Counterstreaming Electron Beams Research Articles

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.

A Mechanism for Large-Amplitude Parallel Electrostatic Waves Observed at the Magnetopause

Large-amplitude electrostatic waves propagating parallel to the background magnetic field have been observed at the Earth’s magnetopause by the Magnetospheric Multiscale (MMS) spacecraft. These waves are observed in the region where there is an intermixing of magnetosheath and magnetospheric plasmas. The plasma in the intermixing region is modeled as a five-component plasma consisting of three types of electrons, namely, two counterstreaming hot electron beams and cold electrons, and two types of ions, namely, cold background protons and a hot proton beam. Sagdeev pseudo-potential technique is used to study the parallel propagating nonlinear electrostatic solitary structures. The model predicts four types of modes, namely, slow ion-acoustic mode, fast ion-acoustic mode, slow electron-acoustic mode and fast electron-acoustic modes. Except the fast ion-acoustic mode, all other modes support solitons. Whereas slow ion-acoustic solitons have positive potentials, both slow and fast electron-acoustic solitons have negative potentials. For the case of 4% cold electron density, the slow ion-acoustic solitons have electric field ∼(40–120) mV m−1. The fast Fourier transforms (FFT) of slow ion-acoustic solitons produce broadband frequency spectra having peaks between ∼100 Hz to 1000 Hz. These theoretical predictions are in good agreement with the observations. The slow and fast electron-acoustic solitons could be relevant in explaining the low-intensity high (>1 kHz) frequency waves which are also observed at the same time.

Whistler Waves as a Signature of Converging Magnetic Holes in Space Plasmas

Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA’s Magnetospheric Multiscale Mission enable us to study the particle dynamics in magnetic holes in the Earth’s magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave–particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole converges, a pair of counter-streaming electron beams form near the hole’s center as a consequence of the combined action of betatron and Fermi effects. The beams trigger the generation of slightly oblique whistler waves. Our conceptual prediction is supported by a remarkable agreement between our observations and numerical predictions from the Arbitrary Linear Plasma Solver. Our study shows that wave–particle interactions are fundamental to the evolution of magnetic holes in space and astrophysical plasmas.

Theoretical and computational studies of the Weibel instability in several beam–plasma interaction configurations

The Weibel instability is investigated theoretically and numerically under three scenarios: counterstreaming electron beams in background plasma, an electron–positron beam and an electron–proton beam in background plasma. These models occur widely in laboratory and astrophysical environments. The Weibel instability growth rates are determined numerically from the corresponding cold-fluid dispersion relations, which are confirmed with two-dimensional particle-in-cell simulations. The maximum growth rates for the counterstreaming beams in background plasma are an order of magnitude smaller than the maximum growth rates for the beams cases in the same range of density ratios and beam energies. The maximum growth rate for the electron–positron beam case is shown to be at most a factor $\sqrt {2}$ greater than the electron–proton beam case with similar dispersion behaviours. A non-monotonic relation is found between the maximum Weibel instability growth rates and the electron–positron beam energy, suggesting that increasing beam energies does not entail an increase in the Weibel instability growth rate.

Theoretical studies of low and high frequency electrostatic solitary waves in the magnetopause associated with asymmetric magnetic reconnection

In a comprehensive analysis of Cluster data, Graham et al. (2015) have reported the existence of slow and fast electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection arising from the merger of the magnetic fields, and mixing, of the hot tenuous magnetospheric plasma and the cooler dense magnetosheath plasma. Their analysis also reveals the presence of four electron species, two background Maxwellian distributions and a pair of counter-streaming electron beams. Using the measured plasma parameters and a plasma model consistent with the observations, together with an ion component for charge neutrality, we use fluid dynamic theory in an attempt to identify the plasma modes associated with the ESWs, as well as the polarity and admissible range in speed of the fast and slow structures. It can be inferred from the data sets in Figure 4 in Graham et al. (2015) obtained during the crossing of the Cluster satellites C3 and C4 of the separatrix near the ion diffusion region that the distributions of the two counterstreaming electron beams vary from having identical characteristics to showing small differences over the period during which the ESWs were observed. Accordingly, we align the theoretical parameters in our study with Cluster observations by considering the effect of identical and non-identical counterstreaming electron beam distributions on the existence of ESWs.

Momentum transfer driven by fluctuations in relativistic counter-propagating electron beams

A semi-Lagrangian relativistic Vlasov–Maxwell solver is used to describe the non-linear momentum transfer between electron beams, which is driven by spontaneous fluctuations in the oblique filamentation instability (a type of Weibel mode) in two-dimensional plasmas. For counter-streaming plasmas, these filamentation instabilities may strengthen the generation of a fine structure of the distribution function in phase space. Properties of such counter-streaming beams are investigated using full-kinetic simulations and a Hamiltonian reduction technique based on the invariance of the transverse canonical momentum, the so-called multi-stream model. In the regime where , being the wavevector and d e the electron skin depth, a momentum transfer takes place when a mesoscale current filamentation mode couples with microscopic phase-space fluctuations. This regime is characterized by the appearance of filamentation modes with large wavenumbers and large amplitude fluctuations, which induce variations of the L 2-norm of the plasma in link with the self-organization of counter-streaming electron beams. We also discuss some theoretical aspects of information theory that highlight the role of the (reversible) entropy production in momentum transfer, thus by clarifying the connections between (microscopic) fluctuations of the distribution function and the fundamental aspects of the filamentation in Vlasov theory. The momentum transfer between beams is quantitatively analyzed by means of both theoretical estimations and numerical experiments.

Oscillatory solutions for a diode with counter-streaming electron and ion beams

A plasma diode with counter-streaming electron and ion beams has as a rule more than one time-independent solution. Stability features of the steady state solution with ion reflection from a potential barrier are studied numerically. It was found that there is a threshold in the diode length beyond which nonlinear oscillations occur as an alternative instead of such solutions. Features of the oscillations are studied.

Electromagnetic Emission Produced by Three-wave Interactions in a Plasma with Continuously Injected Counterstreaming Electron Beams

Abstract Three-wave interactions between Langmuir and electromagnetic waves in plasma with unstable electron flows are believed to be the main cause of type II and III solar radio emissions. The narrow band of type II bursts requires assuming that this radiation is generated in some local regions of shock fronts traveling in the solar corona, where the specific conditions for the enhancement of electromagnetic emissions near the plasma frequency harmonics are created. The reason for such enhancement at the second harmonic may be the formation of counterstreaming electron beams. There are different opinions in the literature on whether the second harmonic electromagnetic emission in the presence of an additional beam can be efficient enough to markedly dominate emissions produced by a single beam. In the present paper, we carry out particle-in-cell simulations of the collision of two symmetric electron beams in plasma with open boundary conditions and show that the efficiency of beam-to-radiation power conversion can be significantly increased compared to models with periodic boundary conditions and reach the level of a few percent if three-wave interactions with electromagnetic waves near the second harmonic of the plasma frequency becomes available for the most unstable, oblique, beam-driven modes.

Electron Mixing and Isotropization in the Exhaust of Asymmetric Magnetic Reconnection With a Guide Field

AbstractWe investigate an exhaust crossing of asymmetric guide field reconnection observed by Magnetospheric Multiscale (MMS) mission at Earth's dayside magnetopause. One MMS spacecraft (MMS 4) observes multicomponent electron distributions, including two counterstreaming electron beams, while the other three MMS spacecraft, with a separation of ∼30 km, record nearly isotropic electron distributions. As counterstreaming electrons are unstable for the electron two‐stream instability, our observations suggest that the electrostatic waves generated by the fast‐growing electron two‐stream instability can contribute to the rapid isotropization of electron distributions in the reconnection exhaust, indicating that wave‐particle interactions play an important role in electron dynamics.

Low- and high-frequency nature of oblique filamentation modes. II. Vlasov–Maxwell simulations of collisionless heating process

The nonlinear regime of electromagnetic oblique instabilities is investigated by means of a “noiseless” semi-Lagrangian Vlasov–Maxwell solver. Starting from an initial equilibrium configuration with two counterstreaming electron beams, qualitatively different nonlinear regimes are shown to exist depending on the nature of the solutions of the linear dispersion relation, whose properties have been discussed in the companion paper I [Ghizzo et al., Phys. Plasmas 27, 072103 (2020)]. This behavior is in contrast with existing theories of the oblique instability, which are based on the excitation of a single eigenmode at a time: nonlinear transitions toward regimes dominated by low-frequency modes are generally shown to be possible. The emphasis here is on gaining a better understanding of the multiplicity of electromagnetic oblique unstable modes and on modeling their back-reaction on plasma wave-particle interactions and energy conversion mechanisms. The latter are shown to depend on the saturation scenario of the different regimes of the oblique instability. A new regime is discussed, in which a stochastic heating occurs at the expenses of the magnetic energy first amplified by the oblique modes and in which a (reversible) violation of entropy conservation is made possible by large amplitude phase-space fluctuations of the distribution function.

Low- and high-frequency nature of oblique filamentation modes. I. Linear theory

The solution of the linear dispersion relation of electromagnetic oblique instabilities, for two counterstreaming electron beams, is investigated by using an extended fluid approach that includes the full dynamics of the pressure tensor. Numerical solutions of the simplified polynomial formulation so obtained are analyzed and compared to full kinetic solutions. They correspond to two classes of eigenmodes: low- and high-frequency oblique modes of resonant character. Coexistence of several oblique modes in neighboring regions of the wave vector plane, having close growth-rates, leads to the possibility of a transition starting from a low wave number mode to an oblique mode of high values in wave numbers. For such counterstreaming plasmas, the oblique instability may strengthen and amplify the filamentation process of the distribution function in velocity space, a property of the Vlasov equation. In addition to its simplicity, useful for solving the dispersion relation in the linear regime and for identifying kinetic solutions difficult to calculate otherwise, this extended fluid model is helpful in gaining insight into the fundamental properties of Vlasov theory, which are possibly relevant to kinetic heating processes.

Electrostatic and electromagnetic waves driven by current free electron beam instability: Effects of positron, background composition, and ion-to-electron mass ratio

Counterstreaming electron beams drifting along the magnetic field in electron–proton plasmas may lead to the generation of electrostatic (ES) waves and structures widely observed in planetary magnetospheres. In electron–positron plasmas, streaming electron/positron beams along the background magnetic field may first result in ES waves followed by the electromagnetic (EM) waves with substantial magnetic field perturbations, as shown by Jao and Hau [Phys. Rev. E 98, 013203 (2018)]. In this study, we examine the formation of ES and EM waves driven by current free counterstreaming electron beams in electron–ion background plasmas and current free electron–positron beams in electron–proton–positron background plasmas based on one-dimensional EM particle-in-cell simulations with the drift velocity being along the background magnetic field. For the former cases, the effects of ion-to-electron mass ratios are examined, which have implications for two- and three-dimensional particle in cell simulations with reduced mass ratios. For the latter cases, the effects of positrons are examined, which have applications to astrophysical plasma environments and laboratory experiments. It is shown that the presence of positrons or light ions may shorten the occurrence times between the ES and EM waves driven by current free electron beam instability. The EM waves have relatively longer wavelengths as compared to the ES waves and the magnetic field evolution resembles parallel proton firehose instability. The effects of positrons, background compositions, and ion-to-electron mass ratios on the occurrence of ES and EM waves are consistent with the linear fluid theory.

Blow-up solitons at the nonlinear stage of the two-stream instability in quantum plasmas

The nonlinear evolution of the quantum two-stream instability in a plasma with counter-streaming electron beams is studied. It is shown that in the long-wave limit the nonlinear stage of the instability can be described by the elliptic nonlinear string equation. We present two types of nonlinear solutions. The first one is an unstable nonlinear mode that is continuously related with the growing linear solution and the second one is a pulsating soliton. We show that both of these solutions blow up in a finite time.

Multivircator as a New Highly Effective Microwave Generator With Multiple Virtual Cathodes: Concept and PIC-Simulation

This article presents the concept of multivircators, in which a chain of virtual cathodes (VCs) is formed in two counter-streaming electron beams (exceeding the space charge limit) that generate microwave radiation. Up to ten VCs were observed in a particle-in-cell (PIC) simulation of this two-beam instability. It is predicted that the efficiency of microwave generation in a multivircator at a certain time interval can reach 50%.

Simulation of Electron-Electron Two Stream Instability (ETSI)

Stream instabilities are widely studied due to their importance in understanding astrophysical phenomena such as acceleration of high velocity of solar wind. In this work, the simulation of electron two stream instability was performed using Vorpal Simulation (VSim) code to explore the kinetic energy of plasma that arises due to the interaction between two counter-streaming electron beams at different velocities as well as different electron densities. The electron beam velocity was varied in the range of 3.58 × 106 m/s - 7.98 × 106 m/s and the resulting kinetic energy of plasma increased from 19 × 10−6J - 210 × 10−6J respectively. Also, increasing the electron density at fixed beam velocity from 1.05 × 1014m−3 - 5.84 × 1014m−3, the kinetic energy was observed to increase from 100 × 10−6J - 200 × 10−6J .However, the kinetic energy of the electron increases more with increasing beam velocity than with increasing electron density. The electric field energy which arose due to the interaction of the streaming beams did not exceed the energy of the beams.

Counterstreaming beams in magnetised Vlasov plasma

In this paper, we investigate nonrelativistic, kinetic, linear phase of the filamentation instability when an external magnetic field is present in the direction of the counterstreaming electron beams using Vlasov simulations in 1D-3V space. We first investigate the growth rate of instability. In the linear growth regime, our results correspond to the previous conclusions that with the increase in strength of the ambient magnetic field, there is a suppression of instability. Interestingly, we established that at a critical / threshold magnetic field, Vlasov simulations and particle-in-cell (PIC) simulations differ in their instability behaviour. At this particular magnetic field, there is a complete suppression of the growth of instability in Vlasov results compared to PIC simulations, where a strong growth of instability is shown. It is believed that thermal noise in the PIC leads to the growth. However, Vlasov simulations show wave–wave coupling which stabilises the modes. In this work, our focus is to demonstrate the difference in this behaviour and to thoroughly analyse the spectra and wave generation for the same.

PLASMA EMISSION BY COUNTER-STREAMING ELECTRON BEAMS

ABSTRACT The radiation emission mechanism responsible for both type-II and type-III solar radio bursts is commonly accepted as plasma emission. Recently Ganse et al. suggested that type-II radio bursts may be enhanced when the electron foreshock geometry of a coronal mass ejection contains a double hump structure. They reasoned that the counter-streaming electron beams that exist between the double shocks may enhance the nonlinear coalescence interaction, thereby giving rise to more efficient generation of radiation. Ganse et al. employed a particle-in-cell simulation to study such a scenario. The present paper revisits the same problem with EM weak turbulence theory, and show that the fundamental (F) emission is not greatly affected by the presence of counter-streaming beams, but the harmonic (H) emission becomes somewhat more effective when the two beams are present. The present finding is thus complementary to the work by Ganse et al.

Evidence of locally enhanced target heating due to instabilities of counter-streaming fast electron beams

The high-current fast electron beams generated in high-intensity laser-solid interactions require the onset of a balancing return current in order to propagate in the target material. Such a system of counter-streaming electron currents is unstable to a variety of instabilities such as the current-filamentation instability and the two-stream instability. An experimental study aimed at investigating the role of instabilities in a system of symmetrical counter-propagating fast electron beams is presented here for the first time. The fast electron beams are generated by double-sided laser-irradiation of a layered target foil at laser intensities above 1019 W/cm2. High-resolution X-ray spectroscopy of the emission from the central Ti layer shows that locally enhanced energy deposition is indeed achieved in the case of counter-propagating fast electron beams.

Thin current sheets with strong bell-shape guide field: Cluster observations and models with beams

Abstract. We study the kinetic structure of intense ion-scale current sheets with strong electron currents and the guide field having a bell-shape profile. We consider four crossings of the Earth magnetotail current sheet by the Cluster mission in 2003. The thickness of these current sheets is about the ion inertial length and significantly smaller than the characteristic ion gyroradius. We analyze the asymmetry of the electron velocity distribution functions and show that the electron current is provided by the small electron subpopulation interpreted as an electron beam or two counter-streaming electron beams. The beam (counter-streaming beams) has a bulk velocity of the order of the electron thermal velocity and a density (difference of beam densities) of about 1–5% of the plasma density. To describe the observed current sheets we develop a kinetic model with particle beams. The model predicts different thickness of the current sheet for different types of current carriers (one electron beam or two counter-streaming electron beams). The observed ion-scale current sheets can be explained assuming that the current is carried by one electron beam and a co-streaming ion beam. Although the ion beam does not carry a significant current, this beam is required to balance the electron current perpendicular to the current sheet neutral plane. The developed model explains the dominance of the electron current and the ion scales of the current sheets.

Electron distributions observed with Langmuir waves in the plasma sheet boundary layer

The present paper investigates the Langmuir turbulence driven by counter-streaming electron beams and its plausible association with observed features in the Earth's plasma sheet boundary layer region. A one-dimensional electrostatic particle-in-cell simulation code is employed in order to simulate broadband electrostatic waves with characteristic frequency in the vicinity of the electron plasma frequency ω/ωpe≃1.0. The present simulation confirms that the broadband electrostatic waves may indeed be generated by the counter-streaming electron beams. It is also found that the observed feature associated with low energy electrons, namely quasi-symmetric velocity space plateaus, are replicated according to the present simulation. However, the present investigation only partially succeeds in generating the suprathermal tails such that the origin of observed quasi power-law energetic population formation remains outstanding.