Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrodinger equation (NLS). The modifications of these basic equations due to the effects of resonant particles and external magnetic fields are discussed.

Solitons and Weakly Nonlinear Waves in Plasmas

For pt.I see ibid., vol.25, no.6, p.665 (1983). The authors review various methods for obtaining an expression for the ponderomotive force on a magnetized plasma; these methods are based on a fluid, kinetic, or a stress-tensor approach. They propose a new method which employs a fluid-dielectric model of the plasma; this method seems to be simple and generally applicable. They first of all calculate an expression for nonstationary waves in an isotropic plasma and find agreement with earlier results. They then derive an expression for the ponderomotive force in a magnetized plasma for the case of stationary waves and compare their result with earlier attempts to obtain such an expression.

Strong turbulence of a magnetized plasma. II. The ponderomotive force

This brief review is devoted to full-scale numerical modeling of the nonlinear interactions between electromagnetic (EM) waves and the ionosphere, giving rise to ionospheric Langmuir turbulence. A numerical challenge in the full-scale modeling is that it involves very different length- and time-scales. While the EM waves have wavelengths of the order 100 meters, the ionospheric Langmuir turbulence involving electrostatic waves and nonlinear structures can have wavelengths below one meter. A full-scale numerical scheme must resolve these different length- and time-scales, as well as the ionospheric profile extending vertically hundreds of kilometers. To overcome severe limitations on the timestep and computational load, a non-uniform nested grid method has been devised, in which the EM wave is represented in space on a relatively coarse grid with a spacing of a few meters, while the electrostatic wave turbulence is locally resolved on a much denser grid in space at the critical layer where the turbulence occurs. Interpolation and averaging schemes are used to communicate values of the EM fields and current sources between the coarse and dense grids. In this manner, the computational load can be drastically decreased, making it possible to perform full-scale simulations that cover the different time- and space-scales. We discuss the simulation methods and how they are used to study turbulence, stimulated EM emissions, particle acceleration and heating, and the formation of artificial ionospheric plasma layers by ionospheric Langmuir turbulence.

Full-scale simulations of ionospheric langmuir turbulence

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 W∼0.1, where W 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.

Parametric instabilities of Langmuir waves in weak/moderate magnetic fields

For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases.

http://iopscience.iop.org/article/10.1088/0741-3335/27/4/011/pdf

Nonlinear electrostatic wave equations for magnetized plasmas.II

The authors derive for the case of a magnetized plasma the analogues of the Zakharov equations for an isotropic plasma. They discuss the linearized dispersion relations following from these equations.

Strong turbulence of a magnetized plasma. I. The generalized Zakharov equations

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Strong turbulence of a magnetized plasma. I. The generalized Zakharov equations