Intense Langmuir Waves Research Articles

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.

Ion heating, burnout of the high-frequency field, and ion sound generation under the development of a modulation instability of an intense Langmuir wave in a plasma

The development of one-dimensional parametric instabilities of intense long plasma waves is considered in terms of the so-called hybrid models, with electrons being treated as a fluid and ions being regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model—ZHM) or greater (Silin's hybrid model—SHM) than the plasma thermal energy. The efficiency of energy transfer to ions and to ion perturbations under the development of the instability is considered for various values of electron-to-ion mass ratios. The energy of low-frequency oscillations (ion-sound waves) is found to be much lower than the final ion kinetic energy. We also discuss the influence of the changes in the damping rate of the high-frequency (HF) field on the instability development. The decrease of the absorption of the HF field inhibits the HF field burnout within plasma density cavities and gives rise to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM.

Nonlinear frequency shift of electrostatic waves in general collisionless plasma: Unifying theory of fluid and kinetic nonlinearities

The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.

Dynamical evidence for nonlinear Langmuir wave processes in type III solar radio bursts

AbstractThe nonlinear processes and evolution of Langmuir waves in the source regions of type III solar radio bursts are explored in detail. Langmuir waves recorded by the Time Domain Sampler of the STEREO/WAVES instrument can be roughly classified into six groups based on the waveform, power spectra, and field strength perpendicular to the local magnetic field. It is argued that these groups correspond to either different stages of the evolution of Langmuir waves generated by electron beams or differ due to the direction of the magnetic field relative to the solar wind velocity. Approximately half of the observed Langmuir waves have strong perpendicular fields, meaning that understanding how these fields are produced is crucial for understanding type III sources. Most events recorded are either localized waveforms consistent with Langmuir eigenmodes or have two or more spectral peaks consistent with electrostatic (ES) decay of Langmuir/z mode waves. The remaining events appear to correspond to either earlier or later stages of Langmuir wave evolution or are decay events for which the Doppler shift is insufficient to distinguish the beam‐driven and product Langmuir waves. This is supported by the fact that most events exceed the threshold for ES decay even though their spectra show no evidence for decay and some of the events are observed when the solar wind flow is approximately perpendicular to the magnetic field, minimizing Doppler shifting. Low‐frequency fields produced by intense Langmuir waves are quantitatively consistent with density perturbations produced by the ponderomotive force, ion‐acoustic waves produced by ES decay, or sheath rectification. Above the observed nonlinear threshold, quantitative analysis suggests that the observed low‐frequency signals are consistent with perturbations produced by ponderomotive effects and ion‐acoustic waves produced by ES decay, but effects of sheath rectification may also contribute.

Harmonic waves and sheath rectification in type III solar radio bursts

AbstractIn type III solar radio bursts and planetary foreshocks, Langmuir waves are produced by electron beams and converted partially to radio waves by linear and nonlinear processes. Lower amplitude second harmonic electric fields are observed simultaneously during the most intense Langmuir wave events in type III source regions. The electric fields at the harmonic frequencies can arise from various mechanisms, such as radio wave emission by either coalescence or antenna mechanisms, nonlinear currents, harmonics of Langmuir waves, electron trapping in Langmuir wave potentials, and Langmuir wave rectification at the sheath surrounding the spacecraft, or they can result from instrumental harmonics. In this paper the relative powers and electric field vectors of Langmuir waves and the harmonic fields are compared for multiple events. The structure of the harmonic field is shown to be determined by the Langmuir waveform, but the harmonic field direction is typically closely aligned with the solar wind flow. The magnitude, structure, and orientation of the harmonic fields is used to determine which processes are responsible. It is shown that the dominant process generating the observed harmonic fields is Langmuir wave rectification at the sheath surrounding the spacecraft.

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.

Size and amplitude of Langmuir waves in the solar wind

[1] Langmuir waves in the solar wind are known to be the origin of many types of solar radio emissions. In situ observations have shown that the most intense Langmuir waves often appear as wave packets. Several models have been proposed to explain this localization, such as kinetic localization and eigenmode formation. In the present paper we investigate the role of background turbulence on the size of the Langmuir wave packets through modeling of both quasi-planar growth in constant density regions and eigenmode growth in density wells. We compute both numerically and analytically the growth of the waves, the size of the wave packets, and the amplitude of these packets. Our theoretical results are compared to the in situ measurements of Ulysses and STEREO and appear to be consistent with the measured amplitude distributions.

Determining the wavelength of Langmuir wave packets at the Earth's bow shock

Abstract. The propagation of Langmuir waves in plasmas is known to be sensitive to density fluctuations. Such fluctuations may lead to the coexistence of wave pairs that have almost opposite wave-numbers in the vicinity of their reflection points. Using high frequency electric field measurements from the WIND satellite, we determine for the first time the wavelength of intense Langmuir wave packets that are generated upstream of the Earth's electron foreshock by energetic electron beams. Surprisingly, the wavelength is found to be 2 to 3 times larger than the value expected from standard theory. These values are consistent with the presence of strong inhomogeneities in the solar wind plasma rather than with the effect of weak beam instabilities.

Eigenmode Structure in Solar-Wind Langmuir Waves

We show that observed spatial- and frequency-domain signatures of intense solar-wind Langmuir waves can be described as eigenmodes trapped in a parabolic density well. Measured solar-wind electric field spectra and waveforms are compared with 1D linear solutions and, in many cases, can be represented by 1-3 low-order eigenstates. To our knowledge, this report is the first observational confirmation of Langmuir eigenmodes in space. These results suggest that linear eigenmodes may be the starting point of the nonlinear evolution, critical for producing solar type II and type III radio bursts.

Radio tracking of the interplanetary coronal mass ejection driven shock crossed by Ulysses on 10 May 2001

We report on the detection of type II radio emission which was observed for more than a day prior to the arrival of an interplanetary shock at Ulysses. We use local spectral emission peaks, computerized from time‐averaged intensity spectra of the type II burst, to track the associated emitting shock. In the spectrogram plotted as a function of time and inverse frequency, these peaks appear as elongated clusters of data points, organized in fundamental‐harmonic bands and delineating drifting emission features. Least squares linear fittings to identified clusters give straight traces with different slopes. Most of these, when extrapolated to the Sun, are found to converge nearly at the same starting time, allowing determination of the average shock speed. Shortly before the shock crossing, intense Langmuir waves were detected at the electron plasma frequency upstream of the shock. This plasma wave enhancement together with the radio emission observed predominantly at the harmonic of the plasma frequency, all point to the occurrence of the type II radio source region in the upstream electron foreshock. We have accurately substracted the thermal noise background from the observed emission intensity to deduce the type II brightness temperatures at the fundamental and harmonic near the shock crossing. The measured brightness temperature of the type II harmonic emission is found to peak at a value of ≃3 × 1013 K just after the shock crossing; just before, the harmonic brightness temperature is ≃1012 K and the fundamental brightness temperature ≃8 × 1011 K.

Field distributions and shapes of Langmuir wave packets observed by Ulysses in an interplanetary type III burst source region

There is no consensus on the mechanisms producing the intense bursty Langmuir wave packets routinely observed in source regions of interplanetary type III radio bursts. Using data from the Ulysses Fast Envelope Sampler (FES) near 4 AU, new analyses of the distributions of wavefields clearly separate the Langmuir waves into “intense localized structures” (ILSs) and “other waves”. The wave amplitude distributions also show that the observed ILSs, but not the other waves, are inconsistent with pure stochastic growth theory (SGT). Furthermore, it is shown that the ILSs are unlikely to be driven thermal waves or generated by pure exponential growth and damping. The wave distributions, structure, and spacing of the ILSs are compared to predictions for collapsing Langmuir wave packets described by the Zakharov equations, in isolated density depressions and in fully developed strong turbulence, either beam driven or driven at long wavelengths. The results show that the observed ILSs are very unlikely to be collapsing wave packets in any of the cases considered. The observed ILSs are inconsistent with the predictions of self‐organized criticality, electron holes, and refractive focusing of waves. Most are also inconsistent with the predictions of kinetic localization, but this mechanism cannot be eliminated for all ILSs. Other mechanisms not eliminated include trapping of Langmuir waves in density depressions at levels below the collapse threshold, superposition of such trapped waves and “free” Langmuir waves, and superposition of trapped waves with a wave packet formed by beam‐driven Langmuir waves beating with products of electrostatic decay.

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.

Generation of strong Langmuir fields during optical breakdown of a dense gas

Results are presented from theoretical studies and computer simulations of the resonant excitation of Langmuir waves during the ionization of a homogeneous gas by high-intensity laser radiation. Two mechanisms for the formation of nonuniform resonant structures in the discharge are examined: plasma-resonance ionization instability, resulting in the density modulation along the electric field vector, and gas breakdown in the field of a transversely inhomogeneous laser beam (a Bessel beam produced by an axicon lens). In both cases, the transition of the plasma density through the critical value is accompanied by the generation of intense Langmuir waves, the formation of fast ionization fronts, and the appearance of long-lived quasi-turbulent states.

Quasi‐linear Zakharov simulations of Langmuir turbulence at rocket altitudes in the auroral ionosphere

A quasi‐linear Zakharov simulation model has been constructed to study intense Langmuir waves and precipitating field‐aligned electrons observed in the auroral ionosphere at altitudes below 1000 km. This self‐consistent model couples the magnetized Zakharov equations to a modified quasi‐linear diffusion equation, which includes an advective term describing electrons streaming into the simulation region. Two‐dimensional beam‐driven simulations demonstrate that for the parameters of the auroral ionosphere below altitudes of 1000 km, Langmuir wave‐wave and wave‐particle interactions occur on similar timescales. The resulting reduced electron distribution has multiple shoulders and is a result of a balance between quasi‐linear beam‐flattening, wave‐wave instabilities and beam replenishment due to streaming electrons.

Analytic treatment of weak-turbulence Langmuir wave electrostatic decay

The three-wave decay of beam-driven Langmuir waves into ion-sound waves, and backscattered Langmuir waves is analyzed. Realistic approximations are used for the spectra of Langmuir and ion-sound waves to enable calculations of growth rates of ion-sound and backscattered Langmuir waves in terms of a single well behaved integral. This integral is evaluated numerically, and approximated analytically and the results are compared with previous estimates. The case of intense beam-driven Langmuir waves decaying amid a weak thermal background of pre-existing Langmuir and ion-sound waves is examined in detail and the analytical approximation in this case is found to reproduce the numerical results accurately.

Ulysses observations of nonlinear wave-wave interactions in the source regions of type III solar radio bursts

The Ulysses Unified Radio and Plasma Wave Experiment (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50–300 Hz (in the spacecraft frame) electric field signals, corresponding to long-wavelength ion-acoustic waves are often observed coincident in time with the most intense Langmuir wave spikes, providing evidence for the electrostatic decay instability. Langmuir waves often occur as envelope solitons, suggesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist with weak turbulence processes, such as electrostatic decay, in a few type III burst source regions.

Statistical studies of plasma waves and backstreaming electrons in the terrestrial electron foreshock observed by Geotail

We present statistical studies of the direction finding of 2ƒp radiation and the spatial distribution of plasma waves and energetic particles in the terrestrial electron foreshock observed by Geotail. First, we investigate the geometry of the electron foreshock which is assumed to be the “2ƒp radio source.” The 2ƒp radio source is likely to be in the leading region of the electron foreshock where the most intense Langmuir waves are observed. The Langmuir wave activities and the population of energetic electrons gradually decrease in the region beyond 10 RE from the contact point. The decreasing rate of Langmuir wave activity is very small, about 10−0.008/RE. We also find that in the region around the contact point of the tangential interplanetary magnetic field (IMF) lines and the bow shock, the observed amplitude of the 2ƒp radiation seems to become weak. We think that it is due to the weak activities of Langmuir waves in the region close to the contact point and/or the directivity of 2ƒp radiation along the tangential IMF line. Next, we investigate the influence of the solar wind conditions on the activities in the electron foreshock. We confirm a positive correlation of the 2ƒp radio activity with the solar wind kinetic energy flux and a decrease of 2ƒp radio activity with decreasing IMF cone angle resulting in IMF lines tangent to the far flank of the bow shock. The 2ƒp radio activity is more affected by both parameters than the amplitude of Langmuir waves is affected. This suggests that the 2ƒp radio emissivity is very sensitive to the energy of Langmuir waves as expected from the generation process of 2ƒp radiation. Such high sensitivity also supports the concentration of the radio emissivity in the leading region of the electron foreshock and the limitation of the radio source extension along the magnetic field line. We also reinvestigate the comparison between the terrestrial and Venusian foreshocks. The differences between them suggest the nonsimilarity of shocks with different sizes.

Ulysses Observations of Nonlinear Wave-wave Interactions in the Source Regions of Type III Solar Radio Bursts

AbstractThe Ulysses Unified Radio and Plasma Wave Experiment (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50–300 Hz (in the spacecraft frame) electric field signals, corresponding to long-wavelength ion-acoustic waves are often observed coincident in time with the most intense Langmuir wave spikes, providing evidence for the electrostatic decay instability. Langmuir waves often occur as envelope solitons, suggesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist with weak turbulence processes, such as electrostatic decay, in a few type III burst source regions.

Rocket observations of banded structure in waves near the Langmuir frequency in the auroral ionosphere

Using data from the PHAZE II sounding rocket, launched from Poker Flat, Alaska, we present high‐resolution observations of structure in auroral HF waves at and below the local plasma frequency. These observations were made in the altitude range of 390–945 km where the local plasma frequency is below the electron cyclotron frequency. We observe monochromatic, long‐lived, narrowband emissions occuring below the local plasma frequency during times of intense HF wave emission. We have termed these emissions “HF bands” due to their appearance in spectrogram images. These emissions are probably identical to the “spike” emissions identified by previous observers using lower time resolution data from the AUREOL/ARGAD3 satellite which showed a narrow peak spectra below the local plasma frequency. HF bands often occur when the local plasma density is varying and are associated with regions of intense Langmuir wave generation. We investigate the hypothesis that the HF bands are created when a Langmuir wave propagates from a low‐density region into a higher density region. The wave moves onto the whistler mode branch and propagates as an HF band. Theoretical calculations of propagation times of whistler mode waves support this hypothesis.