Dispersion relation of quasi-static electromagnetic modes in relativistic plasmas

2018 ◽  
Vol 25 (1) ◽  
pp. 012116 ◽  
Author(s):  
Y. C. Medjkoune ◽  
K. Bendib-Kalache ◽  
A. Bendib
Keyword(s):  
Dispersion Relation ◽  
Relativistic Plasmas

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 relation of transverse oscillation in relativistic plasmas with non-extensive distribution

2011 ◽  
Vol 77 (5) ◽  
pp. 653-662 ◽  
Author(s):  
SAN-QIU LIU ◽  
XIAO-CHANG CHEN
Keyword(s):  
Dispersion Relation ◽  
Wavelength Region ◽  
Transverse Oscillation ◽  
Analytic Method ◽  
Short Wavelength Region ◽  
Relativistic Plasmas ◽  
Long Wavelength ◽  
Relativistic Regime ◽  
Analytical Result ◽  
Good Agreement

AbstractThe generalized dispersion equation for superluminal transverse oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma with non-extensive q-distribution is derived. The analytical dispersion relation is obtained in an ultra-relativistic regime, which is related to q-parameter and temperature. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. Using the numerical method, we obtain the full dispersion curve that cannot be given by an analytic method. It is shown that the numerical solution is in good agreement with the analytical result in the long-wavelength and short-wavelength region for ultra-relativistic plasmas.

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