Cold Collisionless Plasma Research Articles

An Application of Multiple-Time Scale Perturbation Method to Nonlinear Ion-Acoustic Waves

In this work, by utilizing the multiple-time scale expansion method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the multiple-time scale expansion method.

Propagation characters of Gaussian laser beams in collisionless plasma: Effect of plasma temperature

This paper presents an investigation of the propagation characters of Gaussian laser beam in cold collisionless plasma by considering the plasma temperature variation. The ponderomotive nonlinearity is involved and induces the nonlinear self-focusing against spatial diffraction. The second-order differential equation of dimensionless beam width parameter f(ξ) in terms of plasma temperature is established from Maxwell’s equations with paraxial approximation. The initial (P0,ρ0) plane, behaviors of f(ξ) parameter, and perturbed density n/nn0n0 of different plasma temperatures are plotted and analyzed. The plasma temperature is divided into four regions, which leads to different propagation characters including oscillatory divergence, self-trapping, self-focusing, and steady divergence. The plasma density distribution modified by the electric field intensity and plasma temperature is discussed.

The Theoretical Simulation of Fabry-Perot Interferometer with a Cold Collisionless Plasma Layer

The pattern of intensity transmitted due to the interference in a non-dissipative dispersive thin layer (NDDTL) is investigated. For the layer mentioned the generalized relations for line width, power resolution, magnitude of the minima and visibility of interference fringes are presented. Finally the interference patterns of a cold collisionless plasma layer as a NDDTL sample are simulated.

The resonant nonlinear Schrödinger equation in cold plasma physics. Application of Bäcklund–Darboux transformations and superposition principles

Abstract.A system of nonlinear equations governing the transmission of uni-axial waves in a cold collisionless plasma subject to a transverse magnetic field is reduced to the recently proposed resonant nonlinear Schrödinger (RNLS) equation. This integrable variant of the standard nonlinear Schrödinger equation admits novel nonlinear superposition principles associated with Bäcklund–Darboux transformations. These are used here, in particular, to construct analytic descriptions of the interaction of solitonic magnetoacoustic waves propagating through the plasma.

Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model is transformed to the reaction-diffusion analog of the NLS equation for which the bilinear representation, soliton solutions and their mutual interactions are studied.

Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.

The Frequency of Nonlinear Plasma Waves

We study steady-state plane nonlinear plasma waves in a cold collisionless plasma in the absence of a magnetic field. The main conclusion following from the performed analysis is that allowance for the motion of the ion component of the plasma is of fundamental importance when studying nonlinear plasma waves. It is shown that, in general, the frequency of waves is essentially determined by the ion-component mass and depends equally on the velocity and amplitude of the waves.

Localization of plasmon under nonlinear interaction of whispering-gallery modes with electron plasma of spherical microcavity

Self-localization mechanisms and conditions of laser radiation in a cold collisionless plasma of spherical microcavity have been studied taking into account the striction nonlinearity and the relativistic effects connected with the stimulated oscillatory movement of electrons. A spherical plasmon localized close to the centre of microcavity has been shown to excite under nonlinear interaction of whispering-gallery modes with electron plasma. It is determined that the realization of self-localized spherical structures of electromagnetic field and spherical plasmons inside the microcavity filled with electron plasma is caused by manifestation of relativistic nonlinearity of the medium.

Current layer cascade in collisionless electron-magnetohydrodynamic reconnection and electron compressibility effects

The nonlinear phase of a magnetic field line reconnection instability in a collisionless two-dimensional cold plasma is investigated in the Hall dominated regime, described by the electron-magnetohydrodynamic equations, which corresponds to the frequency range of whistler waves. It is found that the regular pattern of current density layers that forms in the initial nonlinear phase of the reconnection instability is destroyed by the onset of a Kelvin–Helmholtz-type instability and the formation of current jets that develop into vortex rings. These processes can be interpreted in terms of a Hasegawa–Mima-type regime inside the magnetic island and lead to the creation of magnetic vortices. It is shown that electron compressibility, which is related to charge separation, tends to stabilize these processes.

Nonlinear interaction of a Gaussian intense laser beam with plasma: Relativistic modulational instability

The nonlinear interaction of a circularly polarized Gaussian intense laser pulse in a collisionless cold plasma with immobile ions is analyzed. The laser beam is assumed to have a nonuniform intensity distribution (along its wave front) in a plane transverse to the direction of propagation. To properly include the nonuniformity of the laser field, the wave equation is integrated over the transversal distribution. In this way, the mean transversal effects are taken into account. In this frame of work the relativistic modulational instability (RMI) of a long pulse is analyzed. A general dispersion relation is derived and solved. Plots of the temporal growth rate as a function of the laser beam power and the modulation wave number are presented and compared with the case when a uniform intensity distribution along the laser wave front is assumed. It is found that the nonuniformity of the laser beam has a significant effect on the characteristics of RMI. It is shown as a conclusion that the effect of transverse distribution in the growth rate reduction, in comparison with the case when it was neglected, becomes more significant for shorter wavelength of the RMI and stronger pump waves.

Effect of electron inertia on the speed and shape of ion-acoustic solitary waves in plasma

Conditions for the existence of ion-acoustic solitary waves are investigated in a cold collisionless plasma taking into account the electron inertia. The Sagdeev’s pseudopotential is derived in terms of u, the ion velocity. It is found that there exists a critical value of u0(≠0), the value of u at which (u′)2=0, beyond which the soliton solution ceases to exist and the electron inertia plays a non-insignificant role in determining this critical value. This result reproduces the result of Johnston and Epstein [Phys. Plasmas. 7, 906 (2000)] when the effect of electron inertia is neglected.

Truncated Painleve expansion and reduction of sine-Poisson equation to a quadrature in collisionless cold plasma

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions is considered. The resulting system of equations for stationary and non-stationary equations in two-dimensions can be reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the travelling wave solutions of the sine-Poisson equation describing the charge density equilibrium configuration model.

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.

Neutrino-driven wakefield plasma accelerator

A classical fluid description is used to investigate the nonlinear interaction between neutrino bursts and a relativistic collisionless cold unmagnetized plasma. It is shown that during the interaction large amplitude electron plasma waves are excited in such a way that charged particles trapped in this high gradient potential can be accelerated to extremely high energies.

Solitary Wave Interaction in a Cold Collisionless Plasma

The interaction between two solitary waves in a cold collisionless plasma having different velocities has been studied using the multiscale expansion method. The propagation of nonlinear waves through a cold collisionless plasma is described by mKdV and KdV equations in (1+1) dimensions and mKP and KP equations in (2+1) dimensions for different orders of a small perturbation parameter under the same time and space scale transformations. The interacting system of equations are derived for mKdV and KdV equations as well as for mKP and KP equations. We have also analysed the interacting system of equations in (1+1) dimensions.

Solitary waves in media with dispersion and dissipation (a review)

The latest results relating to the theory of nonlinear waves in dispersive and dissipative media are reviewed. Attention is concentrated on small-amplitude solitary waves and, in particular, on the classification of types of solitary waves, their conditions of existence, the evolution of local perturbations associated with the presence of solitary waves of various types, and problems of the existence of nonlinear waves localized with respect to a particular direction as the space dimension increases (spontaneous dimension breaking). As examples of dispersive and dissipative media admitting plane solitary waves of various types, we consider a cold collisionless plasma, an ideal incompressible fluid of finite depth beneath an elastic plate and with surface tension, and a fluid in a rapidly oscillating rectangular vessel (Faraday resonance). Examples of spontaneous dimension breaking are considered for the generalized Kadomtsev-Petviashvili equation.

On the exact amplitude, speed and shape of ion-acoustic waves

Nonlinear ion-acoustic solitary waves in cold collisionless plasma are investigated by a direct analysis of the field equations. The exact amplitude is obtained by simply solving an algebraic equation. The results are compared to those of a third-order perturbation approach and the error associated with using the perturbation technique is determined.

A method for higher-order expansion in non-linear ion-acoustic waves

The basic equations describing the non-linear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified multiple-scale expansion method. Expanding the field quantities into a power series of the smallness parameter ε, a set of evolution equations is obtained for various terms in the perturbation expansion. To illustrate the present derivation, a localized travelling wave solution is studied for the derived field equations and the result is compared with those of Malfliet and Wieers (J. Plasma Phys. 56 (1996) 441–450), who employed the dressed solitary wave approach from the outset of their study.

Shock wave structure in a cold collisionless plasma with two ion species in a magnetic field

Shock wave structure in a cold collisionless plasma with two ion species in a magnetic field

A Modified Reductive Perturbation Method as Applied to Nonlinear Ion-Acoustic Waves

The basic equations describing the nonlinear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified reductive perturbation method. Introducing the concept of a scale parameter and expanding the variables and the scale parameter into a power series of the smallness parameter ε, a set of evolution equations is obtained for various order terms in the perturbation expansion. To illustrate the present derivation, a localized travelling wave solution is studied for the derived field equations and the result is compared with those of obtained by Sugimoto and Kakutani [rf:3] who introduced some slow scales, Kodama and Taniuti [rf:4] who employed the renormalization method and Malfliet and Wieers, [rf:6] who employed the dressed solitary wave approach from the outset of their study.