Langmuir Solitons Research Articles

Finite amplitude envelope solitons

A general theory of finite amplitude envelope Langmuir solitons is presented. Comparison with recent beam-plasma experiments suggests identification of the observed localized structures with these solitons.

Numerical study of two-dimensional generation and collapse of Langmuir solitons

Numerical studies of various aspects of two-dimensional Langmuir solitons, are made, viz., (i) instability and collapse of a planar soliton perturbed in the perpendicular direction, (ii) the effect of an approximate Landau damping on the collapse, and (iii) the generation and subsequent collapse of planar solitons by an external pump field. These computations verify the flow of energy from long wavelength pump fields, through soliton formation and collapse, to shorter wavelengths, where the energy is transferred to the electrons.

Collisions between Langmuir solitons

Collisions between two equal Langmuir solitons with opposite velocities are studied numerically, as a function of soliton strength, velocity, and relative phase angle. The computations show that all three parameters are important in the outcome of a collision, for which qualitative estimates are given.

On the theory of Langmuir solitons

We find a Lagrangian density from which the equations of motion for the Lang-muir solitons follow in the usual way. We show how this Lagrangian leads to the usual conservation laws. For the one-dimensional case we discuss how a consideration of these conservation laws can help us to understand some of the results obtained in numerical experiments on the behaviour of a strongly turbulent plasma. We point out that the situation in the three-dimensional case may be fundamentally different, and we discuss near-sonic perturbations and Karpman's treatment of these.

Numerical simulations of one-dimensional solitons

Numerical simulations of (i) the propagation and interactions of one-dimensional Langmuir solitons and (ii) their generation from random fluctuations by an external pump field are presented. The results of particle simulations are compared with computations based on Zakharov’s fluid model. Those computations establish that Langmuir solitons are reasonably long lived entities in one dimension and are accurately described by Zakharov’s equations, provided that resonant particle interactions are taken into account by the inclusion of a damping term. The power spectrum of the electron field fluctuations resulting from the generation of many solitons by an external pump field is compared with the theory of Kingsep, Rudakov, and Sudan.

Interaction among Langmuir solitons, coupled solitons and sound waves

Including the effect of nonlinearity and dispersion of sound waves, we discuss interactions among Langmuir solitons, coupled solitons and sound waves in terms of conservation laws. It is found that coupled solitons play the role of high frequency field energy carriers.

Interaction of plane Langmuir solitons

The formation and interaction of Langmuir solitons is governed by the Schrödinger equation with a self-consistent potential. Generally, two kinds of interaction - quasi-static and dynamic - are considered. In the former case, the problem reduces to solving the Schrödinger equation with a cubic term, while in the latter, the self-consistent potential satisfies the wave equation. It is maintained that in the quasi-static description, solitons do not asymptotically interact with each other if uninteresting shifts of the soliton phases are disregarded. In the dynamic approach - which is physically more consistent - solitons may interact with each other and with acoustic waves. The article considers the problem of the interaction of two identical solitons moving towards each other. Semi-quantitative estimates have been used in order to determine the region of parameters in which fusion of solitons is possible. The numerical modelling results which refine the analytical estimates are discussed. The analysis shows that there is practically no region where the quasi-static approximation can be applied, since this approximation disregards the low-frequency motions which are fundamentally important for the process of Langmuir turbulence instability. The process of soliton formation from a non-symmetrical Langmuir-wave packet is investigated. A study is made of the influence of the boundary conditions, especially the periodic ones, on the formation and interaction of solitons. Applying numerical modelling, the authors show that great caution must be exercised in using the periodic boundary conditions for unbounded systems. Wave boundary conditions have been suggested.

Dynamics of Langmuir turbulence. Formation and interaction of solitons

We present a computer study of the formation and interaction of Langmuir solitons allowing for the generation of ion-sound waves.