Decay Of Langmuir Waves Research Articles

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.

Laser-Plasma Interaction Experiment for Solar Burst Studies.

A new experimental platform based on laser-plasma interaction is proposed to explore the fundamental processes of wave coupling at the origin of interplanetary radio emissions. It is applied to the study of electromagnetic (EM) emission at twice the plasma frequency (2ω_{p}) observed during solar bursts and thought to result from the coalescence of two Langmuir waves (LWs). In the interplanetary medium, the first LW is excited by electron beams, while the second is generated by electrostatic decay of Langmuir waves. In the present experiment, instead of an electron beam, an energetic laser propagating through a plasma excites the primary LW, with characteristics close to those at near-Earth orbit. The EM radiation at 2ω_{p} is observed at different angles. Its intensity, spectral evolution, and polarization confirm the LW-coalescence scenario.

Langmuir wave decays into O-mode and ICW in Earth's magnetosphere with inhomogeneous magnetic field

The parametric decay of Langmuir waves into ordinary waves (O-mode) and low frequency ion cyclotron waves is studied in the Earth's magnetosphere plasma. An evolution of a density gradient due to the non-uniform ambient magnetic field is taken care of. The fluid model is employed to investigate the linear and nonlinear responses of plasma species to the coupled field of three waves in magneto-plasmas. It is observed that the magnetic field gradient modifies the dispersion relations of both electrostatic and electromagnetic waves. The nonlinear growth rate of the parametric instability is calculated by coupling the dispersion relations of pump and side band modes. The normalized growth rate is analyzed numerically for different sets of parameters under typical conditions. It is noticed that the gradient in the magnetic field contributes as a significant energy source to enhance the growth rate of the three wave interaction.

Parametric decay of wide band Langmuir wave spectra

Previous results obtained for modulational instability of a Langmuir wave spectrum are extended to account also for the Langmuir wave decay. The general model is tested by considering first the parametric decay of single-mode Langmuir waves, and also two-wave models, where several combinations are considered: one wave is modulationally unstable, another decay unstable and one where both waves are unstable with respect to decay. For the general case with continuous wave spectra it is found that distribution of the Langmuir wave energy over a wide wavenumber band reduces the decay rate when the correlation length for the spectrum becomes comparable to the wavelength of the most unstable sound wave among the possible decay products.

Ion dynamics in electron beam–plasma interaction: particle-in-cell simulations

Abstract. Electron beam–plasma interaction including ions is studied by particle-in-cell (PIC) simulations using a one-dimensional, electrostatic code. Evidence for Langmuir wave decay is given for sufficiently energetic beams, as in previous Vlasov–Maxwell simulations. The mechanism for the generation of localized finite-amplitude ion density fluctuations is analyzed. Amplitude modulation due to interference between the beam-generated Langmuir waves causes random wave localization including strong transient spikes in field intensity which create bursty ion density structures via ponderomotive forces. More dense beams may quench the decay instability and generate low-frequency variations dominated by the wave number of the fastest growing Langmuir mode.

Exact evaluation of the rates of electrostatic decay and scattering off thermal ions for an unmagnetized Maxwellian plasma

Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α(2) (or, equivalently, the quadratic longitudinal susceptibility χ(2)), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α(2) that is valid where two of the wave fields are fast (i.e., vϕ=ω/k≫Ve where ω is the angular frequency, k is the wavenumber, and Ve is the electron thermal speed) and one is slow (vϕ≪Ve). Recently, an exact expression was derived for α(2) that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α(2) is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α(2), and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (vϕ/Ve≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay and scattering off thermal ions are calculated for a range of parameters using the exact expressions for the rates; electrostatic decay is found to have the larger growth rate over the whole range of parameters, consistent with previous approximate calculations.

Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.

Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines

Observations by, for instance, the EISCAT Svalbard Radar (ESR) demonstrate that the symmetry of the naturally occurring ion line in the polar ionosphere can be broken by an enhanced, nonthermal, level of fluctuations (naturally enhanced ion-acoustic lines, NEIALs). It was in many cases found that the entire ion spectrum can be distorted, also with the appearance of a third line, corresponding to a propagation velocity significantly slower than the ion acoustic sound speed. It has been argued that selective decay of beam excited primary Langmuir waves can explain some phenomena similar to those observed. We consider a related model, suggesting that a primary nonlinear process can be an oscillating two-stream instability, generating a forced low frequency mode that does not obey any ion sound dispersion relation. At later times, the decay of Langmuir waves can give rise also to enhanced asymmetric ion lines. The analysis is based on numerical results, where the initial Langmuir waves are excited by a cold dilute electron beam. By this numerical approach, we can detect fine details of the physical processes, in particular, demonstrate a strong space-time intermittency of the electron waves in agreement with observations. Our code solves the full Vlasov equation for electrons and ions, with the dynamics coupled through the electrostatic field derived from Poisson’s equation. The analysis distinguishes the dynamics of the background and beam electrons. This distinction simplifies the analysis for the formulation of the weakly nonlinear analytical model for the oscillating two-stream instability. The results have general applications beyond their relevance for the ionospheric observations.

Particle-in-cell simulation of incoherent scatter radar spectral distortions related to beam-plasma interactions in the auroral ionosphere

[1] An electrostatic parallel particle-in-cell (EPPIC) code that allows for particle beam injections and multiple boundary conditions is used to investigate the beam-plasma interaction and its manifestations in the incoherent scatter (IS) spectrum. Specifically, the code is used to investigate anomalous enhancements in the ion acoustic line through the destabilization of the plasma by injection (or precipitation) of low-energy electron beams. This enhancement of the ion acoustic line is a form of IS distortion commonly observed in the vicinity of auroral arcs called the naturally enhanced ion-acoustic line (NEIAL). Simulations confirm the parametric decay of Langmuir waves as a plausible mechanism, assuming a mechanism for the formation of dense low-energy (<10 eV) electron beams in the ionosphere. The spectral distortions are similar at aspect angles as large as ±15° from the beam direction. Simulations also show that the first Langmuir harmonic can have a power intensity higher than that of the ion acoustic line of a thermal plasma. Conditions which would allow the detection of Langmuir harmonics with existing incoherent scatter radars are discussed.

Theory of plasmon decay in dense plasmas and warm dense matters

The prevalent Landau damping theory for classical plasmas does not fully explain the Langmuir wave decay in dense plasmas. A dielectric function theory adapted from the condensed matter physics is extended to be applicable for the dense plasmas and warm dense matters. This theory, accounting for the Umklapp process, predicts much higher decay rates than the Landau damping theory, which results in better agreement with the available experimental data obtained from the metals. The detailed calculations are presented for the following four cases: classical plasmas, Maxwellian plasmas, degenerate quantum plasmas, and partially degenerate plasmas.

Plasmon band gap generated by intense ion acoustic waves

In the presence of an intense ion acoustic wave, the energy-momentum dispersion relation of plasmons is strongly modified to exhibit a band gap structure. The intensity of an ion acoustic wave might be measured from the band gap width. The plasmon band gap can be used to block the nonlinear cascading channel of the Langmuir wave decay.

Electromagnetic plasma emission during beam‐plasma interaction: Parametric decay versus induced scattering

Two‐dimensional electromagnetic particle‐in‐cell simulations are performed for examination of electromagnetic plasma emission at twice the electron plasma frequency. Electromagnetic “2fp” waves are considered to be excited by nonlinear three‐wave processes in beam‐plasma interactions. In this paper, nonlinear development of an electron‐beam‐plasma instability is studied as an initial value problem. The present simulation result confirmed that electromagnetic 2fp waves are strongly enhanced by the wave‐wave interaction between forward and backward Langmuir waves, which is in agreement with the previous studies. It is also demonstrated that large‐amplitude forward Langmuir waves decay into backward Langmuir waves and ion acoustic waves via a parametric decay and that electromagnetic 2fp waves are also enhanced by the decay of Langmuir waves. However, the growth rate of the electromagnetic 2fp waves due to the parametric decay of Langmuir waves is not as high. It should be noted that induced backscattering of Langmuir waves by enhanced thermal fluctuations of ions cannot be neglected in the excitation of backward Langmuir waves. Hence, low‐noise simulations are necessary to suppress the effect of enhanced thermal fluctuations in the particle‐in‐cell method.

Decay of beam-driven Langmuir wave into ion-acoustic turbulence in two dimensions

The decay of beam-generated Langmuir wave into another Langmuir wave and an ion-acoustic wave is a well-known problem with wide-ranging applications. However, most discussions in the literature are based upon simple one-dimensional approximation. Recently, the present authors carried out a fully self-consistent two-dimensional analysis of the beam-driven Langmuir wave decay problem. The main focus of the present authors' work to date had been on the nonlinear evolution of Langmuir turbulence and its influence on the electrons. Relatively little attention had been paid to the ion-acoustic wave generation. In the present discussion, the focus is placed on the dynamics of ion-acoustic turbulence that results from the decay of beam-generated Langmuir wave. The present analysis considers three electron components, the dense core, a primary beam and a counter-streaming beam. We find that the ion-sound turbulence level sensitively depends on the properties of the counter-streaming beam.

An optical study of multiple NEIAL events driven by low energy electron precipitation

Abstract. Optical data are compared with EISCAT radar observations of multiple Naturally Enhanced Ion-Acoustic Line (NEIAL) events in the dayside cusp. This study uses narrow field of view cameras to observe small-scale, short-lived auroral features. Using multiple-wavelength optical observations, a direct link between NEIAL occurrences and low energy (about 100 eV) optical emissions is shown. This is consistent with the Langmuir wave decay interpretation of NEIALs being driven by streams of low-energy electrons. Modelling work connected with this study shows that, for the measured ionospheric conditions and precipitation characteristics, growth of unstable Langmuir (electron plasma) waves can occur, which decay into ion-acoustic wave modes. The link with low energy optical emissions shown here, will enable future studies of the shape, extent, lifetime, grouping and motions of NEIALs.

Dynamics of Langmuir wave decay in two dimensions

The present paper reports on the first two-dimensional (2D) self-consistent solution of weak turbulence equations describing the evolution of electron-beam-plasma interaction in which quasilinear as well as nonlinear three-wave decay processes are taken into account. It is found that the 2D Langmuir wave decay processes lead to the formation of a quasicircular ring spectrum in wave number space. It is also seen that the 2D ring-spectrum of Langmuir turbulence leads to a tendency to isotropic heating of the electrons. These findings contain some important ramifications. First, in the literature, isotropization of energetic electrons, detected in the solar wind for instance, is usually attributed to pitch-angle scattering. The present finding constitutes an alternative mechanism, whose efficiency for other parametric regimes has to be investigated. Second, when projected onto the one-dimensional (1D) space, the 2D ring spectrum may give a false impression of Langmuir waves inverse cascading to longer wavelength regime, when in reality, the wavelength of the turbulence does not change at all but only the wave propagation angle changes. Although the present analysis excludes the induced scattering, which is another process potentially responsible for the inverse cascade, the present finding at least calls for an investigation into the relative efficacy of the inverse-cascading process in 1D vs 2D.

Resonant excitation of counterpropagating surface waves at a Langmuir wave decay

A study is made of the resonant excitation of surface waves via the decay of a Langmuir wave propagating perpendicularly to a plasma-dielectric interface. The excitation dynamics in the initial stage of decay instability is studied, expressions for the growth rates are obtained, and the threshold amplitude of the Langmuir wave above which parametric instability occurs is found.

Nonlinear decay of foreshock Langmuir waves in the presence of plasma inhomogeneities: Theory and Cluster observations

The intense high‐frequency electrostatic waves observed in the terrestrial foreshock often have a form of a superposition of two monochromatic waves close to the plasma frequency. We suggest an interpretation of these spectra as signatures of nonlinear decay of Langmuir waves to electron‐sound and ion‐sound secondary waves. This decay instability is known to have different properties in inhomogeneous plasma, namely the threshold amplitude of this instability is inversely proportional to the scale of the inhomogeneity. We show that the observed dependence of the wave amplitude on the modulation scale of the wave packets is consistent with this property and the theory of absolute decay instability in inhomogeneous plasma can be applied to explain the satellite observations. In this study we used electric field data from the Wide Band Data instrument on board Cluster satellites.

Langmuir wave self-focusing versus decay instability

Electron trapping in a finite amplitude Langmuir wave (LW) leads to a frequency shift, \Delta\omega_{TP} < 0, and reduced Landau damping. These may lead to modulational instability. Its growth rate and damping threshold, due to escape of trapped electrons at rate \nu, are calculated for the first time in the short wavelength regime. If the background plasma is in thermal equilibrium, it is shown that this trapped particle modulational instability (TPMI) is not possible when k \lambda_D > 0.46, while for 0.33 < k \lambda_D < 0.46, TPMI requires that the fluctuation wavevector have a component perpendicular to k, the LW wavevector, with \lambda_D the electron Debye length. Its nonlinear evolution leads to self-focusing. Comparison is made with a re-evaluated LW ion acoustic decay instability (LDI): compared to classical estimates, the new LDI threshold is lowered by primary LW \Delta\omega_{TP} since frequency matching leads to wavenumber and hence damping reduction of the daughter LW. For parameters estimates relevant to a recent stimulated Raman scatter experiment (Kline et al., submitted to PRL), the LDI and TPMI thresholds cross in the range 0.28 < k \lambda_D < 0.34, consistent with the observed LDI regime change. However, if \nu exceeds a critical value, estimated to be order 1% of the electron plasma frequency, then TPMI is not possible at any wavenumber.

Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data

Abstract. We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena)

Evidence for electrostatic decay in the solar wind at 5.2 AU

The Unified Radio and Plasma wave Experiment (URAP) on the Ulysses spacecraft provides in situ observations of Langmuir waves and ion‐acoustic waves in the solar wind. The observations presented in this paper were obtained at 5.2 AU from the Sun. Low‐frequency (20–200 Hz in the spacecraft frame) electric field signals are observed coincident in time with the most intense Langmuir waves. The low‐frequency wave signals are identified as long‐wavelength ion‐acoustic waves. These observations provide evidence for the decay of Langmuir waves into daughter Langmuir and ion‐acoustic waves (the electrostatic decay process) in the solar wind.