Electron density dependence of impedance probe plasma potential measurements

Abstract

In earlier works, we used spheres of various sizes as impedance probes in demonstrating a method of determining plasma potential, φp, when the probe radius is much larger than the Debye length, λD. The basis of the method in those works [Walker et al., Phys. Plasmas 13, 032108 (2006); ibid. 15, 123506 (2008); ibid. 17, 113503 (2010)] relies on applying a small amplitude signal of fixed frequency to a probe in a plasma and, through network analyzer-based measurements, determining the complex reflection coefficient, Γ, for varying probe bias, Vb. The frequency range of the applied signal is restricted to avoid sheath resonant effects and ion contributions such that ωpi ≪ ω ≪ ωpe, where ωpi is the ion plasma frequency and ωpe is the electron plasma frequency. For a given frequency and applied bias, both Re(Zac) and Im(Zac) are available from Γ. When Re(Zac) is plotted versus Vb, a minimum predicted by theory occurs at φp [Walker et al., Phys. Plasmas 17, 113503 (2010)]. In addition, Im(Zac) appears at, or very near, a maximum at φp. As ne decreases and the sheath expands, the minimum becomes harder to discern. The purpose of this work is to demonstrate that when using network analyzer-based measurements, Γ itself and Im(Zac) and their derivatives are useful as accompanying indicators to Re(Zac) in these difficult cases. We note the difficulties encountered by the most commonly used plasma diagnostic, the Langmuir probe. Spherical probe data is mainly used in this work, although we present limited data for a cylinder and a disk. To demonstrate the effect of lowered density as a function of probe geometry, we compare the cylinder and disk using only the indicator Re(Zac).