RF Impedance of a Spherical Probe at High and Low Gas Pressure

The plasma electron density n$_{eo}$ is most often determined using a Langmuir probe to measure the dc current as a function of the applied dc voltage V$_{dc}$. The dc impedance Z$_{dc}$ varies strongly with V$_{dc}$, and models are needed to relate Z$_{dc}$ to n$_{eo}$. Secondary electron emission, ion collisions, and other effects further complicate the analysis. Alternatively, a variable rf voltage can be applied while holding V$_{dc}$ fixed. As long as the rf voltage is small, the rf impedance Z$_{rf}$ varies with the frequency f but not the amplitude of the voltage, and for a fixed frequency, Z$_{rf}$ depends only on n$_{e}$(r) and the neutral gas density N. In this talk theoretical and experimental results for Z$_{rf}$ are related to n$_{eo}$ for a small spherical probe. At low N, Z$_{rf}$ becomes resistive whenever f equals the local plasma frequency, and both the real and imaginary parts of Z$_{rf}$ peak when f equals the bulk plasma frequency. The peaks make n$_{eo}$ easy to determine, and the resistance at lower frequencies can be used to determine n$_{e}$(r) within the sheath and presheath. At high N, the resistance depends mainly on n$_{eo}$/N, so n$_{eo}$ is again easy to determine. Theoretical and experimental results for several spheres will be compared with Langmuir-probe data at high and low gas pressure.