Intense Langmuir Waves Research Articles

A search for Langmuir solitons in the Earth's foreshock

The Earth's foreshock region, the region which is magnetically connected to the bow shock, is a region of intense Langmuir waves. Some of these waves have an envelope similar to that expected for one‐dimensional Langmuir solitons. A computer search for such waveforms has identified a number sufficient for statistical investigation. It is concluded that there is no evidence for stable waveforms like one‐dimensional Langmuir solitons.

Ion Acoustic Wave Frequencies and Onset Times during Type III Solar Radio Bursts

Conflicting interpretations exist for the low-frequency ion acoustic (S) waves often observed by ISEE 3 in association with intense Langmuir (L) waves in the source regions of type III solar radio bursts near 1 AU. Two indirect lines of observational evidence, as well as plasma theory, suggest they are produced by the electrostatic (ES) decay L yields L(PRIME) + S. However, contrary to theoretical predictions, an existing analysis of the wave frequencies instead favors the electromagnetic (EM) decays L yields T + S, where T denotes an EM wave near the plasma frequency. This conflict is addressed here by comparing the observed wave frequencies and onset times with theoretical predictions for the ES and EM decays, calculated using the time-variable electron beam and magnetic field orientation data, rather than the nominal values used previously. Field orientation effects and beam speed variations are shown analytically to produce factor-of-three effects, greater than the difference in wave frequencies predicted for the ES and EM decays; effects of similar magnitude occur in the events analyzed here. The S-wave signals are extracted by hand from a sawtooth noise background, greatly improving the association between S waves and intense L waves. Very good agreement exists between the time-varying predictions for the ES decay and the frequencies of most (but not all) wave bursts. The waves occur only after the ES decay becomes kinematically allowed, which is consistent with the ES decay proceeding and producing most of the observed signals. Good agreement exists between the EM decay's predictions and a significant fraction of the S-wave observations while the EM decay is kinematically allowed. The wave data are not consistent, however, with the EM decay being the dominant nonlinear process. Often the observed waves are sufficiently broadband to overlap simultaneously the frequency ranges predicted for the ES and EM decays. Coupling the dominance of the ES decay with this frequency overlap provides support for a previous suggestion that fundamental emission occurs when the EM decay is stimulated by the ES decay product waves. The periods in which the ES and EM decays produce observable S waves are consistent with the observed and (independently) predicted times of fundamental and harmonic radio emission. This supports interpretation of fundamental emission as stimulated EM decay and harmonic emission as the coalescence L + L(prime) yields T of beam-generated L waves and L(prime) waves produced by the ES decay, where T denotes an electromagnetic wave at twice the plasma frequency. Analysis of the electron beam data reveals that the time-varying beam speed is consistent with ballistic beam propagation with minimal energy loss, implying that the beam propagates in a state close to time- and volume-averaged marginal stability. This confirms a central tenet of the stochastic growth theory for type III bursts.

Langmuir turbulence in moderately magnetized space plasmas*

Beam-driven Langmuir turbulence is studied in two moderately magnetized (Ωe≊ωe) space-plasma regimes: regions of the lower solar corona and the Earth’s auroral ionosphere. The turbulence is modeled using modified Zakharov equations, which are employed in two-dimensional numerical simulations. For coronal parameters, highly anisotropic coherent wave packets form and collapse when Ωe<ωe. By contrast, the turbulence is phase incoherent when Ωe≳ωe, as a result of change in the topology of the Langmuir dispersion relation. In the auroral ionosphere, intense Langmuir waves (up to 500 mV/m) have been measured, in conjunction with field-aligned electron streams and nonthermal electron tails. Approximate agreement with high-time-resolution electric-field measurements, is found in the simulations. However, because of strong damping on nonthermal electrons, wave collapse is inhibited, irrespective of the ordering of Ωe and ωe.

Langmuir turbulence in the auroral ionosphere: 2. Nonlinear theory and simulations

A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (≤ 500 mV/m) driven by a stream of 20 eV ‐ 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 µs sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam‐driven Langmuir turbulence in the presence of a moderate magnetic field (Ωe ≈ ωpe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream‐driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.

Evaluation of Emission Mechanisms at omega P E Using ULYSSES Observations of Type III Bursts

We present the first observational tests of existing theories for the generation of type III radio bursts emitting at the fundamental plasma frequency, ω pe . This study is based on local radio emission and in situ wave phenomena associated with four interplanetary type III radio bursts observed by the unified radio and plasma wave experiment on the Ulysses spacecraft. Intense Langmuir wave peaks with energy densities and rapid time variations indicative of Langmuir solitons are observed for some events. Low-frequency waves below 500 Hz are not observed

Fine structure of Langmuir waves produced by a solar electron event

Highly structured bursts of Langmuir waves produced by energetic electrons ejected from a solar flare have been observed using wideband plasma wave measurements on the Galileo spacecraft. The wideband sampling system on Galileo provides digital electric field waveforms at sampling rates up to 201,600 samples s−1, much higher than any previous instrument of this type. The solar flare of interest occurred on December 10, 1990, while the spacecraft was at a radial distance of 0.98 AU from the Sun. This flare emitted a stream of energetic electrons and an associated type III radio event, both of which were detected by Galileo. Starting about 1 hour after the onset of the flare, a large number of intense Langmuir wave bursts were detected near the local electron plasma frequency, which was about 25 kHz. The Langmuir wave bursts, which lasted about 1.5 hours, coincided with the arrival of the solar electrons. The bursts are highly structured and consist mainly of isolated wave packets with durations as short as 1 ms and beat‐type waveforms with beat frequencies ranging from 200 to 500 Hz. The peak electric field strengths are about 1.7 mV m−1. The highly structured envelopes of these waves are strongly suggestive of nonlinear parametric decay processes such as those predicted by various theories dealing with the saturation of beam‐driven electrostatic instabilities. However, the intensities are too low for strong turbulence effects to be important.

Electromagnetic radiation emitted by supersonic Langmuir turbulence in active experiments in space

Experimental evidence of supersonic Langmuir turbulence has been reported by Pulinets and Selegey (1986; J. atmos. terr. Phys. 48, 149) and Shuiskaya et al. (1987; Report, Space Research Institute of the U.S.S.R.) in the vicinity of a satellite when high-power radio waves were transmitted for topside sounding of the ionosphere. It is shown that, in the presence of supersonic Langmuir turbulence, electromagnetic radiation near the local electron plasma frequency can be emitted through the electromagnetic parametric instabilities driven by intense Langmuir waves. The growth rates of these electromagnetic parametric instabilities are shown to be identical to the corresponding growth rates of the electrostatic Langmuir parametric instabilities. It is suggested that the stimulated electromagnetic emission can become a useful diagnostic technique for active experiments in space.

Langmuir wave growth and electron bunching: Results from a wave‐particle correlator

Recent measurements of auroral electrons and intense Langmuir waves on a high‐altitude sounding rocket show that these waves were produced by dispersive bursts of low‐energy electrons. The sounding rocket was launched northward into the evening auroral zone during a substorm expansion and crossed several discrete auroral arcs having electron energy peaks greater than 25 keV. The large‐amplitude Langmuir waves, which appeared in ∼ 100‐ms bursts and had amplitudes greater than 200 mV/m, were seen only during periods of enhanced low‐energy (0.3–3.0 keV), field‐aligned electron precipitation. The enhanced electron flux displayed a dispersive signature in which the higher‐energy electrons arrived before the lower‐energy electrons. A wave‐particle correlator, a new instrument that performed a direct correlation of the arrival times of electrons with the phase of the high‐frequency wave field, detected electron bunching at the wave frequency during the bursts of intense Langmuir waves. The electron bunching events, which had amplitudes of a few percent, provided a direct identification of the energy (velocity) of the resonant electrons and therefore established the parallel wavelength (∼15 m). The electron bunching events were detected at or near the energy at which a positive slope in the electron distribution function was seen. During a dispersive burst, the phase velocity (or wavelength) of the Langmuir waves changed in response to the changing velocity at which the positive slope occurred. We conclude that the velocity dispersion in the low‐energy, field‐aligned electrons created the unstable electron distribution that was responsible for Langmuir wave growth. The proposed growth mechanism is similar to that suggested for Langmuir wave growth during solar type III radio bursts.

On plasma processes in the solar corona

Abstract This paper reviews theoretical research on the solar corona performed in Brazil. Three coronal processes are discussed: (1) coronal heating by surface Alfven waves, (2) coronal heating by global Alfven waves, and (3) generation of type III radio emission. The surface Alfven waves can power, directly, at least 10% of the required coronal flux density; in the case of mode conversion into kinetic Alfven waves the bulk of energy flux density can be provided. The global waves can power at least 20% of the required coronal energy flux density. It is shown that the electromagnetic oscillating two-stream instability driven by intense Langmuir waves, can be a likely generation mechanism of type −III radio bursts.

Two-component model of strong Langmuir turbulence: Scalings, spectra, and statistics of Langmuir waves

A two-component model of strong Langmuir turbulence is developed, in which intense coherent Langmuir wave packets nucleate from and collapse amid a sea of low-level background waves. Power balance between these two components determines the overall scalings of energy density and power dissipation in the turbulence, and of the rate of formation, number density, volume fraction, and characteristic nucleation time of collapsing wave packets. Recent insights into the structure and evolution of collapsing wave packets are employed to estimate the spectra and field statistics of the turbulence. Extensive calculations using the Zakharov equations in two and three dimensions demonstrate that the predictions of the model are in excellent agreement with numerical results for scalings, spectra, and the distribution of fields in the turbulence in isotropic systems; strong support is thus found for the nucleation model. The scaling behavior proves to be insensitive to the form of the damping of the waves at large wave numbers. Wave collapse is approximately inertial between the nucleation and dissipation scales, yielding power-law energy spectra and field distributions in this range. The existence of a fixed arrest scale manifests itself in exponentially decreasing energy and dissipation spectra at high wave numbers and exponentially decreasing field distributions at high field strengths. It is suggested that such an exponential decrease may explain the field distributions seen in recent beam–plasma experiments. Generalizations to turbulence driven anisotropically by beams or governed by equations other than the Zakharov equations are outlined. It is shown that a previously unrecognized scaling observed in beam-driven systems is correctly predicted by the generalized model.

Wavenumber-in-cell simulation of weak Langmuir turbulence.

A wave-number-in-cell code was developed for simulation of a model proposed by Vendenov, Gordeev, and Rudakov for studying weak Langmuir turbulence. The model uses a WKB approach for describing the Langmuir wave field. Theoretical results for damping of ion acoustic waves caused by resonant interaction of Langmuir waves with group velocity around the sound speed were confirmed. Simulations corresponding to an initial condition with an intense wave burst demonstrate a formation of almost stationary localized cavities of intense wideband self-trapped Langmuir wave fields. These cavities have features in common with phase-space vortices.

Dynamics of intense Langmuir waves in current-carrying plasmas

Basic equations including ponderomotive effects of Langmuir waves in a current-carrying plasma are presented. In such a system, dynamics of an initially monochromatic plasma wave is investigated both analytically and numerically. Various regimes of developed modified decay and modulational instabilities of the wave are modelled by using a macroparticle numerical code. In this way the cooperative nature of both ponderomotive and drift effects supporting plasma heating is demonstrated. The underlying physical processes are discussed and relation to the solar flare theory is suggested.

Solar flares and the dynamics of Langmuir waves in current-carrying plasmas

The dynamics of intense Langmuir waves in current-carrying plasmas is studied both analytically and numerically. Starting with the widely used Zakharov equations, adapted to these systems, specific features of this problem are pointed out. Further, the role of resonant particles is analyzed. By using 1-D macroparticle numerical code, nonlinear regimes of the modified-decay and modulational instabilities are then modelled. Efficient cooperation of essentially ponderomotive and electron-ion drift effects its demonstrated. It appears that the heating of a current-carrying plasma can be activated through releasing of the inductively stored energy, due to the enhanced conversion of energy associated with the electron drift motion. The underlying physics is discussed and its relationship to solar flare theory is suggested.

Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system

The mechanism by which unstable electron plasma waves are converted into electromagnetic waves in a uniform plasma is investigated. Electromagnetic radiation is generated upon injection of an electron beam (500 eV) into a collisionless quiescent magnetoplasma (ne ≲1012 cm−3, kTe ≊2 eV). The emission (ω0) is observed to peak near the plasma frequency (ωp) which is well above the cyclotron frequency (ωc ≪ωp≲ω0). It is shown that electromagnetic waves (ω0, k0) are produced by the scattering of electrostatic plasma waves (ωe, ke) off self-consistently produced ion-acoustic waves (ωi, ki). At low beam intensities the frequency and wave vector matching conditions are experimentally verified (ωe=ωi+ω0, ke=ki+k0≂ki). The emission is found to be polarized, negligible in intensity at ω0=2ωp, and its source is localized. The space-time evolution of the three-wave interaction is presented. Besides these nonlinear wave–wave interactions the wave–particle interactions are investigated. It is found that the strong Langmuir turbulence exhibits a three-dimensional character. Cross-correlation surfaces are measured, and their characteristic scale lengths are found to decrease with increasing wave intensity toward the Debye length (λD ≂20 μm) although the resolution is probe limited (Lmin ≂1 mm). The beam electrons are diagnosed using a novel directional velocity analyzer which is capable of resolving the true three-dimensional distribution function. After interacting with the intense Langmuir waves, the beam electrons are scattered in velocity space, both parallel and perpendicular to their injection velocity. The background electron distribution is observed to develop an energetic anisotropic tail (E≲50 eV, kTe ≂1 eV). The energization of the background electrons coincides with the strong damping of the Langmuir waves. The nonlinear damping is seen as an anomalous ac resistivity produced by large amplitude ion-density fluctuations (δni/ni ≂5%) in the electron beam region.

Breakup and reconstitution of Langmuir wave packets

Recursive behavior has been observed in a two-dimensional electrostatic particle simulation of a coherent intense Langmuir wave packet. The recursion may be associated with the fact that the plasma frequency has a spatial variation in the density depression created by the ponderomotive force.

Cascade and collapse of Langmuir waves in two dimensions

The temporal evolution of intense Langmuir waves in an unmagnetized plasma of two spatial dimensions is studied numerically. When the inequality W≳ (kλe)2 is satisfied, the evolution quickly leads to a state of collapsing solitons. Here, W is the ratio of electric field energy density to the particle kinetic energy density, k is a typical Langmuir wavenumber, and λe is the electron Debye length.

The role of field‐aligned ionization irregularities in the generation of the HF‐induced plasma line at Arecibo

By using the data from the July 1976 ionospheric modification experiments at Arecibo it was discovered that the Langmuir waves responsible for the enhanced plasma line are generated at the height in the ionosphere at which the Airy function, which describes the standing electric field of the high‐frequency (HF) modifying wave near reflection, has its main maximum. It would be impossible for the enhanced Langmuir waves which backscatter the 430‐MHz radar signal to exist at this height in a uniformly varying ionosphere. This implies that underdense ionization irregularities exist in the ionosphere that allow the Langmuir waves to be generated and to propagate to the appropriate ionization density for detection by the incoherent backscatter radar. This discovery puts a new light on the generation mechanism of the HF‐enhanced plasma line, since up until now it has been implicitly assumed in theoretical work that the parametric decay process occurs in a uniformly varying ionosphere, that is, an ionosphere without irregularities. The ionization irregularities responsible for the HF‐enhanced plasma line are probably field aligned with an electron density deviation decrease of about 4% or more and with a diameter between about 1 m and a few hundred meters. It is proposed that Langmuir waves are amplified parametrically as they propagate in the duct to where their wave normals are parallel to the radar beam. The observed frequency displacement from the radar frequency (430 MHz) of the parametric decay line at Arecibo is about fHF ‐ 3.5 kHz, where fHF is the frequency of the HF heating wave (4–10 MHz). Numerical calculations for typical daytime conditions show that the maximum coupling between the HF and Langmuir waves occurs for a frequency offset between the two waves of about 3.4 kHz for the field‐aligned irregularity or duct model, which is in good agreement with observations. The observed frequencies of the peaks in the HF‐enhanced plasma line spectrum, which are displaced from 430 MHz ± fHF by approximately odd harmonics of the ion acoustic or offset frequency, can be explained with the duct model. The ‘broad bump’ observed in some plasma line spectra probably results from cascading of intense Langmuir waves which are produced parametrically and propagate approximately along the axis of the duct. It is proposed that the background or ‘immature’ spectrum may result from a four‐wave decay process. The ‘overshoot’ phenomenon (intense plasma line signals occurring immediately after transmitter turn‐on) may be due to the effects of HF heating on the ducts and on the ambient plasma.

Dissipative Langmuir shock

Intense Langmuir waves in a uniform, one‐dimensional plasma are described by a nonlinear Schrodinger equation. When the effect of linear damping is included, steady‐state shock wave solutions are found. Infinitely extended shock waves are produced by Landau damping; these shocks are moving with respect to the laboratory frame. Semi‐infinitely extended shock waves are produced by either collisional or Landau damping; these shocks are stationary in the laboratory frame, and have an energy flux through the boundary.

Nonlinear Penetration of a Langmuir Wave into a Plasma Density Gradient

The nonlinear Schrödinger equation, descriptive of an intense Langmuir wave near critical density, is solved for the steady state of reflection from a linear unperturbed density profile.