Periodic, highly superluminous, nonlinear waves in a cold, unmagnetized plasma

1982 ◽  
Vol 27 (2) ◽  
pp. 267-276 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Perturbation Method ◽  
Nonlinear Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Electron Plasma ◽  
Periodic Wave ◽  
Electric Vector ◽  
Third Wave ◽  
Transverse Waves ◽  
Unmagnetized Plasma

With respect to the propagation through a cold, unmagnetized, electron plasma of nonlinear, highly superluminous, plane waves of fixed profile, with electric vector in a fixed plane parallel to the direction of propagation, it is known that, in addition to the familiar longitudinal and quasi-transverse waves, there can also be a third periodic wave. The perturbation method by which this third wave has previously been analysed is of restricted validity, and fails to describe how the wave disappears in the approach to the small-amplitude limit, where the longitudinal and transverse waves alone survive.

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.

scholarly journals The relativity theory of plane waves

1926 ◽  
Vol 111 (757) ◽  
pp. 95-104 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Cumulative Effect ◽  
Relativity Theory ◽  
Transverse Waves ◽  
Propagation Of Light ◽  
Cumulative Change ◽  
The Waves

Weyl has shown that any gravitational wave of small amplitude may be regarded as the result of the superposition of waves of three types, viz.: (i) longitudinal-longitudinal; (ii) longitudinal-transverse; (iii) transverse-transverse. Eddington carried the matter much further by showing that waves of the first two types are spurious; they are “merely sinuosities in the co­ordinate system,” and they disappear on the adoption of an appropriate co-ordinate system. The only physically significant waves are transverse-transverse waves, and these are propagated with the velocity of light. He further considers electromagnetic waves and identifies light with a particular type of transverse-transverse wave. There is, however, a difficulty about the solution as left by Eddington. In its gravitational aspect light is not periodic. The gravitational potentials contain, in addition to periodic terms, an aperiodic term which increases without limit and which seems to indicate that light cannot be propagated indefinitely either in space or time. This is, of course, explained by noting that the propagation of light implies a transfer of energy, and that the consequent change in the distribution of energy will be reflected in a cumulative change in the gravitational field. But, if light cannot be propagated indefinitely, the fact itself is important, whatever be its explana­tion, for the propagation of light over very great distances is one of the primary facts which the relativity theory or any like theory must meet. In endeavouring to throw further light on this question, it seemed desirable to avoid the assumption that the amplitudes of the waves are small; terms neglected on this ground might well have a cumulative effect. All the solu­tions discussed in this paper are exact.

Padé approximants and nonlinear waves

1979 ◽  
Vol 21 (3) ◽  
pp. 549-571 ◽  
Author(s):  
F. J. Romerias ◽  
J. P. Dougherty
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Nonlinear Waves ◽  
Wave Amplitude ◽  
Plane Waves ◽  
Electron Plasma ◽  
Cold Electron ◽  
Small Wave ◽  
The Waves ◽  
Approximant Method

The perturbation solution of the ordinary differential equations that describe exact nonlinear travelling plane waves leads to asymptotic expansions in powers of the (small) wave amplitude for both the proffle and the frequency of the waves. This paper shows how the Padé approximant method can be used to extend the validity of those expansions to larger amplitudes. The method is applied to the Duffing equation and to two types of nonlinear waves in a cold electron plasma: longitudinal oscillations and coupled transverse–longitudinal relativistic waves.

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.

Further analysis of nonlinear, periodic, highly superluminous waves in a magnetized plasma

1982 ◽  
Vol 27 (1) ◽  
pp. 177-187 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Power Series ◽  
Periodic Solutions ◽  
Wave Speed ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Electron Plasma ◽  
Finite Amplitude ◽  
Magnetized Plasma ◽  
Cold Electron

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.

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.

Plane waves in nano-composite materials

2019 ◽  
pp. 198-201
Author(s):  
K. V. Savelieva ◽  
O. G. Dashko ◽  
Y. V. Simchuk
Keyword(s):  
Longitudinal Wave ◽  
Plane Waves ◽  
Wave Interaction ◽  
Elastic Interaction ◽  
Nanocomposite Materials ◽  
Successive Approximations ◽  
Harmonic Waves ◽  
Transverse Waves ◽  
Nonlinear Properties ◽  
Hyper Elastic

The propagation of plane waves in a hyper-elastic medium is theoretically investigated. Two methods of research were used: the method of slowly variable amplitudes and the method of perturbations (successive approximations). The results obtained by these methods are analyzed. The wave interaction in nanocomposite materials is studied. A theoretical study of the cubically nonlinear elastic interaction of plane harmonic waves is carried out for a material whose nonlinear properties are described by the Murnaghan elastic potential. The solution for self-generation of the longitudinal wave is obtained by the method of slowly varying amplitudes. The interaction of transverse horizontally and vertically polarized harmonic waves are studied using the perturbing method. The pumping of energy between different harmonics of a longitudinal wave and various types of transverse waves is described analytically. The results of numerical analysis for various types of nanocomposite materials are presented.

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