Approximate relativistic dispersion relation for electron Bernstein waves in a Maxwellian plasma

2005 ◽  
Vol 47 (11) ◽  
pp. 2003-2017 ◽  
Author(s):  
A N Saveliev
Keyword(s):  
Dispersion Relation ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion ◽  
Bernstein Waves

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 1. Ordinary modes

1987 ◽  
Vol 37 (3) ◽  
pp. 435-447 ◽  
Author(s):  
P. A. Robinson
Keyword(s):  
Dispersion Relation ◽  
Uniform Magnetic Field ◽  
Cold Plasma ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Infinite Family ◽  
Companion Paper ◽  
Maxwellian Plasma ◽  
Bernstein Waves ◽  
Plasma Theory

Ordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. Weakly relativistic resonance broadening, frequency downshift and damping are found to alter dramatically the dispersion predicted by the corresponding strictly non-relativistic (‘classical’) theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. All classical resonances and cut-offs are removed except the cut-off at the plasma frequency ωp. At frequencies above ωp the infinite family of classically predicted modes is replaced by a single weakly damped mode whose dispersion differs only slightly from that predicted by cold plasma theory. No weakly damped modes exist in the range of harmonics s satisfying (ωp/Ωe)⅔/8 ≲ S < Ωp/Ωe, however, one such mode is located immediately below each harmonic for s ≲ (ωp/Ωe)⅔/8. A companion paper investigates extraordinary solutions of the dispersion relation.

Effect of longitudinal electric fields on electrostatic electron cyclotron waves

1983 ◽  
Vol 29 (1) ◽  
pp. 35-40 ◽  
Author(s):  
Armando L. Brinca ◽  
Kristian B. Dysthe
Keyword(s):  
Dispersion Relation ◽  
Iterative Method ◽  
Electric Fields ◽  
Homogeneous Medium ◽  
Modified Dispersion Relation ◽  
Poisson Equations ◽  
Adopted Model ◽  
Bernstein Waves ◽  
Locally Homogeneous ◽  
Electron Cyclotron Waves

We study the influence of static parallel electric fields on the characteristics of obliquely propagating electron Bernstein waves. Analysis of the equilibrium state defines the range of validity of the adopted model, viz. a collisionless, locally homogeneous medium described by the Vlasov and Poisson equations. An iterative method yields the modified dispersion relation whose numerical solution, for an idealized medium, suggests the relevance of the effects induced by static parallel electric fields in natural plasmas.

scholarly journals Electron Bernstein waves in a collisionless magnetoplasma with Cairns distribution function

2018 ◽  
Vol 96 (4) ◽  
pp. 406-410
Author(s):  
M. Usman Malik ◽  
W. Masood ◽  
Aman-ur Rehman ◽  
Arshad M. Mirza ◽  
Anisa Qamar
Keyword(s):  
Dielectric Constant ◽  
Distribution Function ◽  
Dispersion Relation ◽  
Dispersion Curves ◽  
Magnetized Plasma ◽  
Modified Dispersion Relation ◽  
Bernstein Waves

In this paper, we have investigated the electrostatic electron Bernstein waves in a collisionless magnetized plasma using the Cairns distribution function. In this regard, we have derived a generalized dielectric constant for the Bernstein waves and derived the modified dispersion relation in the presence of Cairns distribution function. We have found that the dispersion curves for the electron Bernstein waves using the Cairns distribution function show a very significant deviation from the Maxwellian results. It has been found that the behavior of the Bernstein waves across the entire band between the adjacent harmonics shows a departure from the Maxwellian result for the different values of the non-thermality parameter for the Cairns distribution function.

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