Langmuir Wave Packets Research Articles

Electron Modulational Instability in the Strong Turbulent Regime for an Electron Beam Propagating in a Background Plasma.

We study collective processes for an electron beam propagating through a background plasma using simulations and analytical theory. A new regime where the instability of a Langmuir wave packet can grow locally much faster than ion frequency is clearly identified. The key feature of this new regime is an electron modulational instability that rapidly creates a local Langmuir wave packet, which in its turn produces local charge separation and strong ion density perturbations because of the action of the ponderomotive force, such that the beam-plasma wave interaction stops being resonant. Three evolution stages of the process and observed periodic burst features are discussed. Different physical regimes in the plasma and beam parameter space are demonstrated for the first time.

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.

Evidence for the Three Wave Interactions in the Vicinity of an Interplanetary Shock

We present the high time resolution in situ observations of coherent one-dimensional magnetic-field-aligned Langmuir wave packets with well-defined low frequency modulations (beats) in the upstream region of a coronal mass ejection driven supercritical quasi-perpendicular interplanetary (IP) shock. We show that these beat-type waveforms provide what is believed to be the first observational evidence for one of the most important three wave interactions, called the electrostatic decay instability (ESD) (L is the pump Langmuir wave excited by the shock accelerated electron beam, and L′ and S are the daughter Langmuir and ion sound waves, respectively). We also show that (1) the spectra of these wave packets contain the signatures of L, L′, and S, which satisfy the resonance conditions required for excitation of ESD, (2) the peak intensities of these wave packets well exceed the ESD threshold values, and (3) the speed of the electron beam estimated using the resonance conditions is very close to the typical observed speeds of the IP shock accelerated electron beams. The implication of these findings is that (1) the shock accelerated electron beams probably are stabilized by the three wave interaction , and (2) the second harmonic radio emission of solar type II radio bursts probably is excited by the three wave merging .

Particle-in-cell simulations of THz emission from plasma by oblique collision of two-electron beams

We studied the THz radiation generated by a beam-plasma system using two-dimensional (2D) particle-in-cell (PIC) simulations. The Langmuir waves excited by two counterpropagating electron beams, via two-stream instability, collide with each other at an oblique angle, which forms a high beam-density modulation near the collision region, where both beam electrons become trapped. As a result, spatially localized Langmuir wave packets with large longitudinal-electric field amplitudes are formed, which give rise to bursts of electromagnetic radiation. Our 2D PIC simulations of the two thin, low-density, asymmetric, electron beams colliding obliquely show that a strong THz emission is obtained at the second harmonic of the plasma frequency (f = 1.0 THz), with a narrow spectral width (∼0.80%) in vacuum and significantly higher efficiency than the head-on-collision case. The efficiency of power conversion from electron beams to THz radiation measured in vacuum reaches around ∼0.0289, for a continuous injection of beams into the plasma, making it suitable for applications requiring high-power narrow-band THz radiation sources.

Detection of Extreme and Exceptional Langmuir Wave Packets in Solar Type III Radio Bursts

AbstractWe report the STEREO observations of two extreme and exceptional Langmuir wave packets, which are the most intense wave packets ever detected in solar type III bursts; their peak intensities Et∼ 215 and ∼ 161 mVm−1 beat out the previous 107 mVm−1 record, reported by Thejappa and MacDowall (2018a; https://doi.org/10.3847/1538-4357/aaca3b). These observations provide new evidence for (1) the four‐wave interaction called the oscillating two‐stream instability (OTSI), which is the coupling of two beam‐excited Langmuir waves with an ion sound wave yielding downshifted and upshifted side bands, and (2) Langmuir solitons formed as a result of OTSI, and (3) density cavities created by their ponderomotive forces. The fast Fourier transform spectra of these wave packets provide what is believed to be the first evidence for harmonics of the electron plasma frequency, fpe up to the order of 5 with peak intensities falling off with increasing harmonic number. The higher order spectral analysis indicates that these harmonics probably correspond to the electromagnetic waves excited as a result of various three‐wave interactions. We argue that although the observed characteristics also indicate that these wave packets could be collapsing wave packets formed as a result of nucleation instability, the observed evidence for OTSI and Langmuir solitons trapped inside the self‐generated density cavities strongly favor the OTSI as the route for the spatial collapse of Langmuir waves in the present case. The implication of these findings for theories of solar type III radio bursts is discussed.

Characteristics of a Langmuir Soliton Observed in a Solar Type III Burst

We present the high time resolution in situ observations of a Langmuir wave packet obtained by the STEREO WAVES experiment in the source region of a solar type III radio burst. This wave packet is unique in the sense that it occurs as an intense localized one-dimensional magnetic field aligned wave packet with peak intensity well in excess of the threshold for the oscillating two stream instability (OTSI), soliton formation and related strong turbulence processes. Most importantly, the measured half-width of this wave packet is approximately equal to the expected half-width of a Langmuir soliton with the same peak intensity as that of the wave packet. Furthermore, a density cavity is created by the ponder-motive force of this wave packet as expected of a Langmuir soliton. These findings indicate that the observed wave packet is most likely a Langmuir soliton formed as a result of the balance between the non-linearity related self-compression and the dispersion related spreading. We discuss the implication of these observations for theories of solar type III radio bursts.

Langmuir Solitons in Solar Type III Radio Bursts: STEREO Observations

Abstract The source regions of solar type III radio bursts are regions of very intense Langmuir wave packets excited by the bump-on-tail distributions of energetic electrons accelerated during solar flares. We report the high time resolution observations of some of these wave packets, which provide unambiguous evidence for Langmuir solitons formed as a result of oscillating two-stream instability (OTSI), since (1) they occur as intense localized one-dimensional magnetic field aligned wave packets, (2) their measured half-widths and peak amplitudes are inversely correlated with each other, so that the narrower the wave packet is, the greater its amplitude; this inverse correlation is the characteristic feature of Langmuir solitons formed as a result of balance between the nonlinearity related self-compression and dispersion related broadening of the wave packets, (3) their FFT spectra contain peaks corresponding to sidebands and low frequency enhancements in addition to pump Langmuir waves, whose frequencies and wave numbers satisfy the resonance conditions of the four-wave interaction known as the OTSI, and (4) they are accompanied by their ponderomotive force induced density cavities. The implication of these observations for theories of solar radio bursts is discussed.

Observational Evidence for Langmuir Wave Collapse in the Source Region of a Solar Type III Radio Burst

Abstract High-time-resolution in situ wave observations show that Langmuir waves associated with solar type III radio bursts often occur as coherent localized one-dimensional magnetic-field-aligned wave packets with short durations of a few milliseconds and peak intensities well above the strong turbulence thresholds. In this paper, we report observations of a wave packet obtained by the time domain sampler of the STEREO WAVES experiment, which is unique in the sense that it is the most intense wave packet ever detected in association with a solar type III radio burst, with a peak intensity E t ∼ 107 mVm−1. We show that this wave packet provides evidence for (1) oscillating two-stream instability (OTSI), (2) a collapsing soliton formed as a result of OTSI, (3) the formation of a soliton–caviton pair, and (4) excitation of second and third harmonic electromagnetic waves. We also show that the peak intensity and spatial width satisfy the threshold condition for this wave packet to be the collapsing Langmuir wave packet formed as a result of nucleation processes even when δn b > δn p , where δn b and δn p are the levels of background and ponderomotive-force-induced density fluctuations, respectively. Thus, these observations provide unambiguous evidence for the spatial collapse of Langmuir waves in the source region of a type III radio burst, and the observed spectral evidence for OTSI and the ponderomotive-force-induced density cavity strongly suggest that OTSI is mostly likely responsible for the collapse of the observed wave packet.

Beam-plasma instability and density holes: Langmuir wave-packet formation and particle acceleration

The role of density perturbations of the background plasma in the development of Langmuir waves generated by beam-plasma instabilities is a very debated issue in space physics. The presence of clumpy electrostatic wave-packets (in particular Langmuir waves), from in situ observations, is indeed puzzling. Several processes have been proposed to explain the formation of waveforms, such as Stochastic Growth Theory and trapping in eigenmodes. Here we explore another mechanism considering the seeding of the beam-plasma instability by density holes. We have performed several 1D-1V Vlasov simulations in the electrostatic limit. We show that in the presence of a density hole, a large amplitude solitary wave-packet of Langmuir waves is formed and that it evolves towards clumpier waveforms. Moreover, the large-amplitude wave-packets generated near the hole can reach saturation and accelerate the electrons of the beam: their velocity distribution is strongly distorted, leading to a multi-peaked structure that generates new unstable modes having phase velocities both larger and smaller than the average speed of the beam. The relationship between the wave amplitude and the characteristics of the density hole is also described, showing how the electron beam may select specific holes to generate enhanced localised Langmuir wave-packets.

Modulation and nonlinear evolution of multi-dimensional Langmuir wave envelopes in a relativistic plasma

The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\theta} plane, where k is the wave number and {\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.

Particle-in-cell simulations of the relaxation of electron beams in inhomogeneous solar wind plasmas

Previous theoretical considerations of electron beam relaxation in inhomogeneous plasmas have indicated that the effects of the irregular solar wind may account for the poor agreement of homogeneous modelling with the observations. Quasi-linear theory and Hamiltonian models based on Zakharov’s equations have indicated that when the level of density fluctuations is above a given threshold, density irregularities act to de-resonate the beam–plasma interaction, restricting Langmuir wave growth on the expense of beam energy. This work presents the first fully kinetic particle-in-cell (PIC) simulations of beam relaxation under the influence of density irregularities. We aim to independently determine the influence of background inhomogeneity on the beam–plasma system, and to test theoretical predictions and alternative models using a fully kinetic treatment. We carry out one-dimensional (1-D) PIC simulations of a bump-on-tail unstable electron beam in the presence of increasing levels of background inhomogeneity using the fully electromagnetic, relativistic EPOCH PIC code. We find that in the case of homogeneous background plasma density, Langmuir wave packets are generated at the resonant condition and then quasi-linear relaxation leads to a dynamic increase of wavenumbers generated. No electron acceleration is seen – unlike in the inhomogeneous experiments, all of which produce high-energy electrons. For the inhomogeneous experiments we also observe the generation of backwards-propagating Langmuir waves, which is shown directly to be due to the refraction of the packets off the density gradients. In the case of higher-amplitude density fluctuations, similar features to the weaker cases are found, but also packets can also deviate from the expected dispersion curve in $(k,\unicode[STIX]{x1D714})$-space due to nonlinearity. Our fully kinetic PIC simulations broadly confirm the findings of quasi-linear theory and the Hamiltonian model based on Zakharov’s equations. Strong density fluctuations modify properties of excited Langmuir waves altering their dispersion properties.

LANGMUIR WAVE DECAY IN INHOMOGENEOUS SOLAR WIND PLASMAS: SIMULATION RESULTS

Langmuir turbulence excited by electron flows in solar wind plasmas is studied on the basis of numerical simulations. In particular, nonlinear wave decay processes involving ion-sound (IS) waves are considered in order to understand their dependence on external long-wavelength plasma density fluctuations. In the presence of inhomogeneities, it is shown that the decay processes are localized in space and, due to the differences between the group velocities of Langmuir and IS waves, their duration is limited so that a full nonlinear saturation cannot be achieved. The reflection and the scattering of Langmuir wave packets on the ambient and randomly varying density fluctuations lead to crucial effects impacting the development of the IS wave spectrum. Notably, beatings between forward propagating Langmuir waves and reflected ones result in the parametric generation of waves of noticeable amplitudes and in the amplification of IS waves. These processes, repeated at different space locations, form a series of cascades of wave energy transfer, similar to those studied in the frame of weak turbulence theory. The dynamics of such a cascading mechanism and its influence on the acceleration of the most energetic part of the electron beam are studied. Finally, the role of the decay processes in the shaping of the profiles of the Langmuir wave packets is discussed, and the waveforms calculated are compared with those observed recently on board the spacecraft Solar TErrestrial RElations Observatory and WIND

Waveforms of Langmuir turbulence in inhomogeneous solar wind plasmas

AbstractModulated Langmuir waveforms have been observed by several spacecraft in various regions of the heliosphere, such as the solar wind, the electron foreshock, the magnetotail, or the auroral ionosphere. Many observations revealed the bursty nature of these waves, which appear to be highly modulated, localized, and clumped into spikes with peak amplitudes typically 3 orders of magnitude above the mean. The paper presents Langmuir waveforms calculated using a Hamiltonian model describing self‐consistently the resonant interaction of an electron beam with Langmuir wave packets in a plasma with random density fluctuations. These waveforms, obtained for different profiles of density fluctuations and ranges of parameters relevant to solar type III electron beams and plasmas measured at 1 AU, are presented in the form they would appear if recorded by a satellite moving in the solar wind. Comparison with recent measurements by the STEREO and WIND satellites shows that their characteristic features are very similar to the observations.

Introduction to the special section on Sun‐Earth system response to extreme solar and seismic events

Introduction to the special section on Sun‐Earth system response to extreme solar and seismic events

Stochastic electron motion driven by space plasma waves

Abstract. Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is responsible for the dynamical balance between the accelerating process and relativistic electron precipitation events. We have also considered the efficiency of the mechanism of stochastic surfing acceleration of cosmic electrons at the supernova remnant shock front, and the accelerating process driven by a Langmuir wave packet in producing cosmic ray electrons. The dynamics of cosmic electrons is formulated in terms of a dissipative map involving the effect of synchrotron emission. We present analytical and numerical methods for studying Hamiltonian chaos and dissipative strange attractors, and for determining the heating extent and energy spectra.

Observational evidence for the collapsing Langmuir wave packet in a solar type III radio burst

High time resolution observations from the STEREO spacecraft show that in solar type III radio bursts, Langmuir waves often occur as very intense one‐dimensional magnetic field aligned field structures. One of these events represents the most intense Langmuir wave packet with ever detected in a type III radio burst until now (WL is the peak energy density, and ne and Te are the electron density and temperature, respectively). The detailed analysis of this wave packet indicates that (1) its peak intensity is well above the threshold for the oscillating two‐stream instability (OTSI) and supersonic collapse; (2) its peak intensity and spatial scale satisfy the criterion for it to be a collapsing envelope soliton; (3) its low‐frequency components provide evidence for a density cavity, whose depth, width, and temporal coincidence indicate that probably it is the ponderomotive force generated density cavity; and (4) its spectrum contains harmonic peaks at 2fpe and 3fpe (in addition to the main Langmuir wave peak at the electron plasma frequency, fpe), which, as indicated by the bispectral analysis, probably are of the electromagnetic waves generated as a result of coalescence of two oppositely propagating Langmuir waves, and a Langmuir wave and a second harmonic electromagnetic wave, respectively. These characteristics strongly suggest that this wave packet and its associated density cavity represent the collapsing envelope soliton‐caviton pair formed as a result of OTSI, and in the present case, the strong turbulence processes probably play key roles in the beam stabilization as well as conversion of Langmuir waves into escaping radiation at 2fpe and 3fpe.

Do Langmuir wave packets in the solar wind collapse?

Intense localized Langmuir waves in the solar wind are often associated with type III solar radio bursts. Wave packets with a Gaussian fall‐off of electric field with distance are shown to be consistent with strong turbulence simulations. The collapse threshold for these Gaussian wave packets is calculated analytically and shown to be consistent with previous estimates and simulations. We then assess whether intense Langmuir events detected by the SWAVES instrument on the twin STEREO spacecraft during type III bursts are consistent with known conditions for wave packet collapse. Eight different type III events are selected and a total of 167 wave packets analyzed. An approximate analysis of the observed spatial scales and electric fields shows that none of the wave packets are consistent with collapse. The electric field structures predicted for collapsing wave packets, based on the nucleation mechanism and extensive three‐dimensional electrostatic and electromagnetic Zakharov simulations, are also fitted to the observed data: about a third of the packets are well fitted by a potential with a Gaussian radial function. Where good fits can be found, the wave packets do not meet the requirements for collapse. Good eigenmode fits are found for wave packets with waveforms well fitted by the structural form of collapsing wave packets. This is because the electric field envelopes of collapsing wave packets and trapped Langmuir eigenmodes are both Hermite‐Gauss functions. This rules out the possibility of wave packet collapse and strong turbulence being important processes in type III source regions.

EVIDENCE AGAINST THE OSCILLATING TWO-STREAM INSTABILITY AND SPATIAL COLLAPSE OF LANGMUIR WAVES IN SOLAR TYPE III RADIO BURSTS

Recently Thejappa et al. studied a specific Langmuir wave packet observed by STEREO A and argued based on the electric field from one of the three antennas that this packet satisfied the conditions for the oscillating two-stream instability (OTSI) and was undergoing wave collapse. We analyze the same event using all three electric components and show that, while the wave packet has structure consistent with collapse simulations and theory, the field strength is well below that required for collapse to proceed. Analyzing the three electric field components shows that the power spectrum and dominance of wave power perpendicular to the local magnetic field are inconsistent with OTSI. We show that this packet and other more intense packets are inconsistent with collapse and show no evidence of OTSI, but are likely trapped eigenmodes in density wells. Therefore, OTSI and collapse are unlikely explanations for intense Langmuir events observed in the solar wind.

Improving understanding of type III solar radio bursts

Solar radio bursts are associated with solar events that can interfere with GPS and communications systems, so scientists would like to learn more about the dynamics of these bursts. Type III solar radio bursts, which are generated when high‐energy electrons are ejected from the Sun, are characterized by a rapid drift in frequency from hundreds of megahertz to tens of kilohertz. Scientists believe that the process of producing type III solar radio bursts is associated with the excitation of Langmuir waves, which are oscillations in the electron density in a plasma, followed by the conversion of these waves into radio emissions. However, there are some open questions about these bursts.Thejappa et al. applied a method known as trispectral analysis to an observed Langmuir wave packet associated with a type III solar radio burst. The scientists show that four different spectral components of this wave packet interact strongly with one another in an interaction known as the oscillating two‐stream instability. The researchers suggest that this could explain some features of the solar radio bursts. (Geophysical Research Letters, doi:10.1029/2012GL051017, 2012)

Phase coupling in Langmuir wave packets: Evidence of four wave interactions in solar type III radio bursts

It is reported that one of the Langmuir wave packets in a type III solar radio burst is observed as a localized field structure with a short duration ∼3.2 ms and high intensity exceeding the strong turbulence thresholds. The peak intensity and short time scale well satisfy the criterion for the observed wave packet to be the collapsing Langmuir envelope soliton. The spectrum of this wave packet contains a resonant peak at the local electron plasma frequency, fpe, a Stokes peak at a frequency slightly lower than fpe, anti‐Stokes peak at a frequency slightly higher thanfpe, and a low frequency enhancement below a few hundred Hz, which satisfy the frequency and wave number resonance conditions of the oscillating two stream instability (OTSI) type of four wave interaction. Here, for the first time, we apply the trispectral analysis technique, and show that the spectral components of this wave packet, namely, the beam‐generated Langmuir wave, Stokes and anti‐Stokes modes are coupled to each other with a high degree of phase coherency (high tricoherence). This conclusively shows that the observed characteristics of the wave packet provide evidence for the OTSI.