Two-stream Instability Research Articles

Suppression and excitation by collisions of two-stream and bump-on-tail instabilities

Two-stream (TS) and bump-on-tail (BOT) electron distributions in plasma can lead to electrostatic instabilities and turbulence, and they have been extensively studied. Collisions usually mitigate these instabilities since they tend to hinder the motion of the participating electrons. Here, we numerically solve the full Vlasov–Poisson equations with Krook collisions to reconsider the evolution of the TS and BOT instabilities. It is found that even in the stable parameter regime predicted by linear theory, during the initial evolution (i.e., damping) stage, collisions can excite the TS instability. The reason is that during the evolution, efficient Krook collisions cause rapid thermalization of the TS electrons, leading to broadening of the initial velocity distributions of the two beams and appearance of regimes with unstable velocity gradients and trapped electrons. On the contrary, such a behavior does not occur for the BOT instability.

Beam–plasma dynamics in finite-length, collisionless inhomogeneous systems

This study investigates the streaming instability triggered by ion motion in a plasma system that is finite in length, collisionless, and inhomogeneous. Employing numerical simulations using particle-in-cell techniques and kinetic equations, the study examines how inhomogeneity emerges from integrating a cold ion beam with a background plasma within a confined system. The findings suggest that steady ion flow can modify ion sound waves through acoustic reflections from system boundaries, leading to instability. Such phenomena are known to be a hydrodynamic effect. However, there are also signatures of the beam-driven ion sound instability where kinetic resonances play a pivotal role. The main objective is to understand the impact of a finite-length system on beam–plasma instability and to identify the wave modes supported in such configurations.

Observation of an Extraordinary Type V Solar Radio Burst: Nonlinear Evolution of the Electron Two-Stream Instability

Solar type V radio bursts are associated with type III bursts. Several processes have been proposed to interpret the association, electron distribution, and emission. We present the observation of a unique type V event observed by e-CALLISTO on 7 May 2021. The type V radio emission follows a group of U bursts. Unlike the unpolarized U bursts, the type V burst is circularly polarized, leaving room for a different emission process. Its starting edge drifts to higher frequency four times slower than the descending branch of the associated U burst. The type V processes seem to be ruled by electrons of lower energy. The observations conform to a coherent scenario where a dense electron beam drives the two-stream instability (causing type III emission) and, in the nonlinear stage, becomes unstable to another instability, previously known as the electron firehose instability (EFI). The secondary instability scatters some beam electrons into velocities perpendicular to the magnetic field and produces, after particle loss, a trapped distribution prone to electron cyclotron masering (ECM). A reduction in beaming and the formation of an isotropic halo are predicted for electron beams continuing to interplanetary space, possibly observable by Parker Solar Probe and Solar Orbiter.

Quasi-monoenergetic ion acceleration and neutron generation from laser-driven transverse collisionless shocks

Experiments using the OMEGA EP laser system were performed to study collisionless shock acceleration of ions driven by the interaction of a relativistically intense laser pulse with underdense plasma. The energy spectrum of accelerated ions in the direction transverse to laser propagation is measured to have several narrow-band peaks which are quasi-monoenergetic with a typical energy bandwidth of 3%. In deuterium plasmas, these ions generate a significant number of fast fusion neutrons. Particle-in-cell simulations confirm that these ions were accelerated by the interaction of transverse shocks and that the appearance of quasi-monoenergetic spectral features depends on the growth of an ion-electron two-stream instability during the interaction.

Wakefield-driven filamentation of warm beams in plasma.

Charged and quasineutral beams propagating through an unmagnetized plasma are subject to numerous collisionless instabilities on the small scale of the plasma skin depth. The electrostatic two-stream instability, driven by longitudinal and transverse wakefields, dominates for dilute beams. This leads to modulation of the beam along the propagation direction and, for wide beams, transverse filamentation. A three-dimensional spatiotemporal two-stream theory for warm beams with a finite extent is developed. Unlike the cold beam limit, diffusion due to a finite emittance gives rise to a dominant wave number and a cutoff wave number above which filamentation is suppressed. Particle-in-cell simulations with quasineutral electron-positron beams in the relativistic regime give excellent agreement with the theoretical model. This paper provides deeper insights into the effect of diffusion on filamentation of finite beams, crucial for comprehending plasma-based accelerators in laboratory and cosmic settings.

Negative damping of terahertz plasmons in counter-streaming double-layer two-dimensional electron gases

Abstract The plasmon excitation in two-dimensional electron gases (2DEGs) is a significant way of achieving micro-nanoscale terahertz (THz) devices. Here, we establish a kinetic simulation model to study the THz plasmons amplification in a semiconductor double-quantum-well system with counter-streaming electron drift velocities. By comparing the simulation results with theoretical dispersion relations, we confirm two competing mechanisms of negative damping suitable for THz amplification: Cherenkov-type two-stream instability and a new non-Cherenkov mechanism called kinetic relaxation instability. The former is caused by the interlayer coupling of two slow plasmon modes and only exists when the drift velocities are much greater than the fermi velocities. The latter is a statistical effect caused by the momentum relaxation of electron-impurity scattering and predominates at lower drift velocities. We show that an approximate kinetic dispersion relation can accurately predict the wave growth rates of the two mechanisms. The results also indicate that the saturated plasmonic waves undergo strong nonlinearities such as wave distortion, frequency downshift, wave-packet formation, and spectrum broadening. The nonlinear evolution can be interpreted as the merging of bubble structures in the electron phase-space distribution. The present results not only reveal the potential mechanisms of the plasmonic instabilities in double-layer 2DEGs, but also provide a new guideline for the design of on-chip THz amplifiers.

Plasmon scattering at a junction in double-layer two-dimensional electron gas plasmonic waveguide

Abstract The scattering of plasmons at a junction within a double-layer two-dimensional electron gas plasmonic waveguide is studied via a full electromagnetic method. The dispersion relation is derived by utilizing the transfer matrix method and can be extended to the situation of an arbitrary number of layers. By numerically solving the dispersion equations, both the acoustic and optical plasmon modes are identified in this double layer system, and the unstable plasmon modes arising from plasmon coupling in different layers are discussed elaborately. Subsequently, the total fields are expanded with eigenmodes and matched at the interface to analyze the scattering characteristics at the junction. The results indicate that the total power of the plasmon mode is amplified when the electron fluid flows from a high concentration region to a low concentration region, and the amplification is more evident at a higher drift velocity. Additionally, we address the scattering of unstable plasmons caused by the two-stream instability and find that the transmitted plasmons are excited intensively at the incidence of the growing plasmon, leading to the plasmon amplification. The detailed examination of plasmon scattering at junction is the prerequisite for studying more complex structures of terahertz plasmonic devices and comprehending the corresponding amplification mechanism.

Visualizing plasmons and ultrafast kinetic instabilities in laser-driven solids using X-ray scattering

Ultra-intense lasers that ionize atoms and accelerate electrons in solids to near the speed of light can lead to kinetic instabilities that alter the laser absorption and subsequent electron transport, isochoric heating, and ion acceleration. These instabilities can be difficult to characterize, but X-ray scattering at keV photon energies allows for their visualization with femtosecond temporal resolution on the few nanometer mesoscale. Here, we perform such experiment on laser-driven flat silicon membranes that shows the development of structure with a dominant scale of 60 nm in the plane of the laser axis and laser polarization, and 95 nm in the vertical direction with a growth rate faster than 0.1 fs−1. Combining the XFEL experiments with simulations provides a complete picture of the structural evolution of ultra-fast laser-induced plasma density development, indicating the excitation of plasmons and a filamentation instability. Particle-in-cell simulations confirm that these signals are due to an oblique two-stream filamentation instability. These findings provide new insight into ultra-fast instability and heating processes in solids under extreme conditions at the nanometer level with possible implications for laser particle acceleration, inertial confinement fusion, and laboratory astrophysics.

Numerical investigations of spatiotemporal dynamics of space-charge limited collisional sheaths

Electrostatic particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) methods are used to compare the plasma dynamics of collisionless with collisional emissive sheaths in partially ionized environments. Space-charge limited emissive sheaths submersed in a plasma with a density of ∼1017 m−3 are examined using a PIC-DSMC solver, CHAOS. Collisionless emissive sheaths with plasma domains sufficiently long (30 and 60 Debye lengths, λD) are subject to strong oscillations due to two-stream electron instability, whereas emissive sheaths in weakly collisional conditions with a short domain (15 λD) exhibit self-spike (sawtooth) oscillations in the plasma field due to the trapped charge-exchange (CEX) ion population within the virtual cathode (VC) region. The two-stream electron instability leads to strong temporal fluctuations in the total emission current, with maximum deviations of 60% and 100% from the time-averaged current for the long plasma domains, whereas CEX collisions cause strong spikes in the emission current if the domain size is short. Our PIC-DSMC simulations show for the first time that the interaction of the two types of instabilities causes the strength of the self-spike to be weakened due to the strong fluctuations caused by the two-stream instability when a sufficiently long computational domain with ion-neutral collisions is employed. By conducting a two-dimensional Fast Fourier Transform (FFT) on the collisional and collisionless sheaths with long domains, we show that the transient evolution of CEX entrapment in the VC increases frequency of sheath oscillations up to two times the ion-acoustic frequencies observed in the collisionless sheath. CEX collisions weaken the VC region and result in a total emission current more than that obtained from the collisionless case for the same domain length. With a more rarefied neutral environment of 1019 m−3 in the plasma sheath, the total emission current increases only 4% in comparison with 14% for one order of magnitude denser environment, within 20 μs. In addition, the spike period is tested with different neutral temperatures and densities. While we do not observe any self-spike in the more rarefied environment, the spike period increased from 5 to 7.5 μs when the neutral temperature is increased from 300 to 2000 K in the denser environment with the simulation time of 20 μs.

Enhanced energy deposition of laser-produced proton beams in high-density plasmas due to beam density self-steepening

The energy deposition of laser-accelerated proton beams in solid-density plasmas with different ion charge numbers is studied with detailed one-dimensional particle-in-cell simulations. In the plasma with a high ion charge number, in which the plasma collision frequency approaches electron oscillation frequency, the beam protons are strongly decelerated by the electric field induced by the plasma return current. The energy deposition is further enhanced as the beam travel distance increases due to beam density self-steeping, which is also confirmed by multi-dimensional particle-in-cell simulation. A simple analytical model is proposed to estimate the characteristic travel distance for significant density self-steeping, showing agreement with the simulation results. While in the plasma with a low ion charge number, in which the plasma collision frequency is much smaller than the electron oscillation frequency, the proton beam is modulated significantly by the excited two-stream instability.

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

A Theoretical Analysis for the Two-Stream Instability in Dual-Sheet Electron Beam System

A Theoretical Analysis for the Two-Stream Instability in Dual-Sheet Electron Beam System

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

Return Currents in Collisionless Shocks

Collisionless shocks tend to send charged particles into the upstream, driving electric currents through the plasma. Using kinetic particle-in-cell simulations, we investigate how the background thermal plasma neutralizes such currents in the upstream of quasi-parallel non-relativistic electron–proton shocks. We observe distinct processes in different regions: the far upstream, the shock precursor, and the shock foot. In the far upstream, the current is carried by nonthermal protons, which drive electrostatic modes and produce suprathermal electrons that move toward upstream infinity. Closer to the shock (in the precursor), both the current density and the momentum flux of the beam increase, which leads to electromagnetic streaming instabilities that contribute to the thermalization of suprathermal electrons. At the shock foot, these electrons are exposed to shock-reflected protons, resulting in a two-stream type instability. We analyze these processes and the resulting heating through particle tracking and controlled simulations. In particular, we show that the instability at the shock foot can make the effective thermal speed of electrons comparable to the drift speed of the reflected protons. These findings are important for understanding both the magnetic field amplification and the processes that may lead to the injection of suprathermal electrons into diffusive shock acceleration.

Two-stream instability of relativistic electron beam in magnetized plasma waveguide: nonlinear logarithmic electrodynamics model

Two-stream instability of relativistic electron beam in magnetized plasma waveguide: nonlinear logarithmic electrodynamics model

Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas.

Electromagnetic turbulence and ion kinetics in counterstreaming plasmas hold great significance in laboratory astrophysics, such as turbulence field amplification and particle energization. Here, we quantitatively demonstrate for the first time how electromagnetic turbulence affects ion kinetics under achievable laboratory conditions (millimeter-scale interpenetrating plasmas with initial velocity of 2000 km/s, density of 4×10^{19} cm^{-3}, and temperature of 100eV) utilizing a recently developed high-order implicit particle-in-cell code without scaling transformation. It is found that the electromagnetic turbulence is driven by ion two-stream and filamentation instabilities. For the magnetized scenarios where an applied magnetic field of tens of Tesla is perpendicular to plasma flows, the growth rates of instabilities increase with the strengthening of applied magnetic field, which therefore leads to a significant enhancement of turbulence fields. Under the competition between the stochastic acceleration due to electromagnetic turbulence and collisional thermalization, ion distribution function shows a distinct super-Gaussian shape, and the ion kinetics are manifested in neutron yields and spectra. Our results have well explained the recent unmagnetized experimental observations, and the findings of magnetized scenario can be verified by current astrophysical experiments.

An Exactly Energy-conserving Electromagnetic Particle-in-cell Method in Curvilinear Coordinates

In this paper, we introduce and discuss an exactly energy-conserving particle-in-cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains by aligning the grid to the given geometry or by focusing grid resolution on regions of interest without overresolving the surrounding, potentially uninteresting domain. We have achieved this through the introduction of the metric tensor, the Jacobian matrix, and contravariant operators combined with an energy-conserving fully implicit solver. We demonstrate the method’s capabilities using a Python implementation to study several one- and two-dimensional test cases: the electrostatic two-stream instability, the electromagnetic Weibel instability, and the geomagnetic environment modeling reconnection challenge. The test results confirm the capability of our new method to reproduce theoretical expectations (e.g., instability growth rates) and the corresponding results obtained with a Cartesian uniform grid when using curvilinear grids. Simultaneously, we show that the method conserves energy to machine precision in all cases.

Evolution of the electron phase space of the two-stream and bump-on-tail instabilities in collisional plasma

Particle collisions can have significant effects on plasma instabilities, especially in dense and/or low temperature plasmas. To understand the influence of collisional effects on the plasma waves, the Vlasov–Poisson system with Krook collisions is applied to study the long-term evolution of the two-stream (TS) and bump-on-tail (BOT) instabilities. The system is solved numerically with the fourth-order Runge–Kutta scheme and the Thomas algorithm. It is found that collisions can enhance the wave damping and mitigate the energy of the characteristic slow evolving nonlinear Landau damping oscillations associated with the wave-trapped electrons, especially if the collision rate ν is higher than 0.01ωp, where ωp is the plasma frequency of the background plasma. Collisions can also decrease the growth rate and saturation level of the TS and BOT unstable waves and tend to shrink the phase space vortex and narrow the phase-mixed region of the trapped electrons. However, our simulations show that collisions cannot readily prevent the nonlinear Landau damping oscillations. In fact, only with ν>0.001ωp for the TS instability and ν>0.01ωp for the BOT instability, as well as evolution times greater than several hundred ωp−1, the vortex structure of the wave-trapped electrons can be undetectable. The corresponding growth rates also drop dramatically, and the maximum wave energy can be one or two orders lower than that of the collisionless limits.

Pair filamentation and laser scattering in beam-driven QED cascades.

We report the observation of longitudinal filamentation of an electron-positron pair plasma in a beam-driven QED cascade. The filaments are created in the "pair-reflection" regime, where the generated pairs are partially stopped and reflected in the strong laser field. The density filaments form near the center of the laser pulse and have diameters similar to the laser wavelength. They develop and saturate within a few laser cycles and do not induce sizable magnetostatic fields. We rule out the onset of two-stream instability or Weibel instability and attribute the origin of pair filamentation to laser ponderomotive forces. The small plasma filaments induce strong scattering of laser energy to large angles, serving as a signature of collective QED plasma dynamics.

Electromagnetic emission from plasma with counter-streaming electron beams in the regime of oblique instability dominance

In this study, we investigate the generation of electromagnetic emission near the second harmonic of the plasma frequency induced by pairs of counter-propagating electron beams. Such systems can naturally occur in cosmic plasmas when particle acceleration regions are closely spaced, and they can also be implemented in a laboratory device. We specifically focus on the regime where the oblique beam–plasma instability dominates. The emission mechanism relies on the coalescence of counter-propagating plasma waves with different transverse structures. It has been demonstrated that the parameters of the system necessary for efficient radiation generation can be determined using the exact linear theory of beam–plasma instability. Through particle-in-cell numerical simulations, we show that a high beam-to-radiation conversion efficiency can be achieved when the beams excite small-scale oblique plasma oscillations. Importantly, we find that the efficiency and spectral characteristics of the radiation are not dependent on the thickness of the beams. We explore two scenarios involving pairs of symmetric beams: one with relativistic beams having a directed velocity of vb=0.9c and another with sub-relativistic beams at vb=0.7c. Additionally, we consider the injection of two beams with different velocities. In all cases considered, the beam-to-radiation power conversion efficiency reaches a level of a few percent, a sufficiently high value for beam–plasma systems.