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.