Nonlinear waves in a cold plasma by Lorentz transformation

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.

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Nonlinear waves in a hot plasma by Lorentz transformation

Journal of Plasma Physics ◽

10.1017/s0022377800026015 ◽

1975 ◽

Vol 13 (2) ◽

pp. 231-247 ◽

Cited By ~ 16

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.

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Wave Propagation and Screening in a Dense Two-Component Plasma.

The Astronomical Journal ◽

10.1086/109037 ◽

1963 ◽

Vol 68 ◽

pp. 279

Author(s):

J. S. Goldstein

Keyword(s):

Wave Propagation ◽

Two Component ◽

Component Plasma

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Larmor radius effects on the gravitational instability of a two-component plasma

Journal of Plasma Physics ◽

10.1017/s0022377800021061 ◽

1977 ◽

Vol 18 (2) ◽

pp. 273-286 ◽

Cited By ~ 17

Author(s):

R. P. S. Chhonkar ◽

P. K. Bhatia

Keyword(s):

Growth Rate ◽

Wave Propagation ◽

Gravitational Instability ◽

Unstable Mode ◽

Larmor Radius ◽

Physical Parameters ◽

Neutral Gas ◽

Magnetic Resistivity ◽

Two Component ◽

Component Plasma

The gravitational instability of a two-component plasma has been studied here to include simultaneously the effects of neutral gas friction, finite ion Larmor radius, magnetic resistivity and Hall currents. The viscosities of the two components of the plasma have also been taken into account. The mode of the transverse as well as the longitudinal wave propagation have been discussed. The dispersion relations have been obtained for both these cases and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. For the transverse mode of propagation, it is found that the growth rate of the unstable mode increases with magnetic resistivity and with the ratio of the densities of two components. The influence of the magnetic resistivity is, therefore, destabilizing on this mode of wave propagation. The viscosities of the two components are found to have a stabilizing influence on the growth rate in this case since it is found that the increase of hte viscosity effects reduces the growth rate. For the longitudinal mode also it is found that the effects of viscosities as well as that of neutral gas friction are stabilizing. The magnetic resistivity does not affect the growth rate since the equation determining the growth rate is found to be independent of this effect.

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