Surface-charge distribution approach for modeling of quasi-static electric antennas in isotropic thermal plasma

This paper presents the general theory in the quasi-static limit of a modeling method for radio frequency (RF) electrical sensors of any shape, including their real environment, in isotropic and uniform plasma. This is particularly applicable to plasma probes and antennas installed on board spacecraft for purposes such as natural wave investigations and thermal plasma diagnostics. We propose to use the surface-charge distribution (SCD) method, which involves the assumption that all boundary surfaces under consideration, including spacecraft structures and ion sheath interfaces, are submitted to the RF electrostatic equilibrium imposed by the kinetic plasma. The resulting real and fictitious charges are assumed to be distributed among infinitesimal surface elements, so that each of them can be considered as a single pulsating point source. The well-known difficulties with the conventional induced electromotive force (emf) method when the current distribution is not trivial are skirted here since the Green function is solved once and for all in the case of single point source. The problem amounts to solving a set of linear equations resulting from boundary conditions imposed by surface potentials, external fields, and network interconnections. In a companion paper, we present an application of the SCD numerical method to an actual space experiment.