Estimation of plasma density from wave data of cold electron plasma

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.

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Radial Expansion of a Low Energy Positron Beam Passing Through a Cold Electron Plasma within a Uniform Magnetic Field

Physics Procedia ◽

10.1016/j.phpro.2015.05.009 ◽

2015 ◽

Vol 66 ◽

pp. 52-58

Author(s):

F.F. Aguirre ◽

C.A. Ordonez

Keyword(s):

Magnetic Field ◽

Uniform Magnetic Field ◽

Positron Beam ◽

Electron Plasma ◽

Low Energy ◽

Radial Expansion ◽

Cold Electron

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Electron plasma density deduced from lower oblique resonance measurements

The Physics of Fluids ◽

10.1063/1.864614 ◽

1984 ◽

Vol 27 (2) ◽

pp. 506 ◽

Cited By ~ 1

Author(s):

J. Thiel ◽

L. R. O. Storey ◽

J. P. Lebreton

Keyword(s):

Plasma Density ◽

Electron Plasma

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Exact analytic solutions for nonlinear waves in cold plasmas

Journal of Plasma Physics ◽

10.1017/s002237780700699x ◽

2008 ◽

Vol 74 (4) ◽

pp. 569-573 ◽

Cited By ~ 7

Author(s):

G. ROWLANDS ◽

G. BRODIN ◽

L. STENFLO

Keyword(s):

Wave Breaking ◽

Electron Plasma ◽

Analytic Solutions ◽

Field Amplitude ◽

Cold Electron ◽

Electric Field Amplitude ◽

New Class ◽

Exact Analytic Solutions ◽

Lagrangian Variables ◽

Cold Plasmas

AbstractLarge amplitude plasma oscillations are studied in a cold electron plasma. Using Lagrangian variables, a new class of exact analytical solutions is found. It turns out that the electric field amplitude is limited either by wave breaking or by the condition that the electron density always has to stay positive. The range of possible amplitudes is determined analytically.

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Padé approximants and nonlinear waves

Journal of Plasma Physics ◽

10.1017/s002237780002208x ◽

1979 ◽

Vol 21 (3) ◽

pp. 549-571 ◽

Cited By ~ 1

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.

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Stability of strong electromagnetic waves in overdense plasmas

Journal of Plasma Physics ◽

10.1017/s0022377800026568 ◽

1982 ◽

Vol 27 (2) ◽

pp. 239-259 ◽

Cited By ~ 2

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.

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