Hydrodynamic and hydromagnetic stability

Magnetic stabilization of transverse plasma instabilitiest

We derive dispersion formulae for the transverse and longitudinal waves propagating through a Vlassov plasma, valid for relativistic as well as non-relativistic temperatures, and compare them with those of earlier workers. We discuss wave propagation under various limiting conditions of temperature.

Dispersion formulae for waves in a relativistic plasma

The complete solution, for all temperatures and wavenumbers, of the longitudinal and transverse dispersion equations of a relativistic Maxwellian plasma, is presented. It is assumed that the ions are immobile and that there is no zero‐order magnetic field. Analytical methods are used for the very small and very large wavenumber cases, and in the intractable intermediate wavenumber regions numerical results are displayed graphically. The existence at all temperatures of very slightly damped longitudinal plasma waves and slightly damped nonoscillatory transverse excitations is established and the damping constants are evaluated. Necessary and sufficient conditions for the existence of slight Landau damping of longitudinal plasma waves in any general isotropic relativistic Vlasov plasma are also derived. Several new dispersion relations for undamped oscillations, which have phase velocity greater than c, are recorded. One of these, which describes transverse oscillations for large wavenumbers, corresponds to the propagation of light waves in the plasma.

Dispersion Relations in Relativistic Vlasov Plasmas

A relativistic theory of longitudinal oscillations in hot, magnetized, isotropic equilibrium plasmas is presented. The special theory of relativity enters the description, with the requirements that the particle masses are depending on the particle velocities that themselves are limited by the speed of light. Using the relativistic Maxwell–Boltzmann–Juttner distribution correctly describing the equilibrium state of a plasma, the dispersion relations for subluminal, as well as superluminal waves, are formulated using the Trubnikov representation. Besides a discussion of the dispersion curves, it is shown that superluminal oscillations are always undamped, whereas for subluminal waves the relativistic generalization of the Landau damping is derived. It is shown that the resulting damping rates are significantly lower than those obtained with the nonrelativistic theory.

On Landau damping in hot equilibrium plasmas. I. Longitudinal oscillations along an external magnetic field

The general theory for high‐temperature plasmas, in the presence of an external uniform magnetic field, is developed by means of a Laplace‐transform technique. The dispersion relations for the longitudinal and the transverse oscillations, for a relativistic Maxwellian distribution with mass motion as well as for a non‐Maxwellian distribution in the absence of magnetic field are derived. The stability of two streams is investigated in detail both in the nonrelativistic and in the extreme relativistic limits. The longitudinal and the transverse modes are uncoupled only when the stream velocity and the wave velocity are parallel.

Relativistic Effects on Plasma Oscillations and Two‐Stream Instability. I

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Relativistic Effects on Plasma Oscillations and Two‐Stream Instability. I