## 1. Introduction

[2] *Fisher and Gould* [1971] measured the field around a radio frequency antenna in a laboratory magnetoplasma and observed the resonance cone on which this field is a maximum. Fine structure on the edge of this cone was assumed to result from interference between the received signal due to an ES wave and an electromagnetic (EM) field. The EM field was evanescent and so, at a given time, had the same phase everywhere in the plasma. *Gonfalone* [1972] studied the influence of temperature on this structure.

[3] *Kuehl* [1973] derived the potential of an oscillating point charge in a magnetoplasma using inhomogeneous waves. The imaginary component of **k, k**_{i} was taken to be in the direction perpendicular to **H**^{0}. *Thiel and Lembège* [1982, hereafter TL] normalized the potential to the free space value and calculated the potential using the ES approximation to the tensor dielectric constant and obtained good agreement with their experimental results. They referred to this method as the least damped method in which the component of **k** in the direction of **H**^{0} is real and only two modes are considered. Using their technique good agreement is found here with the experimental results of *Gonfalone* [1972], although the method used by TL has been modified slightly.

[4] In this paper an attempt to explain the experimental results applying different approaches using inhomogeneous waves is carried out in order to see which is the most successful. In addition to the least damped method, another method is considered, called the “minimum-*k*_{i}” method, for which the direction of the imaginary part of *k* is varied until *k*_{i} obtains a minimum value. The minimum-*k*_{i} method is more successful than the homogeneous method but cannot explain all the experimental results. A new approach, called the “Im{**k** · **v**_{g}} = 0” method, for lack of a better name, is as successful as the least damped method in explaining the experimental results.

[5] There is no particular reason to assume homogeneous waves in propagation through an absorbing or nonabsorbing medium. Consider plane waves obliquely incident on an absorbing, bounded, horizontally stratified ionosphere. Below the ionosphere, **k**_{i} can be considered to be in any direction since the amplitude does not change with distance; however, once in the ionosphere the amplitude decreases in a direction perpendicular to the horizontal stratification and **k**_{r} is at some oblique angle determined by Snell's law. Hence the wave is inhomogeneous. Inside a plasma, plane waves can be assumed to exist at the source with equal amplitude in all directions; that is, all **k**_{i} are possible just as all **k**_{r} are possible. By using the dispersion relation for inhomogeneous waves, propagation characteristics for any direction of **k**_{r} and **k**_{i} can be determined.

[6] In the work of *Muldrew and Gonfalone* [1974, hereafter MG] the interference results of *Gonfalone* [1972, 1973] measured near the resonance cones and for Bernstein waves are presented and explained using the dispersion equation for homogeneous waves in a hot magnetoplasma. This dispersion equation [*Lewis and Keller*, 1962, hereafter LK] is valid for both ES and EM waves and was programmed by *Muldrew and Estabrooks* [1972]. Isotropic temperatures and approximate plasma frequencies were obtained from the experimental results at both the lower oblique resonance cone (associated with the whistler mode for which the wave frequency *f* is less than both the plasma frequency *f*_{p} and the cyclotron frequency *f*_{c}) and the upper oblique resonance cone (associated with the lower branch of the extraordinary or Z mode in which *f* > *f*_{p} and *f* > *f*_{c} but *f* < *f*_{uh}, where *f*_{uh} is the upper hybrid frequency). These temperatures were compared with the temperature obtained from an interference pattern resulting from the EM field and Bernstein waves with *f*_{c} < *f* < 2*f*_{c} and 2*f*_{c} < *f*_{uh} [*Gonfalone*, 1972, 1973; *Gonfalone and Beghin*, 1973] presented in MG. MG could not explain the complete interference pattern. The complete pattern is explained here using the dispersion relation for inhomogeneous waves for which Im{**k** · **v**_{g}} = 0. This technique allows some understanding of wave propagation for waves with a complex wave vector. The results are close, but not identical, to those obtained using the least damped method.

[7] The reader is referred to MG for details of the experimental setup, the experimental results, and the dispersion curves obtained assuming the real and imaginary components of the wave vector are collinear or parallel. In this paper we present the modifications to LK that are necessary if the real and imaginary components of the wave vector are not parallel (see Appendix A). Dispersion curves are presented that can explain the experimental results. Under the assumption that **k**_{i} is in the plane of **k**_{r} and **H**^{0}, the generalized LK dispersion curves are compared to those obtained with *Stix* [1992]. An unusual discrepancy is found that is not understood. The generalized LK theory is more general than the Stix theory since Stix takes the real and imaginary parts of the component of **k** perpendicular to **H**^{0} to be parallel [see *Stix*, 1992, equation (37), section 10].