A Complete Electrode Model for Plasma Impedance Probes

Plasma impedance probes measure the impedance spectrum of an antenna immersed in a plasma. The 1964 work of Balmain remains the standard method to interpret these data, using the peak in the magnitude at the upper hybrid frequency to infer plasma electron density. The primary limitations of Balmain's model are the assumption of a homogenous plasma and a cylindrical dipole. This work presents a numerical model applicable to inhomogeneous plasma and arbitrary antenna geometry based on the cold, fluid approximation given by Balmain. This model solves Poisson's equation using the finite element method and accounts for the effects of the dipole using the plasma complete electrode model (PCEM). The PCEM is developed in this article and accounts for the voltage shunting effects of the dipole elements, the discrete current to the dipole, and the plasma sheath surrounding the dipole. The sheath is incorporated as a contact impedance between the dipole and the plasma in a manner analogous to the complete electrode model of electrical impedance tomography. The first portion of this work presents the mathematical framework of the PCEM, starting from Maxwell's equations. The second part of the work compares the output of this numerical method to Balmain's work and to data collected by an impedance probe in the Space Physics Simulation Chamber at the U.S. Naval Research Laboratory. The PCEM results agree with both the observed data and the prior modelling done by Balmain. An additional consequence of the numerical study is the observation that of some second-order resonances not predicted by Balmain's model can be attributed to the presence of the plasma sheath.