Langmuir Solitons Research Articles

Generation and collapse of Langmuir solitons in a nonuniform plasma

This numerical study considers the effect of a zero-order density gradient on the development of Langmuir wave collapse in two dimensions. Two different situations are considered; (1) an initial soliton is pertubed in a direction transverse to the density gradient, and (2) the plasma is resonantly driven by an external pump electric field in the presence of transverse density fluctuations. The principal finding is that the density gradient can inhibit the development of Langmuir collapse for both the initial soliton and the externally driven cases. Over the limited parameter space surveyed it is found that collapse occurs for values of the scaled gradient parameter g≲2.5; where g = (9/8)(M/m)3/2(λD/L), M is the ion mass, m is the electron mass, λD is the Debye length, and L is the gradient scale length. For larger values of g, collapse is not observed.

Two-dimensional stability of large amplitude langmuir waves and solitons

The two-dimensional stability of nonlinear wave and soliton solutions of the exponentially nonlinear Schrödinger equation is examined. All stationary entities are unstable to two-dimensional perturbations. It is found that the saturable nonlinearity decreases growth rates in comparison with the small amplitude limit.

The dynamics of Langmuir solitons in the presence of ion-sound damping

The Langmuir soliton in the presence of driven ion-sound damped due to plasma electrons is considered. Starting from the modified Zakharov (1972) equations, the nonlinear Schrodinger equation with small operator term is obtained which describes nonstationary Langmuir soliton evolution. The Karpman-Maslov (1978) perturbation approach based on the inverse scattering method is used to find the variation of solitons, parameters and form.

Harmonic emission from adiabatically collapsing Langmuir solitons

Numerical studies of radiation at 2ωp from a Langmuir envelope collapsing adiabatically in three dimensions show that the emissivity is higher than expected. A volume emissivity obtained from an approximate density of collapsing packets leads to favorable comparisons with measurements of type-III solar radio bursts.

Radiation from a localized Langmuir oscillation in a uniformly magnetized plasma

The electromagnetic radiation at the first and second harmonics of the electron plasma frequency from a localized Langmuir perturbation is computed for the case of a uniformly magnetized plasma. It is assumed that the localized perturbations in both the electrostatic field and plasma density have cylindrical symmetry about the direction of the ambient magnetic field. The analysis is initially performed for such an arbitrary localized perturbation, and then applied to treat the case of a quasi-planar Langmuir soliton propagating in the direction of the magnetic field. An extensive numerical study of the angular dependence of the radiation spectrum as a function of the ratio of the electron plasma and cyclotron frequencies is described.

Liapunov stability of generalized Langmuir solitons

The stability investigations for small amplitude Langmuir solitons are generalized to finite amplitude solitary waves. Previous stability considerations for Langmuir envelope solitons are based on the cubic nonlinear Schrödinger equation or the so-called Zakharov equations. Thus, they are only valid in the weakly nonlinear regime. To discuss the longitudinal stability of finite amplitude solitary waves a more general low-frequency response has to be allowed for. Taking the full nonlinear ion equations, the stability behavior of finite amplitude solitary waves is investigated. The method is completely nonlinear and makes use of Liapunov theory. A stability criterion is derived which proves the longitudinal stability for the known stationary wave solutions. The role of transverse instabilities is also discussed.

An energy principle for soliton solutions with higher nonlinearities

The two-dimensional stability of Langmuir solitons in investigated taking into account the dynamic ion response and electron nonlinearities. A variational principle for the growth rate is derived which allows one to determine growth rates and regions of instability by standard numerical procedures. The validity of previous methods using trial functions and the variation of action method, as well as the limitations of the corresponding results for the growth rates, neglecting the dynamic ion response, are critically examined.

Soliton formation at critical density in laser-irradiated plasmas

The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrödinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrödinger equation are re-examined and found to be more restrictive than previously stated.

Role of Trapped Particles and Waves in Plasma Solitons-Theory and Application

In this tutorial and review paper, we investigate the influence of trapped particles on the propagation of ion acoustic solitons and the role of trapped waves on the propagation of Langmuir solitons. The classical potential method allows us to construct finite amplitude soliton solutions, and trapping phenomena are found to retard the motion of solitons. Thus, ion acoustic solitons have minimum speed when they are based on an isothermal electron equation of state since this corresponds to "maximum electron trapping". In the small amplitude regime, deviations from the Boltzmann law lead to a new nonlinear term. Subsequently, the dynamics of the soliton is governed by a modified KdV-equation [e.g., (23)]. For Langmuir solitons an existence diagram is found and exhibits the comparison between experimentally observed localized structures and theory. The connection with the various small amplitude soliton solutions is also pointed out. Moreover, the inclusion of a pump and of dissipative terms in the coupled nonlinear Schrödinger-ion equation gives rise to a transient phenomenon called soliton flash, whose implication to the laboratory experiments is discussed. Finally, as an application in numerical analysis the propagation of solitons is followed by solving the KdV-equation in Fourier-space. This turns out to be an excellent tool to test stability and accuracy of numerical schemes. Our results reveal that the so-called aliasing interactions lead to erroneous solutions. The conservation of invariants does not guarantee the accuracy of a numerical algorithm, although it is needed for its stability.

Computer and Solitons

The properties of one and more space dimensional solitons are discussed on the basis of the works performed mainly in Dubna at the Joint Institute for Nuclear Research, Laboratory of Computing Techniques and Automation. The conception of near integrable systems is formulated. As an example of interaction of Langmuir solitons it is shown that the Hamiltonian system is able to transform continuously its properties from a deep inelastic state up to the complete integrable one, depending on a physical parameter.The stability and existence problem of many-dimensional solitons is discussed. The results of numerical experiments are given on the dynamics of formation and interaction of many dimensional solitons and pulsons.

The Stability of Three-Dimensional Planar Langmuir Solitons

We discuss the stability of three-dimensional planar Langmuir solitons which are solutions of both the correct Zakharov equations and the simplified, curl-free equations which many authors have considered. We resolve the differences between various results obtained by different authors, show that the simplified equations used by them are unlikely to be a good approximation, and estimate the growth rates for the case of the exact equations.

Prolongation structure for Langmuir solitons

A systematic analysis of nonlinear partial differential equations governing the formation and evolution of Langmuir solitons has been undertaken with the help of differential forms. The technique of Wahlquist and Estabrook has been applied in conjunction with the representation theory of Lie groups to derive the 3×3 inverse scattering formalism previously derived heuristically by Yajima.

Nonlinear Stability of Envelope Solitons

The instability of plane envelope Langmuir solitons subject to transverse perturbations is reconsidered for the cubic nonlinear Schr\"odinger equation as well as the coupled set of high- and low-frequency equations in the case of nonadiabatic ion response. The nonlinear investigation demonstrates instability with a cutoff in all cases and predicts a drastic lowering of the instability growth rates when nonadiabatic ion motion is allowed for. Our analytical results agree with recent numerical computations.

Langmuir solitons in magnetized plasmas

The authors have considered the nonlinear interaction between a high frequency (Langmuir) wave, which propagates at an arbitrary angle to a weak, constant magnetic field, and low frequency (ion-cyclotron or ion-sound) perturbations. In studying Langmuir envelope solitons they have unified and expanded the previous theories. They also discuss the possibilities of steady-state solitons both in 1-dimension (filamentation) and higher dimensions.

Solitons and second harmonic radiation in type III bursts

The emission at the second harmonic (2ωe) of the plasma frequency from self‐consistent Langmuir solitons is calculated. The theory predicts, in a natural way, the observed transition from the region where the intensity is linearly proportional to the electron flux to the region where the radio intensity is proportional to the square of the electron flux. A detailed comparison of the radiation observed at (2ωe), for the burst of 31 March 1976, 18:10 UT with the one expected on the assumption of radiation from solitons, using the correlated in situ measurements of the electric fields at ωe and their spatial structure provides strong evidence that, for the first time, Langmuir solitons have been observed in space.

On electron beam interaction with strong turbulent plasma

Abstract The interaction of a beam with Langmuir solitons is considered. The requirement for the stationarity of the solution is shown to define soliton amplitude and velocity. The energy flow into plasma is calculated. It is shown that according to parameters the heating of both ions and electrons may occur. The conditions of the applicability of such a description and the range of the stationary solution existence are defined.

Instability of coupled Langmuir and ion-acoustic solitons

It is shown that one-dimensional coupled Langmuir and ion-acoustic solitons are unstable against perturbations transverse to their motion. The growth rate of the corresponding instability is obtained.

Coupled localized electron-plasma waves and oscillatory ion-acoustic perturbations

The equations describing the coupling of high-frequency electrostatic waves with ion fluctuations allow stationary one-dimensional localized solutions which have not been reported previously. It is shown that these solutions follow from scaling laws different from those known for sonic Langmuir solitons, but similar to those used for static ion response. The present treatment generalizes the theory for subsonic Langmuir solitons by consistently including the second harmonic contribution in the low-frequency response. The physical importance of the new solutions is discussed.

Stabilization of modulation instability and fast langmuir solitons in nonequilibrium plasmas

Stabilization of modulation instability and fast langmuir solitons in nonequilibrium plasmas

Dynamics of coupled solitons

The stability of coupled Langmuir and ion-acoustic solitons has been investigated by means of numerical computations. Using the Zakharov equation to describe the envelope of the oscillating electric field, and the Korteweg–de Vries equation with the ponderomotive driving term, to describe the low-frequency electron density variation, it was found that (1) Langmuir waves and short scale sound waves do not affect the soliton; (2) two solitons destroy each other when colliding; and (3) a long scale sound wave or ion-acoustic soliton break up a coupled soliton in the interaction. Moreover, no initial condition far from a soliton state was found which would create a coupled soliton.