On the dispersion relation of longitudinal waves in equilibrium plasmas
- Max-Planck-Institut fuer Radioastronomie, Postfach 2024, D-53010 Bonn (Germany)
The dispersion relation of subluminal longitudinal waves in thermal non-degenerated isotropic equilibrium plasmas is investigated. The dispersion relation is derived from the relativistically correct form of the kinetic plasma equations and the appropriate Maxwell--Boltzmann--Juettner plasma equilibrium distribution function. A simple analytic expression for the real part of the dispersion relation is obtained, which holds for all values of the plasma temperature and the index of refraction and improves earlier infinite series approximations. The new form of the dispersion function allows the derivation in implicit form of the wavenumber, real part and imaginary part (for weak damping) of all possible subluminal longitudinal plasma modes. The relativistically correct analysis leads to markedly different result than previous non-relativistic work. The results are illustrated for a one-component electron plasma and a two-component electron-ion plasma. In both cases it is found that Langmuir waves and sound waves are asymptotic solutions of the same longitudinal plasma mode and that they only occur for wavelengths above the electron thermal Debye length. While superluminal Langmuir waves have no Landau damping, subluminal Langmuir waves undergo weak Landau damping. The derived damping rate of subluminal Langmuir waves differs by orders of magnitude from the decrement derived by Landau and corrected by Jackson on the basis of non-relativistic equations. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
- OSTI ID:
- 165778
- Journal Information:
- Physics of Plasmas, Vol. 2, Issue 11; Other Information: PBD: Nov 1995
- Country of Publication:
- United States
- Language:
- English
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