Determination of Average Plasma Conductivity by rf Probes

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Abstract
Study of determination of the spatial average plasma conductivity by a radio-frequency probe is tackled for a cylindrical plasma assumed radially inhomogeneous. The real and imaginary part of the probe impedance vs the probing frequency are found numerically for inhomogeneous plasmas with conductivity profiles of the type σ(ρ) = σmax(1−mρn). With such an analysis only two independent average conductivities are found, both at low frequency. The analytical form of the average conductivities is obtained, comparing, in a low-frequency approximation, the tested inhomogeneous medium with a fictitious homogeneous one for which the real or imaginary part of the probe impedance varies in the same way. As a result of a measurement of the rf energy dissipation in the medium (effected by evaluating the probe Q-factor), the average conductivity is σ*=(4/R4) ∫ 0Rσ(r)r3dr;the average conductivity becomes σ**2=34[(4/R4) ∫ 0Rσ(r)r3dr]2+(3/2R6) ∫ 0Rr5dr[(4/r4) ∫ 0rσ(r)r3dr]2in case of a measurement of the inductance variation. An application of the method is carried out in a flow facility plasma jet; with Q-factor measurements from 0.5 to 1.5 MHz, average conductivity values from 75 to 100 mho/m are obtained. The probe is calibrated with electrolytic solutions (H2SO4) of standard conductivity.