Dispersion relation and group velocity for inhomogeneous waves in a hot magnetoplasma with application to an electron-Bernstein-wave propagation experiment in a laboratory plasma

摘要

Lewis and Keller (1962) derive the dispersion relation for homogeneous waves propagating in a hot magnetoplasma. Homogeneous waves are ones for which the real and imaginary parts of the wave vector, kr and ki, are parallel. In this paper a generalization to Lewis and Keller is made for inhomogeneous waves, that is, waves for which kr and ki are not parallel. If ki is assumed to be in the same plane as kr and the magnetic field H in the Lewis and Keller generalization, comparison can be made with the dispersion relation of Stix (1992); good agreement is found with one exception. This generalization is applied to observations of electrostatic (ES) wave propagation in a laboratory plasma. Bernstein waves propagating perpendicular to H are undamped. The dispersion relation for homogeneous waves indicates that severe damping should occur for propagation slightly off perpendicular. Laboratory experiments indicate that severe damping does not occur. The laboratory results can be explained if inhomogeneous waves are considered. Muldrew and Gonfalone (1974) used the dispersion equation for homogeneous waves in a hot magnetoplasma to explain the signal maxima in the pattern when electron-Bernstein waves interfere with the electromagnetic field. Good agreement is obtained when ki is small compared to kr. However, when ki becomes significant, the pattern can no longer be explained. Different approaches to explaining the results using inhomogeneous waves are presented that are superior to the one using homogeneous waves. In one approach, plasma waves with a complex wave vector can propagate without large attenuation, and propagation characteristics can be determined, by choosing the direction of ki to be a free parameter that makes Im{k · vg} = 0, or have a minimum value; k = kr + iki, vg is the complex group velocity ∂ω/∂k and ω is the real angular wave frequency. When this condition is satisfied, good agreement in the signal maxima is obtained with the laboratory experiments if the direction of energy flow in the plasma is taken to be Re{vg}. This method of calculating the interference pattern is compared with the least damped method which calculates the potential of an oscillating point charge in a plasma. Good agreement between the two methods is found if an assumption is made regarding the wave(s) interfering with the ES Bernstein mode.