The plasma dispersion relation near the two–ion hybrid resonance

1982 ◽  
Vol 27 (2) ◽  
pp. 327-342 ◽  
Author(s):  
S. C. Chiu ◽  
V. S. Chan ◽  
J. Y. Hsu ◽  
D. G. Swanson
Keyword(s):  
Wave Equation ◽  
Critical Temperature ◽  
Dispersion Relation ◽  
Cyclotron Frequency ◽  
Hydrogen Plasma ◽  
Fast Mode ◽  
Temperature Ratio ◽  
Hybrid Layer ◽  
Hybrid Resonance ◽  
Plasma Dispersion

The dispersion relation of a deuterium –hydrogen plasma is investigated near the ion cyclotron frequency of hydrogen at varying hydrogen temperatures. It is found that at low hydrogen-to-deuterium temperature ratios, only the fast mode and the ion Bernstein mode are coupled around the hybrid layer. Above a certain critical temperature ratio Th< Thc, these two modes become coupled also to a third mode. Around and above Thc, the wave equation is of sixth order rather than of the fourth order previously discussed.

Pressure and Shock Waves in Bubbly Liquids

2015 ◽  
Author(s):  
Shahid Mahmood ◽  
Yungpil Yoo ◽  
Ho-Young Kwak
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Sound Propagation ◽  
Relaxation Oscillation ◽  
Bubbly Flow ◽  
Gas Bubbles ◽  
Bubbly Liquid ◽  
Bubbly Liquids ◽  
Pressure Profiles

It is well known that sound propagation in liquid media is strongly affected by the presence of gas bubbles that interact with sound and in turn affect the medium. An explicit form of a wave equation in a bubbly liquid medium was obtained in this study. Using the linearized wave equation and the Keller-Miksis equation for bubble wall motion, a dispersion relation for the linear pressure wave propagation in bubbly liquids was obtained. It was found that attenuation of the waves in bubbly liquid occurs due to the viscosity and the heat transfer from/to the bubble. In particular, at the lower frequency region, the thermal diffusion has a considerable affect on the frequency-dependent attenuation coefficients. The phase velocity and the attenuation coefficient obtained from the dispersion relation are in good agreement with the observed values in all sound frequency ranges from kHz to MHz. Shock wave propagation in bubbly mixtures was also considered with the solution of the wave equation, whose particular solution represents the interaction between bubbles. The calculated pressure profiles are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow. Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factor to affect the relaxation oscillation behind the the shock front.

Relativistic plasma dispersion relation

1969 ◽  
Vol 11 (11) ◽  
pp. 899-902 ◽  
Author(s):  
B N A Lamborn
Keyword(s):  
Dispersion Relation ◽  
Relativistic Plasma ◽  
Plasma Dispersion

The gap over critical temperature ratio in Eliashberg theory

1995 ◽  
Vol 93 (2) ◽  
pp. 113-117 ◽  
Author(s):  
R. Combescot ◽  
G. Varelogiannis
Keyword(s):  
Critical Temperature ◽  
Temperature Ratio ◽  
Eliashberg Theory

Migration of P‐wave reflection data in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 591-596 ◽  
Author(s):  
Suhas Phadke ◽  
S. Kapotas ◽  
N. Dai ◽  
Ernest R. Kanasewich
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Limited Range ◽  
Horizontal Velocity ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Wave propagation in transversely isotropic media is governed by the horizontal and vertical wave velocities. The quasi‐P(qP) wavefront is not an ellipse; therefore, the propagation cannot be described by the wave equation appropriate for elliptically anisotropic media. However, for a limited range of angles from the vertical, the dispersion relation for qP‐waves can be approximated by an ellipse. The horizontal velocity necessary for this approximation is different from the true horizontal velocity and depends upon the physical properties of the media. In the method described here, seismic data is migrated using a 45-degree wave equation for elliptically anisotropic media with the horizontal velocity determined by comparing the 45-degree elliptical dispersion relation and the quasi‐P‐dispersion relation. The method is demonstrated for some synthetic data sets.

Finite-frequency surface waves on current sheets

1991 ◽  
Vol 45 (3) ◽  
pp. 389-406 ◽  
Author(s):  
K. P. Wessen ◽  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Dielectric Tensor ◽  
Magnetic Field Direction ◽  
Field Reversal ◽  
Ion Cyclotron ◽  
The Magnetic Field

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.

Sign in / Sign up

Export Citation Format

Share Document