Longitudinal dielectric function and dispersion relation of electrostatic waves in relativistic plasmas

2017 ◽  
Vol 24 (2) ◽  
pp. 022111 ◽  
Author(s):  
B. Touil ◽  
A. Bendib ◽  
K. Bendib-Kalache
Keyword(s):  
Dispersion Relation ◽  
Dielectric Function ◽  
Electrostatic Waves ◽  
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.

Electromagnetic instability supported by a rippled, magnetically focused relativistic electron beam

1984 ◽  
Vol 31 (2) ◽  
pp. 239-251 ◽  
Author(s):  
S. Cuperman ◽  
F. Petran ◽  
A. Gover
Keyword(s):  
Electron Beam ◽  
Dispersion Relation ◽  
Growth Rates ◽  
Relativistic Electron Beam ◽  
Electron Beams ◽  
Wave Instability ◽  
Electrostatic Waves ◽  
Long Wavelength ◽  
Ripple Amplitude ◽  
Electromagnetic Instability

The coupling of volume, long-wavelength TM electromagnetic and longitudinal space charge (electrostatic) waves by the rippling of magnetically focused electron beams is examined analytically. The dispersion relation is obtained and then solved for these types of wave. Instability, with growth rates proportional to the relative ripple amplitude of the beam, is found and discussed.

Dispersion relation for electrostatic waves in plasmas with isotropic and anisotropic Kappa distributions for electrons and ions

2017 ◽  
Vol 83 (5) ◽  
Author(s):  
L. F. Ziebell ◽  
R. Gaelzer ◽  
F. J. R. Simões
Keyword(s):  
Dispersion Relation ◽  
Dispersion Relations ◽  
Distribution Functions ◽  
Sound Waves ◽  
Kappa Index ◽  
Langmuir Waves ◽  
Electrostatic Waves ◽  
Particle In Cell ◽  
Significant Difference ◽  
Velocity Distribution Functions

Velocity distribution functions which feature extended tails with power-law dependence have been consistently observed in the solar wind environment and are frequently modelled by the so-called Kappa distributions. Different forms of Kappa distributions are commonly employed in analytical studies, and despite their similarities, they can produce different effects on the dispersion properties that occur in a plasma. We consider two different and widely used forms of Kappa distributions, in both isotropic and anisotropic cases, and systematically discuss their effects on the dispersion relations of Langmuir and ion-sound waves. It is shown that in the case of Langmuir waves, one of the forms leads to the expression for the Bohm–Gross dispersion relation, valid for plasmas with Maxwellian velocity distributions, while the other form of Kappa functions leads to a dispersion relation with significant difference regarding the Maxwellian case, particularly in the case of small values of the kappa index. For ion-sound waves, the dispersion relations obtained with the different forms of Kappa distributions are different among themselves, and also different from the Maxwellian case, with difference which increases for small values of the kappa index. Some results obtained from numerical solution of the dispersion relations are presented, which illustrate the magnitude of the perceived differences. Some results obtained with relativistic particle-in-cell simulations are also presented, which allow the comparison between the dispersion relations obtained from analytical calculations and the frequency–wavelength distribution of wave fluctuations which are observed in numerical experiments.

Surface plasmon dispersion on a single-sheeted hyperboloid

1981 ◽  
Vol 59 (4) ◽  
pp. 521-529 ◽  
Author(s):  
R. S. Becker ◽  
V. E. Anderson ◽  
R. D. Birkhoff ◽  
T. L. Ferrell ◽  
R. H. Ritchie
Keyword(s):  
Dispersion Relation ◽  
Dielectric Function ◽  
Surface Plasmon ◽  
Electric Potential ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Oblate Spheroidal ◽  
Spheroidal Coordinates ◽  
Plasmon Dispersion

The surface-plasmon dispersion relation is obtained for a single-sheeted hyperboloid of revolution. The effects of retardation are neglected, and the electric potential is obtained from Laplace's equation in oblate spheroidal coordinates. Our results are applicable to the description of eigenmodes for a submicron hole in a material which may be supposed to have a local dielectric function.

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