Large Amplitude Langmuir Waves Research Articles

Role of spontaneous thermal emissions in inflationary laser Raman instability

The role of thermal fluctuations on the stimulated Raman backscattering instability is investigated by means of Vlasov and particle-in-cell (PIC) simulations in a regime of strong linear Landau damping of the Langmuir wave. The instability is initially convective and amplifies thermal noise, leading to a low-amplitude back-scattered laser sideband. Linear Landau damping of the Langmuir sideband modifies and flattens the electron velocity distribution function at the resonant velocity, leading to a gradual decrease in the Landau damping rate and an increase in the convective amplification. The Langmuir wave traps electrons resulting in a rapid nonlinear absolute instability and large amplitude flashes of backscattered light off large amplitude Langmuir waves with trapped electrons, leading to the production of hot electrons. Conditions for simulating realistic thermal noise with Vlasov and PIC simulations are discussed and defined.

Theoretical Study on Weibel instability in the existence of large amplitude Langmuir wave inside a Plasma

This paper investigates how an electrostatic Langmuir wave having large amplitude affects the Weibel instability (WI) in the existence of ions and an electron beam. Two Langmuir side band waves are produced by coupling of EM perturbation to the Langmuir wave. The Langmuir wave (LW) increases the growth rate beyond its linear value. Here, we noticed that the growth rate Γ(sec−1) scales linearly with the electron beam velocity vbe and 1/2 power of the electron beam density nbe. As we increase the density of ions inside the plasma, the growth rate stabilizes. Additionally, we find that the growth rate is very sensitive to the plasma frequency of ions. Therefore, our work finds an application in space, galactic cosmic rays and supernovas. Also, our work covers a range of application from the development of fusion power to understand the various astrophysical phenomena.

Pulsar radio emission mechanism − I. On the amplification of Langmuir waves in the linear regime

ABSTRACT Observations suggest that in normal period radio pulsars, coherent curvature radiation is excited within 10${{\ \rm per\ cent}}$ of the light cylinder. The coherence is attributed to Langmuir mode instability in a relativistically streaming one-dimensional plasma flow along the open magnetic field lines. In this work, we use a hot plasma treatment to solve the hydrodynamic dispersion relation of Langmuir mode for realistic pulsar parameters. The solution involves three scenarios of two-stream instability, viz. driven by high energy beams, due to longitudinal drift that leads to a separation of electron–positron distribution functions in the secondary plasma and due to cloud–cloud interaction causing spatial overlap of two successive secondary plasma clouds. We find that sufficient amplification can be obtained only for the latter two scenarios. Our analysis shows that longitudinal drift is characterized by high growth rates only for certain multipolar surface field geometry. For these configurations, very high growth rates are obtained starting from a few tens of km from the neutron star surface, which then falls monotonically with increasing distance. For cloud–cloud overlap, growth rates become high starting only after a few hundred km from the surface, which first increases and then decreases with increasing distance. A spatial window of up to around a 1000 km above the neutron star surface has been found where large amplitude Langmuir waves can be excited while the pair plasma is dense enough to account for high brightness temperature.

Wakefields in a cluster plasma

We report the first comprehensive study of large amplitude Langmuir waves in a plasma of nanometer-scale clusters. Using an oblique angle single-shot frequency domain holography diagnostic, the shape of these wakefields is captured for the first time. The wavefronts are observed to curve backwards, in contrast to the forwards curvature of wakefields in uniform plasma. Due to the expansion of the clusters, the first wakefield period is longer than those trailing it. The features of the data are well described by fully relativistic two-dimensional particle-in-cell simulations and by a quasianalytic solution for a one-dimensional, nonlinear wakefield in a cluster plasma.

Detailed characterization of plasma wave behavior using collective Thomson scattering (invited)

Collective Thomson scattering is widely used to measure bulk plasma parameters in high density, laser-produced plasmas, and is used to detect plasma waves from instabilities. However, inhomogeneity in these small plasmas often leads to a spectrum with insufficient resolution to discern phenomena such as wave damping and nonlinear wave effects. Two techniques are discussed for laser-produced plasmas to overcome these limitations, and provide details of wave damping and nonlinear behavior. First, imaging Thomson scattering is used to obtain spatially resolved plasma wave profiles in a 100–200 eV plasma, and allows us to infer ion-ion collisional damping rates. Second, a diffraction-limited laser beam is used to drive stimulated Raman scattering in a hot plasma, generating large amplitude Langmuir waves. The comparatively small interaction volume permits sufficient spectral resolution to observe nonlinear wave behavior previously unresolved in other experiments.

Theory of cavitons in complex plasmas.

Nonlinear coupling between Langmuir waves with finite amplitude dispersive dust acoustic perturbations is considered. It is shown that the interaction is governed by a pair of coupled nonlinear differential equations. Numerical results reveal the formation of Langmuir envelope solitons composed of the dust density depression created by the ponderomotive force of bell-shaped Langmuir wave envelops. The associated ambipolar potential is positive. The present nonlinear theory should be able to account for the trapping of large amplitude Langmuir waves in finite amplitude dust density holes. This scenario may appear in Saturn's dense rings, and the Cassini spacecraft should be able to observe fully nonlinear cavitons, as presented herein. Furthermore, we propose that new electron-beam plasma experiments should be conducted to verify our theoretical prediction.

Modified Zakharov equations in dusty plasmas with variable charges on dust particles

The nonlinear coupling between large amplitude Langmuir waves and dust ion-acoustic waves in a charge-varying dusty plasma is considered. By employing a two-time-scale three fluid approach, modified Zakharov equations are derived. A normal mode analysis of these nonlinearly coupled equations is performed to obtain a general dispersion relation that is useful for studying parametric instabilities. The results show that the impurities can significantly alter the characteristics and damping of these instabilities by reducing their phase velocity and causing charging related damping.

On beam-plasma interaction in a dust-electron plasma

The generation of electron plasma waves by low-energy electron beams in a dust-electron plasma, generated by UV induced photoemission or radiative heating of grains, is considered. It is shown that finite amplitude Langmuir waves might be produced due to the usual two-stream (beam-plasma) instability under certain conditions. Langmuir waves may saturate by beam trapping and attain finite amplitudes. Large amplitude Langmuir waves can nonlinearly interact with dust acoustic waves due to the parametric process. However, for the parameters considered, the rates of the decay and modulational interactions of Langmuir waves in the dust-electron plasma are much smaller than electron collisional damping rates.

Vlasov–Maxwell numerical simulations of large amplitude Langmuir wave dynamics

The classical problem of the nonlinear dynamics of one dimensional large Langmuir waves is investigated numerically in the framework of a kinetic model based on the Vlasov equations for plasma electrons and ions, coupled with the Maxwell equations. The field and plasma quantities are followed in time starting from a given spatial electric field distribution with typical scale length much larger than the Debye length. The temporal evolution of the particle distribution functions and of its moments are investigated during the relaxation of the initial perturbation or under the action of an externally applied oscillating field. The transformation of ordered energy into electron temperature is observed. The frequency spectra of the electron and ion fluctuations are calculated and harmonic generation is studied.

The decay instability of Langmuir waves in the non-neutral electron plasma column

The behaviour of large amplitude Langmuir waves is experimentally observed in a non-neutral electron plasma column with a cylindrical boundary. It is found that a Langmuir wave whose amplitude is above a threshold decays into lower frequency Langmuir waves. Since the dispersion relation is different from that of the unbounded neutral plasma, which is theoretically considered, the three-wave decay process of Langmuir waves becomes possible. In these processes, sidebands due to a large amplitude Langmuir wave satisfy the energy and momentum conservation relation. The threshold of this decay instability depends on the plasma temperature and becomes lower as the temperature becomes higher.

Non‐Markovian electron diffusion in the auroral ionosphere at high Langmuir‐wave intensities

A generalized non‐Markovian diffusion model which describes the interaction of Langmuir waves with field‐aligned electrons in the auroral ionosphere is found to be relevant to the large amplitude Langmuir waves measured by UC Berkeley sounding rockets and by the Freja satellite. This model is valid for any ordering of the diffusion time and the autocorrelation time (the standard quasilinear diffusion model requires the diffusion time to be much longer than the autocorrelation time). We demonstrate that, while the quasilinear diffusion approximation is valid for the lower altitudes studied by the Berkeley sounding rockets, the non‐Markovian model is needed for the intense waves observed at the higher altitudes probed by Freja. A test particle simulation is employed to quantify our estimates of the relevant timescales.

Effect of a large amplitude Langmuir wave on the Weibel instability

The effect of large amplitude Langmuir wave on the Weibel instability in a plasma with an electron beam is studied. The electromagnetic perturbation couples to the Langmuir wave to give rise to two Langmuir sideband waves, which in turn produce a current enhancing the electromagnetic perturbation. The Langmuir wave enhances the growth over its linear value. The enhancement is larger at shorter wavelengths. For v 0 c ∼ 0.15 , the growth rate is enhanced by a factor of 3 2 .

Large amplitude Langmuir and ion-acoustic waves in a relativistic two-fluid plasma

Large amplitude Langmuir and ion-acoustic waves in a weakly relativistic two-fluid plasma are analyzed by the pseudopotential method. The existence conditions for relativistic nonlinear Langmuir waves depend on the relativistic effect, the particular energy, and the ion mass to electron mass ratio. The allowable range of the normalized potential depends on the relativistic effect. It is shown that the Mach number has the significant effect for the formation of relativistic nonlinear ion-acoustic waves rather than the ratio of the ion-acoustic velocity to the velocity of light. The allowable range of the normalized potential depends on the Mach number. The present investigation predicts new findings of relativistic nonlinear Langmuir and ion-acoustic waves in plasmas in which high-speed electrons and ions coexist.

Strongly nonlinear stationary Langmuir waves (T ≪ mc2)

Extremely large-amplitude Langmuir waves are investigated on the basis of relativistic kinetic theory. Analytical formulae for the electron density and the electric field of the wave differ essentially from earlier results obtained using the cold-hydrodynamical equations.

Plasma wakefield generation by multiple short pulses

It is shown that large amplitude Langmuir waves, produced as a wake by short electromagnetic pulses in a plasma, can be generated effectively by a series of short pulses. The nonlinear nature of the Langmuir waves means that a given total energy in the electromagnetic wave is much more effective when delivered in a series of pulses than in a single short pulse. The present analysis treats the generation of the Langmuir wave in both electron-proton and electron-positron-proton plasmas.A plot of phase trajectories shows that the correct phasing of the pulses leads to a dramatic improvement of the wake-field amplitude. For maximum amplification, the pulse maximum of each of the trailing pulses should be spatially coincident with the minimum of the wake-field potential.

Parametric instabilities of Langmuir waves in weak/moderate magnetic fields

A general dispersion equation, which describes the parametric instabilities of some electrostatic waves in a weak/moderate magnetic field, is derived. The dispersion equation is solved numerically to study the effects of a moderately intense magnetic field on the parametric instabilities of relatively large amplitude Langmuir waves. A Langmuir pump wave can couple with various low-frequency branches such as lower-hybrid, electron-acoustic, ion-cyclotron, and ion-acoustic branches. The transverse modulational instability is most sensitive to a magnetic field. Even for a Langmuir wave with W̄∼0.1, where W̄ is the ratio of the time-averaged wave energy to the electron thermal energy, some portions of the transverse modulational instability in the direction exactly perpendicular to the external magnetic field are quite easily suppressed. However, some oblique instabilities may be enhanced by a magnetic field. In general, a moderate magnetic field suppresses most of the oblique instabilities, and the parametric instabilities become essentially one dimensional.

Airglow enhancements associated with plasma cavities formed during Ionospheric Heating Experiments

Optical measurements made at the Arecibo Observatory during the 1987 heating campaign showed large temporal and spatial variations in 630.0‐nm airglow enhancements during times of continuous power transmissions of high‐power radio waves. Photometric data displayed fluctuations of 60 R or more in the red‐line (630.0 nm) emission from atomic oxygen. These fluctuations were associated with heater‐induced cavities which drifted and evolved in the modified ionosphere. Data from the Arecibo incoherent scatter radar were used in conjunction with airglow images to provide a physical interpretation of the modification process. Electrons were accelerated by large amplitude Langmuir waves excited by parametric decay instabilities occurring near the wave reflection points inside the density cavities. Inelastic collisions with oxygen atoms produced excited states which yielded enhanced 630.0‐nm and 557.7‐nm emissions. A numerical model has been used to relate the enhanced airglow intensities to the energy spectrum of the accelerated electrons. The measured airglow could have been produced by an isotropic source at 340 km altitude that accelerated 0.01% of the ambient electrons into a suprathermal Maxwellian distribution with a temperature of 2.05 eV. Experimental and theoretical studies suggest that airglow clouds were directly coupled to plasma density cavities because (1) these cavities trapped the HF radio beam and (2) electrons accelerated out into regions of reduced plasma concentration were less effectively thermalized and, consequently, were more effective for collisional excitation of neutral species.

Bistability and hysteresis in a laser beatwave excited relativistic Langmuir wave

It is shown that the large amplitude Langmuir wave driven by two collinear laser beams with a frequency difference approximately equal to the plasma frequency exhibits bistability and hysteresis. The threshold pump intensity for the occurrence of the bistability is rather low compared to most laser-plasma experiments. By using the hysteretic effect, relatively weak pump intensities can result in a very large amplitude of the Langmuir wave.

The dynamic sheath: Objects coupling to plasmas on electron-plasma-frequency time scales

The time-dependent interaction between solid objects and the unmagnetized plasmas in which they are immersed is investigated. To this end over 1900 high-resolution, one-dimensional particle-in-cell simulations of the plasmas surrounding cylindrical and planar objects are statistically analyzed. Numerical shot noise produces an electron-plasma-frequency ringing in the simulations, the amplitude of which is related to the plasma temperature and to the numerical system temperature. Whenever the potential of an object is rapidly biased, the surrounding plasma rings with a large amplitude at the electron-plasma frequency. During this ringing, a depletion layer forms around the object on ion-acoustic time scales. Positively charged objects discharge via plasma currents in about τpe /4 and negatively charged objects discharge in about τpi . Owing to charge separations in the plasmas, for the first few ion-plasma periods after a perturbation, the potential of an object is not directly related to the charge on it. The electron-plasma-frequency ringing drives large-amplitude Langmuir waves, which energize electrons and drive cavitation in the plasma. The fluxes of electrons reaching the objects are bursty at ωpe, and the energies of the ions striking the object slowly and systematically vary with time.

Relativistic solitary-wave solutions of the beat-wave equations

In the beat-wave accelerator [Phys. Rev. Lett. 43, 267 (1979)], a large-amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The relativistic equations governing this three-wave interaction are shown to admit two types of solitary-wave solutions. Temporal solitary waves propagate at speeds greater than the speed of light and carry no information. Spatial solitary waves propagate at speeds less than the speed of light and do carry information. Analytic expressions are obtained for the envelopes of these waves and for the relationship between their speed and maximum amplitude. For the limit in which the propagation speed of the solitary wave is equal to the speed of light, there is no distinction between a temporal solitary wave and a spatial solitary wave. However, it can be shown that the solitary wave is unstable in this limit. The potential of the spatial solitary waves for particle acceleration [Phys. Rev. Lett. 57, 1421 (1986)] is studied. Although the spatial solitary waves are capable of accelerating particles to high energy, for typical beat-wave parameters the laser–plasma coupling efficiency is too low for this scheme to be practical.