Langmuir Wave Turbulence Research Articles

Electrostatic Wave Decay in the Randomly Inhomogeneous Solar Wind

Despite a few space observations where Langmuir and ion acoustic waves are expected to participate in the mechanism of electrostatic decay, this is to date believed to be the main and fastest nonlinear wave process in the solar wind. However, in such a plasma where random density fluctuations are ubiquitous, the question of whether nonlinear wave processes play a significant role in Langmuir wave turbulence generated by electron beams associated with type III solar radio bursts remains still open. This paper provides several answers by studying, owing to two-dimensional challenging particle-in-cell simulations, the dynamics and the properties of the ion acoustic waves excited by such Langmuir wave turbulence and the role they play in the electrostatic decay. The impact on this process of plasma background density fluctuations and electron-to-ion temperature ratio is studied. Moreover, it is shown that, for a typical solar wind plasma with an average level of density fluctuations of a few percent of the ambient density and a temperature ratio of the order of 1, nonlinear induced scattering off ions occurs, with small intensity low-frequency quasi-modes and only in localized plasma regions where density is depleted or weakly perturbed by low-frequency turbulence.

Second Harmonic Electromagnetic Wave Emissions from a Turbulent Plasma with Random Density Fluctuations

In the solar wind, electromagnetic waves at the harmonic plasma frequency 2ω p can be generated as a result of coalescence between forward- and backward-propagating Langmuir waves. A new approach to calculate their radiation efficiency in plasmas with external background density fluctuations is developed. The evolution of Langmuir wave turbulence is studied by solving numerically the Zakharov equations in a two-dimensional randomly inhomogeneous plasma. Then, the dynamics of the nonlinear electric currents modulated at frequencies close to 2ω p are calculated, as well as their radiation into harmonic electromagnetic waves. In the frame of this non-self-consistent approach where all transformations of Langmuir waves on density inhomogeneities are taken into account, the electromagnetic wave radiation rate (emissivity) is determined numerically as well as analytically, providing in both cases similar results. Moreover, scaling laws of the harmonic wave emissivity as a function of the ratio of the light velocity to the electron plasma thermal velocity are found. It is also shown how the emissivity depends on the average level of density fluctuations and on the isotropic/anisotropic character of the Langmuir waves’ and density fluctuations’ spectra.

Dynamics of Two-dimensional Type III Electron Beams in Randomly Inhomogeneous Solar Wind Plasmas

The dynamics of a type III electron beam generating Langmuir wave turbulence and subsequent electromagnetic emissions is studied owing to two-dimensional Particle-In-Cell simulations performed in both homogeneous and randomly inhomogeneous solar wind plasmas. Important differences in the beam dynamics are highlighted between both cases, due to Langmuir waves’ transformations on the density fluctuations. This paper studies the dynamics of a weak beam interacting with Langmuir wave turbulence scattered by initially applied plasma density fluctuations, in terms of particle acceleration, non-Gaussian suprathermal electron tails, broadening and relaxation of velocity distributions, beam density localization, and electron diffusion or trapping in a turbulent plasma. Density fluctuations are the cause of beam acceleration during its relaxation stage; after Langmuir wave saturation, it gains up to half the energy lost during deceleration while wave turbulence is damping, exhibiting asymptotically a suprathermal tail of electrons carrying around 30% of its initial kinetic energy. Some important features observed for one-dimensional beams exciting Langmuir wave turbulence in randomly inhomogeneous plasmas can be recovered.

Third and Fourth Harmonics of Electromagnetic Emissions by a Weak Beam in a Solar Wind Plasma with Random Density Fluctuations

Electromagnetic emissions and at the third and fourth harmonics of the plasma frequency ω p were observed during the occurrence of type II and type III solar radio bursts. Two-dimensional particle-in-cell simulations are performed using a weak beam, high space and time resolutions, and a plasma with density fluctuations of a few percent, for parameters relevant to regions of type III bursts. For the first time, a detailed study of the different wave coalescence processes involved in the generation of and waves is presented and the impact of density fluctuations on the wave interaction mechanisms is demonstrated. Energy ratios between the second, third, and fourth harmonics , , and are consistent with space observations. It is shown that, in both homogeneous and inhomogeneous plasmas, the dominant processes generating () are the coalescence of () with a Langmuir wave, in spite of the random density fluctuations modifying the waves’ resonance conditions by energy transport in the wavevector space and of the damping of Langmuir waves. The role of the backscattered (forward-propagating) Langmuir waves coming from the first (second) cascade of the electrostatic decay of beam-driven Langmuir waves is determinant in these processes. Understanding such wave coalescence mechanisms can provide indirect information on Langmuir and ion acoustic wave turbulence, the average level of density inhomogeneities, and suprathermal electron fluxes generated in solar wind regions where the harmonics manifest. Causes for the rarity of their observations are discussed.

Fundamental Electromagnetic Emissions by a Weak Electron Beam in Solar Wind Plasmas with Density Fluctuations

Abstract The generation of Langmuir wave turbulence by a weak electron beam in a randomly inhomogeneous plasma and its subsequent electromagnetic radiation are studied owing to two-dimensional particle-in-cell simulations in conditions relevant to type III solar radio bursts. The essential impact of random density fluctuations of average levels of a few percents of the background plasma on the characteristics of the electromagnetic radiation at the fundamental plasma frequency ω p is shown. Not only wave nonlinear interactions but also processes of Langmuir waves’ transformations on the density fluctuations contribute to the generation of such emissions. During the beam relaxation, the amount of electromagnetic energy radiated at ω p in a plasma with density fluctuations strongly exceeds that observed when the plasma is homogeneous. The fraction of Langmuir wave energy involved in the generation of electromagnetic emissions at ω p saturates around 10−4, i.e., one order of magnitude above that reached when the plasma is uniform. Moreover, whereas harmonic emission at 2ω p dominates over fundamental emission during the time evolution in a homogeneous plasma, fundamental emission is strongly dominant when the plasma contains density fluctuations, at least during several thousands of plasma periods before being overcome by harmonic emission when the total electromagnetic energy begins to saturate.

Dynamics of Langmuir Wave Spectra in Randomly Inhomogeneous Solar Wind Plasmas

Abstract Solar coronal and wind plasmas often contain density fluctuations of various scales and amplitudes. The scattering of Langmuir wave turbulence on these inhomogeneities modifies the properties of the radiated electromagnetic emissions traveling from the Sun to the Earth. This paper shows the similarities between the physical results obtained by (i) a model based on the Zakharov equations, describing the self-consistent dynamics of Langmuir wave turbulence spectra in a plasma with external density fluctuations, and (ii) a modeling, within the framework of geometric optics approximation, of quasi-particles (representing plasmon quanta) moving in a fluctuating potential. It is shown that the dynamics of the Langmuir spectra is governed by anomalous diffusion processes, as a result of multiple scattering of waves on the density fluctuations; the same dynamics are observed in the momenta distributions of quasi-particles moving in potential structures with random inhomogeneities. These spectra and distributions are both characterized by a fast broadening during which energy is transported to larger wavevectors and momenta, exhibiting nonlinear time dependence of the average squares of wavevectors and quasi-particle momenta as well as non-Gaussian tails in the asymptotic stage. The corresponding diffusion coefficients depend on the time and are proportional to the square of the average level of density (or potential) fluctuations. It appears that anomalous transport and superdiffusion phenomena are responsible for the spectral broadening.

Electromagnetic radiation from upper-hybrid wave turbulence in inhomogeneous solar plasmas

Type III solar radio bursts have been commonly observed in the solar wind and coronal plasmas. Electron beams accelerated in the Sun’s atmosphere generate weakly magnetized Langmuir (upper-hybrid) wave turbulence producing in turn electromagnetic emissions at the electron plasma frequency ωp and its harmonic 2ωp, via successive processes involving interactions between the background plasma, the waves and the beam particles. The impact of the random density fluctuations inherent to the background plasma on these processes requires the development of novel approaches and models. Owing to a new theoretical modeling, the radiation efficiency of electromagnetic waves radiated at ωp from a plasma source with random density fluctuations and developed upper-hybrid wave turbulence is calculated analytically and numerically. It is shown that the maximum radiation efficiency at frequency ωp scales as the average level of density fluctuations and as the ratio (c/vT)–2 (where vT is the thermal velocity). These scaling laws are found owing to two different and novel methods of determination of the electromagnetic radiation by turbulent inhomogeneous plasma sources through waves’ transformations on randomly fluctuating density irregularities. These results contribute significantly to the understanding of the processes involved in the generation of Type III solar radio bursts. Their presentation is preceded by a summary of previous studies on the dynamics of beam-driven Langmuir turbulence in inhomogeneous solar plasmas.

Turbulence and Microprocesses in Inhomogeneous Solar Wind Plasmas

The random density fluctuations observed in the solar wind plasma crucially influence on the Langmuir wave turbulence generated by energetic electron beams ejected during solar bursts. Those are powerful phenomena consisting of a chain of successive processes leading ultimately to strong electromagnetic emissions. The small-scale processes governing the interactions between the waves, the beams and the inhomogeneous plasmas need to be studied to explain such macroscopic phenomena. Moreover, the complexity induced by the plasma irregularities requires to find new approaches and modelling. Therefore theoretical and numerical tools were built to describe the Langmuir wave turbulence and the beam’s dynamics in inhomogeneous plasmas, in the form of a self-consistent Hamiltonian model including a fluid description for the plasma and a kinetic approach for the beam. On this basis, numerical simulations were performed in order to shed light on the impact of the density fluctuations on the beam dynamics, the electromagnetic wave radiation, the generation of Langmuir wave turbulence, the waves’ coupling and decay phenomena involving Langmuir and low frequency waves, the acceleration of beam electrons, their diffusion mechanisms, the modulation of the Langmuir waveforms and the statistical properties of the radiated fields’ distributions. The paper presents the main results obtained in the form of a review.

Electromagnetic Wave Emissions from a Turbulent Plasma with Density Fluctuations

Abstract In the solar wind, Langmuir turbulence can generate electromagnetic waves at the fundamental plasma frequency ω p . This process can likely result from either linear wave transformations on the ambient random density inhomogeneities or resonant three-wave interactions involving Langmuir waves and ion acoustic oscillations. In the presence of sufficiently intense plasma density fluctuations of scales much larger than the Langmuir wavelengths, the first mechanism may be more efficient than the second one. A new approach to calculate the electromagnetic wave emissions by Langmuir wave turbulence in plasmas with background density fluctuations is developed. The evolution of the Langmuir turbulence is studied by numerically solving the Zakharov equations in such a two-dimensional plasma. The dynamics of the spatial distributions of the electric currents with frequencies close to ω p is calculated, as well as their emission into electromagnetic waves. The efficiency of this radiation is determined as a function of the level of the Langmuir turbulence, the characteristics of the density fluctuations, the background plasma temperature, the position of the satellite receiver, and the durations of the source’s emissions and spacecraft’s observations. The results obtained by the theoretical modeling and numerical simulations are successfully compared with space observations of electromagnetic waves radiated during Type III solar radio bursts.

Identification of Langmuir wave turbulence-supercontinuum transition by application of von Neumann entropy

A transition from Langmuir wave turbulence (LWT) to coherent Langmuir wave supercontinuum (LWSC) is identified in one-dimensional particle-in-cell simulations as the emergence of a broad frequency band showing significant temporal coherence of a wave field accompanied by a decrease in the von Neumann entropy of classical wave fields. The concept of the von Neumann entropy is utilized for evaluation of the phase-randomizing degree of the classical wave fields, together with introduction of the density matrix of the wave fields. The transition from LWT to LWSC takes place when the energy per one plasmon (one wave quantum) exceeds a certain threshold. The coherent nature, which Langmuir wave systems acquire through the transition, is created by four wave mixings of the plasmons. The emergence of temporal coherence and the decrease in the phase randomization are considered as the development of long-range order and spontaneous symmetry breaking, respectively, indicating that the LWT-LWSC transition is a secon...

THE EFFECTS OF ELECTRON-BEAM-INDUCED ELECTRIC FIELD ON THE GENERATION OF LANGMUIR TURBULENCE IN FLARING ATMOSPHERES

The precipitation of an electron beam injected into the solar atmosphere is studied for the generation of Langmuir wave turbulence in the presence of collisional and Ohmic losses. The system of quasi-linear time-dependent kinetic equations describing the evolution of beams and Langmuir waves is solved by using the summary approximation method. It is found that at upper atmospheric levels the self-induced electric field suppresses the generation of Langmuir turbulence to very small regions below injection. With further precipitation into deeper atmosphere the initial single power-law distributions of beam electrons are transformed into energy distributions with maxima at lower energies formed by collisional and Ohmic energy depletion. The electrons with lower energies (<20 keV) generate on large spatial scales intense low-hybrid and high-hybrid Langmuir waves with well-defined patterns in the corona while higher energy electrons generate moderate low-hybrid waves in the chromosphere. The maximum wave density appears at the maximum of the ambient density. The self-induced electric field reduces the level and makes the regions with low-hybrid Langmuir turbulence narrower in the corona and upper chromosphere. The higher the beam energy flux or its self-induced electric field, the narrower the regions with Langmuir turbulence. High-hybrid Langmuir waves in the form of multiple patterns in space (in the corona) and energy (below 20 keV) are found to be generated only by a very intense electron beam. The number of patterns in both dimensions is also shown to be significantly reduced by the self-induced electric field.

Full-scale simulation study of stimulated electromagnetic emissions: The first ten milliseconds

AbstractA full-scale numerical study is performed of the nonlinear interaction between a large-amplitude electromagnetic wave and the Earth's ionosphere, and of the stimulated electromagnetic emission emerging from the turbulent layer, during the first 10 milliseconds after switch-on of the radio transmitter. The frequency spectra are downshifted in frequency and appear to emerge from a region somewhat below the cutoff of the O mode, which is characterized by Langmuir wave turbulence and localized Langmuir envelopes trapped in ion density cavities. The spectral features of escaping O-mode waves are very similar to those observed in experiments. The frequency components of Z-mode waves, trapped in the region between the O- and Z-mode cutoffs show strongly asymmetric and downshifted spectra.

THE EFFECT OF WAVE-PARTICLE INTERACTIONS ON LOW-ENERGY CUTOFFS IN SOLAR FLARE ELECTRON SPECTRA

Solar flare hard X-ray spectra from RHESSI are normally interpreted in terms of purely collisional electron beam propagation, ignoring spatial evolution and collective effects. In this paper we present self-consistent numerical simulations of the spatial and temporal evolution of an electron beam subject to collisional transport and beam-driven Langmuir wave turbulence. These wave-particle interactions represent the background plasma's response to the electron beam propagating from the corona to chromosphere and occur on a far faster timescale than coulomb collisions. From these simulations we derive the mean electron flux spectrum, comparable to such spectra recovered from high resolution hard X-rays observations of solar flares with RHESSI. We find that a negative spectral index (i.e. a spectrum that increases with energy), or local minima when including the expected thermal spectral component at low energies, occurs in the standard thick-target model, when coulomb collisions are only considered. The inclusion of wave-particle interactions does not produce a local minimum, maintaining a positive spectral index. These simulations are a step towards a more complete treatment of electron transport in solar flares and suggest that a flat spectrum (spectral index of 0 to 1) down to thermal energies maybe a better approximation instead of a sharp cut-off in the injected electron spectrum.

Excitation and diagnosis of cascading Langmuir waves in ionospheric plasmas at Gakona, Alaska

Ionospheric plasma heating experiments were conducted at Gakona, Alaska to investigate cascading spectra of Langmuir wave turbulence, excited by parametric instabilities diagnosed by Modular UHF Ionospheric Radar (MUIR). This work is aimed at testing the recent theory of Kuo and Lee (2005 J. Geophys. Res. 110 A01309) that addresses how the cascade of Langmuir waves can distribute spatially via the resonant and non-resonant decay processes. The non-resonant cascade proceeds at the location where parametric decay instability (PDI) or oscillating two-stream instability (OTSI) is excited and severely hampered by the frequency mismatch effect. By contrast, the resonant cascade, which takes place at lower matching heights, has to overcome the propagation loss of the Langmuir pump waves in each cascade step. Our experimental results have corroborated these predictions about the generation of cascading Langmuir waves by the HAARP heater.

Study of plasma–maser instability in an inhomogeneous plasma

The plasma–maser, an interesting nonlinear process in plasmas, is an effective means of energy up-conversion in frequency from low-frequency turbulence to a high-frequency wave. A theoretical study is made of the amplification mechanism of an electrostatic Bernstein mode wave in presence of Langmuir wave turbulence in a magnetized inhomogeneous plasma on the basis of a plasma–maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Langmuir wave turbulence. The growth rate of a test high-frequency Bernstein mode wave is calculated with the involvement of a spatial density gradient parameter. A comparative study on the role of density gradient in the generation of the Bernstein mode on the basis of the plasma–maser effect is presented.

Formation of quasi-power law weak Langmuir turbulence spectrum by harmonic generation

Abstract. Langmuir wave turbulence generated by a beam-plasma interaction has been studied since the early days of plasma physics research. Despite a long history of investigation on this subject, among the outstanding issues is the generation of harmonic Langmuir waves observed in both laboratory and computer-simulated experiments. However, the phenomenon has not been adequately explained in terms of theory, nor has it been fully characterized by means of numerical simulations. In this paper, a theory of harmonic Langmuir wave generation is put forth and tested against the Vlasov simulation results. It is found that the harmonic Langmuir mode spectra exhibit quasi power-law feature implying a multi-scale structure in both frequency and wave number space spanning several orders of magnitude.

Harmonic Langmuir waves. II. Turbulence spectrum

The Langmuir wave turbulence generated by a beam–plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi-power-law spectrum for Langmuir waves have been investigated, since such a spectrum defines the turbulence characteristics. Meanwhile, the generation of harmonic Langmuir modes during the beam–plasma interaction has been known for quite some time, and yet has not been satisfactorily accounted for thus far. In paper I of this series, nonlinear dispersion relations for these harmonics have been derived. In this paper (paper II), generalized weak turbulence theory which includes multiharmonic Langmuir modes is formulated and the self-consistent particle and wave kinetic equations are solved. The result shows that harmonic Langmuir mode spectra can indeed exhibit a quasi-power-law feature, implying multiscale structure in both frequency and wave number space spanning several orders of magnitude.

Nonlinear development of electron-beam-driven weak turbulence in an inhomogeneous plasma.

The self-consistent description of Langmuir wave and ion-sound wave turbulence in the presence of an electron beam is presented for inhomogeneous nonisothermal plasmas. Full numerical solutions of the complete set of kinetic equations for electrons, Langmuir waves, and ion-sound waves are obtained for an inhomogeneous unmagnetized plasma. The results show that the presence of inhomogeneity significantly changes the overall evolution of the system. The inhomogeneity is effective in shifting the wave numbers of the Langmuir waves, and can thus switch between different processes governing the weakly turbulent state. The results can be applied to a variety of plasma conditions, where we choose solar coronal parameters as an illustration, when performing the numerical analysis.

Langmuir wave turbulence transition in a model of stimulated Raman scatter

In a one-dimensional stationary slab model, it is found that once the stimulated Raman scatter (SRS) homogeneous growth rate, γ0, exceeds a threshold value, γT, there exists a local, finite amplitude instability, which leads to Langmuir wave turbulence (LWT). Given energetic enough initial conditions, this allows forward SRS, a linearly convective instability, to be nonlinearly self-sustaining for γ0&amp;gt;γT. Levels of forward scatter, much larger than predicted by the linear amplification of thermal fluctuations, are then accessible. The Stochastic quasilinear Markovian (SQM) model of SRS interacting with LWT predicts a jump in the value of 〈ε〉, the mean energy injection rate from the laser to the plasma, across this threshold, while one-dimensional plasma slab simulations reveal large fluctuations in ε, and a smooth variation of 〈ε〉 with γ0. Away from γT, 〈ε〉 is well predicted by the SQM. If a background density ramp is imposed, LWT may lead to loss of SRS gradient stabilization for γ0≪γT.

A test-bed for Langmuir wave turbulence modeling of stimulated Raman backscatter

Stimulated Raman backscatter (SRS) may incorporate several, qualitatively different regimes of Langmuir wave dynamics, as it grows convectively in space. These typically include a strictly linear regime at the far end of the plasma from the laser, where SRS comes up from thermal Langmuir wave fluctuations; which may progress to a regime where the primary SRS daughter Langmuir wave is unstable to the Langmuir wave decay instability (LDI); and perhaps to a regime of strong Langmuir wave turbulence (SLT). The accurate description of the spatial transition between these regimes, which may involve large Langmuir wave correlation lengths, is a great challenge for turbulence modeling. In this paper a highly idealized model of SRS in periodic geometry is introduced which allows for the presence of a unique Langmuir wave regime for a given set of physical parameters, and therefore presents the minimal challenge for a turbulence model. One- and two-dimensional simulations of this SRS model, which allows for LDI and SLT as described by Zakharov’s model of nonlinear Langmuir wave dynamics, are compared with the predictions of a recently introduced turbulence model, and quantitative agreement is obtained, without the use of any ad hoc parameters, for the SRS reflectivity and correlation length, and Langmuir and acoustic wave energy densities, over an order of magnitude variation of SRS growth rate and ion acoustic damping rate.