Upper Hybrid Mode in an Inhomogeneous Plasma

The dispersion of the normal mode at the upper hybrid frequency (Propagating parallel to a uniform magnetic field) in a spatially inhomogeneous plasma has been calculated. The perturbed potential has been solved in $k$ space for the case of a Maxwellian plasma; in the limit $k_{\parallel }\ll k_{\perp }$, the potential function has been shown to satisfy the Whittaker equation. The results obtained are in good agreement with those obtained from a recent experiment.