Two-stream Instability Research Articles

Inductively-coupled plasma discharge for use in high-energy-density science experiments

Inductively-coupled plasma discharges are well-suited as plasma sources for experiments in fundamental high-energy density science, which require large volume and stable plasmas. For example, experiments studying particle beam-plasma instabilities and the emergence of coherent macroscopic structures — which are key for modelling emission from collisionless shocks present in many astrophysical phenomena. A meter-length, table-top, inductive radio-frequency discharge has been constructed for use in a high-energy density science experiment at CERN which will study plasma instabilities of a relativistic electron-positron beam. In this case, a large volume is necessary for the beam to remain inside the plasma as it diverges to centimeter-scale diameters during the tens-of-centimeters of propagation needed for instabilities to develop. Langmuir probe measurements of the plasma parameters show that plasma can be stably sustained in the discharge with electron densities exceeding 1011 cm-3. The discharge has been assembled using commercially-available components, making it an accessible option for commissioning at a University laboratory.

Analytical Solution for Space-Charge Waves in a Two-Stream Cylindrical Electron Beam

We present an analytical method to compute the wavenumbers and electric fields of the space-charge-wave eigenmodes supported by a two-stream electron beam, consisting of a solid inner cylindrical stream and a coaxial outer annular stream, both contained within a cylindrical metallic tunnel.We extend the analytical model developed by Ramo to the case of two streams. The method accounts for the interaction between the two streams with the presence of the beam-tunnel wall; it can be used to model the complex wavenumbers associated with the two-stream instability and the plasma frequency reduction effects in vacuum electronic amplifiers and other vacuum electronic devices.

A δf PIC method with forward–backward Lagrangian reconstructions

In this work, we describe a δf particle simulation method where the bulk density is periodically remapped on a coarse spline grid using a forward–backward Lagrangian approach. This method is designed to handle plasma regimes where the densities strongly deviate from their initial state and may evolve into general profiles. We describe the method in the case of an electrostatic particle-in-cell scheme and validate its qualitative properties using a classical two-stream instability subject to a uniform oscillating drive.

Particle-in-cell method for plasmas in the one-dimensional electrostatic limit

We discuss the particle-in-cell (PIC) method, which is one of the most widely used approaches for the kinetic description of plasmas. The positions and velocities of the charged particles take continuous values in phase space, and spatial macroscopic quantities, such as the charge density and self-generated electric fields, are calculated at discrete spatial points of a grid. We discuss the computer implementation of the PIC method for one-dimensional plasmas in the electrostatic regime and discuss a desktop application (PlasmAPP), which includes the implementation of different numerical and interpolation methods and diagnostics in a graphical user interface. To illustrate its functionality, the electron-electron two-stream instability is discussed. Readers can use PlasmAPP to explore advanced numerical methods and simulate different phenomena of interest.

Collision rates estimated from exact N-body simulations of a one-dimensional plasma

In a plasma, the charged particles interact via long-range forces, and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible, while collective effects dominate the dynamics. In contrast, when g≈1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the two-stream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations.

Kinetic modeling of solitary wave dynamics in a neutralizing ion beam

In this work, we characterize the formation and evolution of electrostatic solitary waves (ESWs) in the space-charge neutralization of ion beams using particle-in-cell simulations. These waves become excited when the electrons emitted from an external filament source initiate a two-stream instability in the beam. We show that such electrostatic waves become excited in both two-dimensional (2D) and three-dimensional (3D) beams with different shapes and sizes. Through a 1D Bernstein–Greene–Kruskal (BGK) analysis of the 2D beam, we find that the non-Maxwellian nature of the beam electrons gives rise to large-sized ESWs that are not predicted by BGK theory since it assumes a Maxwellian electron velocity distribution in the beam. Finally, we show that a 1D BGK theory is inadequate to describe ESWs in 3D beams because of complex electron trajectories.

Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system

This paper concerns an energy-conserving numerical method to solve the multi-dimensional Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [7]. The globally hyperbolic moment system is deduced for the VM system under the framework of Hermite expansions, where the expansion center and the scaling factor are set as the macroscopic velocity and the local temperature, respectively. Thus, the effect of the Lorentz force term can be reduced into several ODEs regarding the macroscopic velocity and the higher-order moment coefficients, which can significantly reduce the computational cost of the whole system. An energy-conserving numerical scheme is proposed to solve the moment equations and Maxwell's equations, where only a small linear system needs to be solved implicitly. Benchmark examples such as Landau damping, two-stream instability, Weibel instability, and two-dimensional Orszag-Tang vortex problem are studied to validate the efficiency and excellent energy-preserving property of the numerical scheme.

Two-stream instability generation in the lunar ionosphere

The Two-stream Instability (TSI) generation is studied analytically in the lunar ionosphere. The TSI is a tiny perturbation in the electron plasma density, due to which an electric field grows with time and this growth is facilitated by the electron plasma in the background. In lunar ionosphere, the TSI comes into existence when the solar wind interacts unhindered with the tenuous lunar electron plasma in the surface bound exosphere. In this study, the conditions which allow the TSI to form and the subsequent instability growth with time i.e. the growth factor, is estimated. Initially, the threshold condition for the TSI to take place is determined. Thereafter, the solar wind and lunar plasma parameter contribution to trigger TSI is investigated along with the effect of these parameters in the evolution of TSI. The plasma TSI evolution with the passage of time is also depicted in phase space diagram with Particle-In-Cell simulations.

Two-stream plasma instability as a potential mechanism for particle escape from the Venusian ionosphere

In this work we investigate the possibility of two-stream instability in the Venusian atmosphere to lead to momentum transfer to subsequent escape of Hydrogen and Oxygen ions from the ionosphere. We employ the hydrodynamic model and obtain the linear dispersion relation from which the two-stream instability is studied. Further the interaction of solar wind with the ions of Venus ionosphere from which the instability sets in, has been studied with the data from ASPERA-4 of Venus Express (VEX). The data supports the fact that the two-stream instability can provide sufficient energy to accelerate ions to escape velocity of the planet.

Effects of the Wavelength of the Plasma Waves on Cross-Field Electron Transport in Partially Magnetized Plasmas

In this article, the effects of increasing plasma density on the cross-field electron transport driven by kinetic instabilities are investigated. A 2-D collisionless particle-in-cell (PIC) simulation is performed on cases with only singly charged ions and with a mixture of singly and doubly charged ions, at different levels of plasma density. It is observed using the PIC simulations that the level of plasma density affects the plasma waves that are driven by the microinstabilities, including the electron cyclotron drift instability (ECDI) and ion–ion two-stream instability (IITSI). The simulation results suggest that the enhancement of cross-field electron transport is correlated with the excitation of smaller wavelength modes and the increased amplitude of the plasma waves.

Dissipative instabilities in beam-plasma systems

It is known that all types of beam-plasma instabilities (Cherenkov, cyclotron, etc.) at a high level of dissipation turn into dissipative instability (DI). Until recently, only one type of DI was known in the beam-plasma interaction theory. Its maximal growth rate depends on the beam density n b and the collision frequency ν in the plasma as . However, recent studies have shown the existence of two new, previously unknown types of DI. Here, the new DI are briefly justified from the same viewpoint. This became possible due to the developed approach, which makes it possible to solve completely the classical problem of the development of an initial perturbation for various flow instabilities. The first new DI arises in the results of solving of the problem in systems with weak beam-plasma coupling. Its maximal growth rate is inversely proportional to frequency of collisions in plasma . The second new DI manifests itself in the results of the same problem in a magnetized plasma waveguide with an over-limiting e-beam. Its maximal growth rate is . Besides, the presented method of solving the classical problem deserves attention in itself as it is applicable to all instabilities caused by relative motion of plasma components (all types of beam-plasma instabilities, Buneman instability, etc.).

Comparing the Counter-beaming and Temperature Anisotropy Driven Aperiodic Electron Firehose Instabilities in Collisionless Plasma Environments

The electron firehose instabilities are among the most studied kinetic instabilities, especially in the context of space plasmas, whose dynamics is mainly controlled by collisionless wave–particle interactions. This paper undertakes a comparative analysis of the aperiodic electron firehose instabilities excited either by the anisotropic temperature or by the electron counter-beaming populations. Two symmetric counter-beams provide an effective kinetic anisotropy similar to the temperature anisotropy of a single (nondrifting) population, with the temperature along the magnetic field direction larger than that in the perpendicular direction. Therefore, the counter-beaming plasma is susceptible to firehose-like instabilities (FIs), parallel and oblique branches. Here we focus on the oblique beaming FI, which is also aperiodic when the free energy is provided by symmetric counter-beams. Our results show that, for relative small drifts or beaming speeds (U), not exceeding the thermal speed (α), the aperiodic FIs exist in the same interval of wavenumbers and the same range of oblique angles (with respect to the magnetic field direction), but the growth rates of counter-beaming FI (CBFI) are always higher than those of temperature anisotropy FI (TAFI). For U/α > 1, however, another electrostatic two-stream instability is also predicted, which may have growth rates higher than those of CBFI, and may dominate in that case the dynamics.

Physical regimes of electrostatic wave-wave nonlinear interactions generated by an electron beam propagating in a background plasma.

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of the quasilinear and weak turbulence theories, their validities are limited by the requirements of a sufficiently dense mode spectrum and a small wave amplitude. In this paper, we extensively study the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing high-resolution two-dimensional particle-in-cell simulations and using analytical theories. We confirm that, during the initial stage of two-stream instability between the beam and background cold electrons, it is saturated due to the well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the regimes are analyzed in detail. We identify a new regime in the strong Langmuir turbulence featured by what we call electron modulational instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually, the beam-plasma wave interaction stops being resonant due to the strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a repetitive (intermittent) process. The beam electrons are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa (κ) distribution and a wave-energy spectrum E^{2}(k)∼k^{-5} are observed in the strong turbulent regime.

Propagation of Alfvén waves in the charge starvation regime

ABSTRACT We present numerical simulation results for the propagation of Alfvén waves in the charge starvation regime. This is the regime where the plasma density is below the critical value required to supply the current for the wave. We analyse a conservative scenario where Alfvén waves pick up charges from the region where the charge density exceeds the critical value and advect them along at a high Lorentz factor. The system consisting of the Alfvén wave and charges being carried with it, which we call charge-carrying Alfvén wave (CC-AW), moves through a medium with small, but non-zero, plasma density. We find that the interaction between CC-AW and the stationary medium has a two-stream like instability which leads to the emergence of a strong electric field along the direction of the unperturbed magnetic field. The growth rate of this instability is of the order of the plasma frequency of the medium encountered by the CC-AW. Our numerical code follows the system for hundreds of wave periods. The numerical calculations suggest that the final strength of the electric field is of the order of a few per cent of the AW amplitude. Little radiation is produced by the sinusoidally oscillating currents associated with the instability during the linear growth phase. However, in the non-linear phase, the fluctuating current density produces strong EM radiation near the plasma frequency and limits the growth of the instability.

A charge-momentum-energy-conserving 1D3V hybrid Lagrangian–Eulerian method for Vlasov–Maxwell system

Here we propose hybrid Lagrangian–Eulerian (HLE) method for kinetic simulations of plasmas. The HLE method solves advection equations of shape functions unlike particle-in-cell (PIC) method. Although the PIC method cannot preserve the conservation laws of momentum and energy simultaneously, the HLE method can resolve this issue while the particle velocity is formulated by the Lagrangian description. The HLE method discretizes the advection equations and Maxwell's equations with the same scheme, so the momentum and energy exchange between charged particles and electromagnetic field exactly balances in discrete level. Numerical experiments show that linear growth rates of two-stream and Weibel instabilities are reproduced well, and global conservation is exactly preserved except for round-off errors although the velocity space is discretized by the Lagrangian description like the PIC method.

Proton beam-driven instabilities in an inclined magnetic field

In this paper, the electrostatic and electromagnetic instabilities of a magnetized proton–DT plasma relevant to the fast ignition scheme of inertial fusion were examined. The magnetic field and proton beam define a plane and the magnetic field vector has the orientation angle of θ. The dispersion relation of two-stream and filamentation modes was first derived using the conservation, Euler, and Maxwell equations. Then, the more general case describing the wave propagation in an arbitrary direction in the two-dimensional case was derived symbolically. It is demonstrated that in a magnetized beam–plasma system, the two-stream instability depicts two separated growth curves, one larger than the other and there exists a stable frequency band between them. This zone will grow as the magnetic field inclination angle increases such that the smaller two-stream peak vanishes at the limiting angle of θ→π/2. The splitting in the growth rate curve becomes obvious at magnetic field parameter Ωe>0.5. The pure filamentation instability of the beam–plasma is about two orders of magnitude smaller than the two-stream instability and it just contributes to magnetic field orientation θ=0. In a two-dimensional case, the mixed electrostatic/electromagnetic instabilities contribute to the final growth rate curve producing an X-like shape. The interface point of two growth curves is characterized by coordinate (∼1.0, tan(θ)) in the zx-plane.

High power terahertz radiation generated by beam-plasma system in multi-filament regime

In the particle-in-cell simulation study of this paper, it is found that the high-power terahertz radiation at twice the plasma frequency can be generated by the interaction between a weakly relativistic, large-radius, focused electron beam and an overdense plasma. The terahertz radiation is emitted from a multi-filament structure in the electron beam, which is caused by the coupling of the longitudinal two-stream instability and the transverse filamentation instability. The analysis of the k space of the plasma waves indicates that the radiation can be explained by the mode coupling among a forward oblique mode, a backward oblique mode, and a second harmonic radiation mode. The influences of the beam Lorentz factor and plasma density on the radiation power, efficiency, and coherence are also investigated. The present results not only contribute to the development of novel megawatt-level narrowband terahertz radiation sources, but also propose a potential terahertz radiation mechanism for the fundamental research of the beam-plasma system.

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

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

Kinetic investigations of nonlinear electrostatic excitations in quantum plasmas.

For plasmas in an extremely high-density state, like stellar cores or compressed fuel in inertial fusion facilities, their behavior turns out to be quite different when compared with those plasmas in interstellar space or magnetic confinement devices. To figureout those differences and uncover the kinetic physics in electrostatic excitations, a quantum kinetic code solving Wigner-Poisson equationshas been developed. Basic plasmon decay, Landau damping, and two-stream instability of extremely high-density plasmas are investigated by using our newly developed code. Numerical simulations show that in the linear region, the dispersion relations of intrinsic modes can be significantly affected by quantum effects, and such simulation results can be well described by the existing analytical theory. Especially in the nonlinear region, since the space-time scale of collective modes of plasmas is comparable to the electron de Broglie wavelength, their couplings produce some new physics: the energy exchange between the electron and the collective mode results in an abnormal oscillation that does not exist in classical plasmas.

Numerical impact of symmetric two-stream instability on fractional-order plasma model based on specific geometry with LASER light

Numerical impact of symmetric two-stream instability on fractional-order plasma model based on specific geometry with LASER light