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.

A comparative study of the instabilities of two classes of nonlinear waves in cold plasmas

1986 ◽  
Vol 35 (3) ◽  
pp. 529-539 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Nonlinear Waves ◽  
Transverse Electric ◽  
Longitudinal Direction ◽  
Dispersion Relations ◽  
Cold Electron ◽  
Circularly Polarized ◽  
Electron Plasmas ◽  
Cold Plasmas ◽  
Set Up ◽  
The Stability

Results are presented of the stability analysis against small parallel perturbations of two classes of nonlinear waves in cold unmagnetized electron plasmas emphasizing similarities and differences. The first class is a stationary longitudinal wave set up by two counter-streaming cold electron beams; the second class is a mixed transverse-longitudinal standing wave in a relativistic plasma with a circularly polarized transverse electric field whose amplitude is periodically modulated in the longitudinal direction. The perturbation dispersion relations are discussed for all perturbation wavenumbers and all nonlinear wave amplitudes. Particular attention is given to the appearance of gaps in those dispersion relations.

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

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.

Resistive instability in a uniformly rotating magnetoplasma

1971 ◽  
Vol 6 (1) ◽  
pp. 73-85
Author(s):  
A. D. Lunn
Keyword(s):  
Magnetic Field ◽  
Growth Rates ◽  
Larmor Radius ◽  
Closed Set ◽  
Finite Larmor Radius ◽  
Integral Methods ◽  
Stabilizing Effect ◽  
Instability Growth ◽  
Linear Differential ◽  
The Stability

A closed set of guiding centre equations, derived for a rotating plasma in a static magnetic field, is applied to the problem of the stability of a plasma in a sheared field. The rotation is found to have a stabilizing effect in the absence of resistivity.A pair of coupled, linear differential equations is derived for the rotating plasma in a weakly sheared field. Dispersion relations are obtained by phase integral methods and, in the absence of finite Larmor radius effects and rotation, instability growth rates proportional to η½13 are found which become proportional to when either is included. The inclusion of both finite Larmor radius and rotation gives growing instabilities proportional to η which are stabilized by the rotation when the finite Larmor radius terms predominate.

Stability of relativistic transverse cold plasma waves Part 1. Circularly polarized waves

1978 ◽  
Vol 20 (3) ◽  
pp. 479-501 ◽  
Author(s):  
F. J. Romeiras
Keyword(s):  
Nonlinear Wave ◽  
Nonlinear Waves ◽  
Unstable Mode ◽  
Polynomial Equation ◽  
Eighth Order ◽  
Small Perturbations ◽  
Large Wave ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Wide Range

This paper is concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized electron–ion plasma. These nonlinear waves are of fixed profile, superluminous, period.ic and transverse. The small perturbations are assumed to propagate in the same direction as the nonlinear wave. A Lagrangian method is used to derive the perturbation equations. The analysis is carried out in the frame where the nonlinear waves are space independent and then the results Lorentz transformed to the laboratory frame. Part 1 refers to circularly polarized waves. In this case it is possible to integrate the equations and obtain an algebraic dispersion relation in the form of an eighth order polynomial equation in the frequency. The analytical and numerical solution of this equation, for a wide range of variation of the parameters involved, reveals the existence of a very unstable mode. Particular attention is given to very large wave amplitudes for which the plasma behaves like an electron–positron plasma; in this case the growth rate of the unstable mode can be as high as the frequency of the nonlinear wave.

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.

Scattering of circularly polarized electromagnetic waves off a straight electron beam propagating along a constant magnetic field

1991 ◽  
Vol 46 (2) ◽  
pp. 201-207
Author(s):  
Alexander Bogdanov
Keyword(s):  
Magnetic Field ◽  
Nonlinear Dynamics ◽  
Electron Beam ◽  
Electromagnetic Waves ◽  
Electron Beams ◽  
The Other ◽  
Free Electron Lasers ◽  
Circularly Polarized ◽  
Beam Density ◽  
The Stability

The stability of straight field-aligned electron beams, immersed in an external magnetic field of finite magnitude, with respect to the excitation in them of circularly polarized (spiral) electromagnetic waves is a problem calling for detailed investigation, particularly in the context of the study and development of free-electron lasers. Traditionally the problem is treated using the theory of electromagnetic waves scattering off electron-beam density oscillations. This is done, however, without considering the inverse influence of the beam on the dispersion properties of the electromagnetic waves. On the other hand, it is well known that the presence of the beam introduces substantial changes in the characteristics of the electromagnetic waves interacting with the beam, and, moreover, this results in the appearance of radically new types of waves that are entirely absent in free space. The paper is dedicated to the study of the nonlinear dynamics of the interaction of such radically changed electromagnetic waves with the beam density oscillations.

The Stability of a Magnetized Electron Plasma in the Field of a Circularly Polarized Electromagnetic Wave

1980 ◽  
Vol 22 (2) ◽  
pp. 147-150
Author(s):  
V S Paverman ◽  
I Svimonishvili ◽  
D D Tschakaya ◽  
Lars Falk
Keyword(s):  
Electromagnetic Wave ◽  
Electron Plasma ◽  
Circularly Polarized ◽  
The Stability

scholarly journals Медленные электромагнитные волны в левой среде на основе магнитоактивного плазменного метаматериала

2020 ◽  
Vol 46 (24) ◽  
pp. 33
Author(s):  
А.В. Богомолова ◽  
С.В. Гришин ◽  
Ю.П. Шараевский
Keyword(s):  
Electromagnetic Waves ◽  
Theoretical Study ◽  
Electron Plasma ◽  
Ring Resonators ◽  
Active Plasma ◽  
Cold Electron ◽  
Split Ring ◽  
Left Handed ◽  
Study Results ◽  
Strip Waveguide

The paper presents the theoretical study results of the control of the spectrum of slow electromagnetic waves (EMWs) existing in a “left-handed” medium based on a magnetically active plasma metamaterial. The investigated metamaterial is a strip waveguide completely filled with a longitudinally magnetized “cold” electron plasma, containing a periodic structure of perfectly conducting split-ring resonators (SRRs). It is shown that either one (ordinary), either two (ordinary and unordinary) slow EMWs can exist in a “left-handed” medium based on the magnetically active plasma and the spectrum of these waves depends on the SRR own frequency and magnetic induction. The unordinary slow EMW possesses by the negative dispersion and the dispersion characteristic of the ordinary EMW has the sections with both the negative and positive dispersions.

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