Impedance and Voltage Power Spectra of a Monopole Antenna in a Warm Plasma—Derivation and Application to CubeSats

Abstract

The impedance for a monopole antenna in a warm plasma is derived and compared with the cases for wire dipole and double-sphere antennas. This derivation produces a new expression for the monopole antenna response function, F-m1(x), which is very similar to the double-sphere antenna response function. The monopole, wire dipole, and double-sphere response functions are compared by modeling an antenna in Earth's ionospheric plasma (i.e., electrostatic and collisionless) and predicting the antenna capacitance and voltage power spectra for quasi-thermal noise (QTN) and shot noise. Specifically, we assume the antennas are part of a CubeSat, which has spurred this research as most interplanetary craft carry a dipole or more complicated antenna designs on board (Imbriale, 2006, ; Imbriale, Gatti et al., 2006, ). The monopole antenna current distribution is assumed to be a half-triangular current distribution (considering only the positive half of the triangular distribution), which follows that of prior authors (Balmain, 1965, ; Kuehl, 1966, ; Couturier et al., 1981, ) and simplifies comparison. The predictions for the shot noise and capacitance presented problems, as the integral over wave number space or k space did not converge for large values of k. The derived expression therefore remains a current problem in these situations, and no alternative has been found in the existing literature, necessitating future work to determine a more general expression. In this paper we bring the problem of an appropriate analytic monopole antenna response function to the attention of the community and outline a number of tests that can be used to verify any future expression.