Admittance of a cylindrical antenna coated with an inhomogeneous cold plasma sheath with a resonance

In this paper a perfectly conducting, infinitely long, cylindrical antenna is considered. The antenna is driven by an alternating voltage V applied uniformly around an infinitesimally thin, circumferential gap. Furthermore, the antenna is surrounded by a sheath that goes smoothly over into the surrounding plasma so that the electron density increases smoothly with the distance from the antenna. For this two-parameter family of electron-density profiles the admittance of the antenna is calculated for all values of the driving frequency ω > 0 and as a function of the parameters, i.e., of the radius of the antenna and the plasma frequency far away from it. The calculated admittance is further compared with that of the same antenna in vacuum for which Papas’ (1949) results have been generalized. It is shown that a measurement of the admittance of the antenna at only one frequency is, in general, not sufficient to determine uniquely the plasma frequency far away from the antenna. At least two measurements at two different frequencies or with two antennas with different radii are necessary to determine uniquely the electron density far away from the antenna.