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 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.

Cerenkov and cyclotron instabilities in a plasma stream

1967 ◽  
Vol 1 (1) ◽  
pp. 1-27 ◽  
Author(s):  
C. F. Knox
Keyword(s):  
Magnetic Field ◽  
Plane Wave ◽  
Cold Plasma ◽  
Numerical Calculations ◽  
Graphical Form ◽  
Plasma Stream ◽  
Wave Growth ◽  
Stationary Medium ◽  
Phase Propagation ◽  
Positive Ion

The model of a stationary medium traversed by a weak plasma stream directed along a magnetic field is investigated. The usual linear treatment is adopted, and the stream is taken to be ‘cold’, with only electron (perturbation) motions considered. The objective is to assess the plane-wave growth associated with both Cerenkov and cyclotron instabilities; in particular, the dependence of the growth on frequency and angle of phase propagation. The main discussion is of the case when the stationary medium is a cold plasma in which both electron and positive ion motions are taken into account. Various expressions for the growth are derived, and numerical calculations are presented in graphical form.

An early formulation by Stokes of the theories of the rotatory polarizations of light

1924 ◽  
Vol 22 (1) ◽  
pp. 76-81 ◽  
Author(s):  
Joseph Larmor
Keyword(s):  
Magnetic Field ◽  
Frame Of Reference ◽  
Spatial Frame ◽  
Fixed Direction ◽  
Early Formulation ◽  
Magneto Optic

AbstractThe two letters now communicated are from G. G. Stokes to W. Thomson, of dates Dec. 12–13, 1848, three years after Faraday's great magneto-optic discovery. They formulated already the permissible types for general equations of propagation, virtually on the basis of the very modern criterion of covariance,—relative to all changes of the spatial frame of reference in the case of active fluids, but having regard to the fixed direction of the extraneous magnetic field in the Faraday case. Their form was elucidated in each case by correlation with a remarkable and significant type of rotational stress in a propagating medium.

Resonance tunnelling of waves in a stratified cold plasma

1979 ◽  
Vol 290 (1374) ◽  
pp. 405-433 ◽  
Keyword(s):  
Refractive Index ◽  
Incident Wave ◽  
Cold Plasma ◽  
Oblique Incidence ◽  
Formal Proof ◽  
The Other ◽  
Governing Equations ◽  
Free System ◽  
Transmitted Waves ◽  
Incident Waves

The theory of the tunnelling of waves through a barrier in which the square of the effective refractive index is zero at one boundary and infinite at or near the other is studied. An infinity of the refractive index is called a resonance and so we speak of resonance tunnelling. The sum of the powers in the reflected and transmitted waves is less than the power in the incident wave even in a loss free system where there is no mechanism for the absorption of energy. A formal proof is given that there must be such a disappearance of energy, associated with the solution of the governing equations that is singular at the resonance. The problem of what has happened to the lost energy is discussed. Some previous treatments dealt only with normally incident waves, but this is a degenerate case. The theory is extended to include oblique incidence and some new features are revealed. Some specific examples are worked out as illustrations.

Photometrical Evidences in Favour of the “Flat Solar Corona”

1994 ◽  
Vol 144 ◽  
pp. 111-113
Author(s):  
R. A. Gulyaev ◽  
N. Ya. Vanyarkha ◽  
E. S. Vanyarkha
Keyword(s):  
Solar Corona ◽  
Current Sheet ◽  
Physical Meaning ◽  
Quantitative Description ◽  
Sunspot Cycle ◽  
Standard Technique ◽  
Heliospheric Current Sheet ◽  
Frame Of Reference ◽  
Clear Physical Meaning ◽  
Conventional View

AbstractThe conventional way of quantitative description of coronal forms is shown to be inadequate as compared with actual coronal configurations. The standard technique of determining the Ludendorff’s parameter in the heiiographic reference has no physical meaning. However the similar parameter as determined in the heliomagnetic frame of reference is of quite clear physical meaning since it depicts the actual concentration of the coronal material towards the heliospheric current sheet. Conclusion of a need to revise the conventional view on relation of coronal forms with the sunspot cycle is pointed out.

scholarly journals Recovery of steady periodic wave profiles from pressure measurements at the bed

2013 ◽  
Vol 714 ◽  
pp. 463-475 ◽  
Author(s):  
D. Clamond ◽  
A. Constantin
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Periodic Wave ◽  
Classical Solutions ◽  
Periodic Waves ◽  
Pressure Measurements ◽  
Governing Equations ◽  
Shallow Water Waves ◽  
Wave Profiles

AbstractWe derive an equation relating the pressure at the flat bed and the profile of an irrotational steady water wave, valid for all classical solutions of the governing equations for water waves. This permits the recovery of the surface wave from pressure measurements at the bed. Although we focus on periodic waves, the extension to solitary waves is straightforward. We illustrate the usefulness of the equation beyond the realm of linear theory by investigating the regime of shallow-water waves of small amplitude and by presenting a numerical example.

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 Some Applications of Transformation to the Space?independent Frame in the Processes of Strong Radiation in Plasmas

1983 ◽  
Vol 36 (1) ◽  
pp. 67 ◽  
Author(s):  
SN PauI ◽  
B Chakraborty
Keyword(s):  
Dispersion Relation ◽  
Differential Equations ◽  
Cold Plasma ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Transverse Waves ◽  
Nonlinear Plasma ◽  
Circularly Polarized ◽  
Unmagnetized Plasma ◽  
Strong Radiation

Transformation of nonlinear plasma equations from a lab frame S to the space-independent frame S' (both inertial) for an electromagnetic (EM) wave in an unbounded plasma reduces the nonlinear partial differential equations in S to ordinary nonlinear differential equations in S'. This relativistically correct transformation is used (1) to find the intensity induced precessional rotation of the polarization ellipse of vibration of an EM wave, (2) in the S-frame Lagrangian of the particles and field produced by them to derive the exact nonlinearly correct dispersion relation for a strong circularly polarized wave in a cold unmagnetized plasma, and (3) to rectify some much discussed differential equations obtained by Akhiezer and Polovin (1956) to study the evolution of longitudinal and transverse waves in a cold plasma.

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