On the reflection coefficient of a plasma profile of exponentially tapered electron density and fixed collision frequency

The reflection coefficient (ratio of reflected to incident electric fields) is found at an arbitrary point within a plasma profile of exponentially tapered electron density and fixed collision frequency. To facilitate the analytical solution of the problem it is found advantageous to terminate the profile in a perfectly conducting plate. This artifice has little physical significance if the plate is positioned in the region of reflection, where the electromagnetic field is negligible. But there is some indeterminancy in locating this region. In the present analysis the plate is located at the level of electron density, where the magnitude of the complex relative dielectric constant passes through a minimum, or where the real dielectric constant goes through zero since in the region of these points the electromagnetic field is evanescent. Reflection factors for both plate locations are computed and compared. Evidently, when the plate is positioned at the lower electron density, the magnitude of the reflection coefficient is larger so that an upper bound on the size of the coefficient is established.