution functions in the secondary plasma and due to cloud–cloud interaction causing spatial overlap of two successive secondary plasma clouds. We find that sufficient amplification can be obtained only for the latter two scenarios. Our analysis shows that longitudinal drift is characterized by high growth rates only for certain multipolar surface field geometry. For these configurations, very high growth rates are obtained starting from a few tens of km from the neutron star surface, which then falls monotonically with increasing distance. For cloud–cloud overlap, growth rates become high starting only after a few hundred km from the surface, which first increases and then decreases with increasing distance. A spatial window of up to around a 1000 km above the neutron star surface has been found where large amplitude Langmuir waves can be excited while the pair plasma is dense enough to account for high brightness temperature.

Cross-field electron diffusion due to the coupling of drift-driven microinstabilities.

In this paper, the nonlinear interaction between kinetic instabilities driven by multiple ion beams and magnetized electrons is investigated. Electron diffusion across magnetic field lines is enhanced by the coupling of plasma instabilities. A two-dimensional collisionless particle-in-cell simulation is performed accounting for singly and doubly charged ions in a cross-field configuration. Consistent with prior linear kinetic theory analysis and observations from coherent Thomson scattering experiments, the present simulations identify an ion-ion two-stream instability due to multiply charged ions (flowing in the direction parallel to the applied electric field) which coexists with the electron cyclotron drift instability (propagating perpendicular to the applied electric field and parallel to the E×B drift). Small-scale fluctuations due to the coupling of these naturally driven kinetic modes are found to be a mechanism that can enhance cross-field electron transport and contribute to the broadening of the ion velocity distribution functions.

Resonance overlap and nonlinear features of the beam–plasma system

The beam–plasma instability can be addressed as a reduced model in several contexts of plasma physics, from space to fusion plasma. In this paper, we review and refine some nonlinear features of this model. Specifically, by analysing the dependence of the nonlinear velocity spread as a function of the linear growth rate, we discuss the effective size of the resonance in view of its role in the spectral overlap at saturation. The relevance of this characterization relies on the necessity of a quantitative determination of the overlap degree to discriminate among different transport regimes of the self-consistent dynamics. The analysis is enriched with a study of the phase-space dynamics by means of the Lagrangian coherent structure technique, in order to define the transport barriers of the system describing the relevant features of the overlap process. Finally, we discuss relevant features related to the mode saturation levels.

A relativistic particle pusher for ultra-strong electromagnetic fields

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above$\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to$10^{15}$or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

Model of a Plasma Layer Formed by an Electron Beam

Results are presented of the particle-in-cell numerical simulations by the KARAT code of the formation of a plasma–beam discharge in the absence of both the longitudinal magnetic field and the initial plasma. Oscillations of the electric field generated by the plasma–beam instability in the electron beam region almost do not affect the plasma at the periphery of the system. Simulation results are compared to the results obtained earlier by a simplified model and to the results of test experiments. The spatial distributions of the plasma density and electron temperature qualitatively agree with the experimental results.

Towards experimental investigation of hosing instability mitigation at the PITZ facility

Beam-driven plasma wakefield acceleration (PWFA) allows for high gradient acceleration of electron beams and hence is a promising candidate for compact and cost-efficient drivers of applications demanding high brightness beams. One of the main challenges in these accelerators is to control beam-plasma instabilities with rapid growth rates which are induced by the strong transverse components of the wakefields. The hosing instability, a growing transverse oscillation of the beam centroid caused by coherent coupling between bunch slice centroids and transverse wakefields, was predicted to set severe limits on the possible acceleration distance in PWFAs. Several methods have been proposed to damp or even suppress the hosing of the beam, prevent beam-breakup and thus allow stable operation. Here, we present preparations and simulation studies aiming at the experimental investigation of hosing suppression mechanisms at the PITZ facility.