Nonlinear waves in a hot plasma by Lorentz transformation

1975 ◽  
Vol 13 (2) ◽  
pp. 231-247 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Nonlinear Waves ◽  
Cold Plasma ◽  
Electron Plasma ◽  
Temperature Correction ◽  
Governing Equations ◽  
Longitudinal Waves ◽  
Circularly Polarized ◽  
The Third ◽  
Hot Plasma ◽  
Space Dependence

Wave propagation in a hot, collisionless electron plasma (without ambient magnetic field) is analyzed by coisidering the frame of reference in which the field has no space dependence. It is shown that the governing equations are of the same form as those for a cold plasma, and are likely to have corresponding exact (nonlinear, relativistic) solutions. In particular, it is shown that there exists a solution representing a purely transverse, circularly polarized, monochromatic wave. Three approximate forms of the dispersion relation of this wave are obtained explicitly, the first being valid when the temperature correction is small, the second applying to weak waves, and the third to strong waves. Purely longitudinal waves are also discussed.

Stability of strong electromagnetic waves in overdense plasmas

1982 ◽  
Vol 27 (2) ◽  
pp. 239-259 ◽  
Author(s):  
F. J. Romeiras
Keyword(s):  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Longitudinal Direction ◽  
Electron Plasma ◽  
Cold Electron ◽  
Small Perturbations ◽  
Circularly Polarized ◽  
Instability Growth ◽  
Linear Differential ◽  
The Stability

We consider the stability against small perturbations of a class of exact wave solutions of the equations that describe an unmagnetized relativistic cold electron plasma. The main feature of these nonlinear waves is a transverse circularly polarized electric field with periodic amplitude modulation in the longitudinal direction. Floquet's theory of linear differential equations with periodic coefficients is used to solve the perturbation equations and obtain the instability growth rates.

Nonlinear, periodic waves in a cold plasma: a quantitative analysis

1975 ◽  
Vol 14 (3) ◽  
pp. 505-527 ◽  
Author(s):  
A. C.-L. Chian ◽  
P. C. Clemmow
Keyword(s):  
Cold Plasma ◽  
Quantitative Description ◽  
Transverse Component ◽  
Frame Of Reference ◽  
Graphical Form ◽  
Periodic Waves ◽  
Governing Equations ◽  
Fixed Direction ◽  
Unmagnetized Plasma ◽  
Space Dependence

The exact theory of a wave of fixed profile travelling with speed c/n (0 < n < 1) through a uniform, cold, collisionless, unmagnetized plasma is investigated for the case in which the electric field has a non-zero transverse component, which lies in a fixed direction. The governing equations, referred to the frame of reference in which there is no space dependence, are studied analytically in each limit n→0, n→1. and by computation for other values of n. It is shown that, for each value of n, there is, in general, just one periodic solution of an arbitrarily given amplitude; and a quantitative description of these periodic solutions is provided in graphical form. A simple ‘dispersion relation’ is obtained for large- amplitude waves.

Nonlinear waves in a cold plasma by Lorentz transformation

1974 ◽  
Vol 12 (2) ◽  
pp. 297-317 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Wave Propagation ◽  
Lorentz Transformation ◽  
Nonlinear Waves ◽  
Free Parameter ◽  
Cold Plasma ◽  
Stream Velocity ◽  
Special Cases ◽  
Two Component ◽  
Component Plasma ◽  
Space Dependence

Wave propagation in a cold, collisionless, two-component plasma is analyzed by considering, first, the frame of reference in which the field has no space dependence, and then applying a Lorentz transformation to obtain a wave whose space-time dependence is a function of t — nz / c only, where n is a constant. Exact (nonlinear, relativistic) results for known special cases, and some others, are given; and it is shown that, when there is no ambient magnetic field, the general problem in essence reduces to the solution of one second-order, nonlinear differential equation. The desirabifity of introducing a free parameter representing a stream velocity in the direction of wave propagation is emphasized; and the significance of the choice of this parameter is discussed.

scholarly journals Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yun Wu ◽  
Zhengrong Liu
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Blow Up ◽  
Periodic Waves ◽  
The Third ◽  
Bifurcation Phenomena ◽  
Kink Waves ◽  
Fourth Kind

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

Parametric excitation in an inhomogeneous plasma

1971 ◽  
Vol 5 (1) ◽  
pp. 107-113 ◽  
Author(s):  
C. S. Chen
Keyword(s):  
Electric Field ◽  
Parametric Excitation ◽  
Growth Rates ◽  
Inhomogeneous Plasma ◽  
Electron Plasma ◽  
Transverse Waves ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Oscillating Electric Field ◽  
Unmagnetized Plasma

An infinite, inhomogeneous electron plasma driven by a spatially uniform oscillating electric field is investigated. The multi-time perturbation method is used to analyze possible parametric excitations of transverse waves and to evaluate their growth rates. It is shown that there exist subharmonic excitations of: (1) a pair of transverse waves in an unmagnetized plasma and (2) a pair of one right and one left circularly polarized wave in a magnetoplasma. Additionally, parametric excitation of two right or two left circularly polarized waves with different frequencies can exist in a magnetoplasma. The subharmonic excitations are impossible whenever the density gradient and the applied electric field are perpendicular. However, parametric excitation is possible with all configurations.

Anomalous absorption of the circularly polarized electromagnetic beams near the plasma frequency in a magnetized electron plasma

2007 ◽  
Vol 73 (3) ◽  
pp. 315-330 ◽  
Author(s):  
S. R. SESHADRI
Keyword(s):  
Resonant Frequency ◽  
Plasma Frequency ◽  
Unit Length ◽  
Plane Waves ◽  
Electron Plasma ◽  
Magnetostatic Field ◽  
Power Absorption ◽  
Circularly Polarized ◽  
Focused Beams ◽  
Electromagnetic Beams

AbstractThe propagation of circularly polarized electromagnetic beams along the magnetostatic field in an electron plasma is investigated. As a consequence of a strong interaction with the medium, the beam spreads rapidly on propagation near the cutoff frequencies and the cyclotron resonant frequency of the corresponding plane waves, as well as near the plasma frequency. The power absorption for unit length near the cyclotron frequency and the plasma frequency are determined. For tightly focused beams, there is significant power absorption near the plasma frequency as compared with that at the cyclotron resonant frequency.

Weakly nonlinear dispersive waves: group velocity

1982 ◽  
Vol 27 (3) ◽  
pp. 507-514
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Group Velocity ◽  
Acoustic Waves ◽  
Specific Problem ◽  
Electron Plasma ◽  
Hot Electron ◽  
Ion Acoustic Waves ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Longitudinal Waves ◽  
Wave Trains

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

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