A study of dispersion in plasmas

The wave propagation characteristics in a stationary unbounded plasma in a static arbitrary magnetic field are reviewed. If the plasma is drifting, a Lorentz transformation can be made to obtain the ω-k relations in the reference frame where the plasma is moving. The transformation is a simple one for the slow waves with non-relativistic drift velocities. The modified waves for the drifting plasma have an important bearing on the instability of the transverse modes in a system of a drifting plasma in a plasma. The dispersion for bounded (cylindrical geometry) plasmas is studied, where the propagation vector is along the z-axis. The salient features of these waves are obtained by studying the circularly symmetric mode. The general features predicted by the quasi-static approximation are verified and the exact and quasi-static solutions are compared. The range of validity of the quasi-static approximation is determined and the h-values are plotted. As the radius becomes larger these modes evolve into the plane wave cases of the unbounded plasma. When a fast beam of charged particles, electrons, ions or a plasma, traverses a stationary plasma in a magnetic field, there is a possibility of unstable transverse modes of propagation. If the drifting particles are either electrons or ions, the circularly polarized waves exhibit an instability over a very narrow frequency range near the ion and electron cyclotron frequencies respectively. When a plasma drifts through a plasma, in addition to the instabilities noted above, there can be an instability near zero frequency, and the growth condition is determined. For typical parameter values these transverse modes have greater growth constants than the longitudinal mode. These unstable transverse modes have possible applications in the generation of high frequencies, and are possible explanations for various instabilities in the ionosphere