New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Abstract

We describe a procedure to obtain the plasma parameters from the I-V Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, q and r, to the usual plasma parameters: plasma potential (Vp), floating potential (Vf), electron density (n), and electron temperature (T). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the I-V Langmuir curve with the q-Weibull distribution function, and is motivated by recent works which use the q-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the q-exponential distribution function, and the q-Weibull distribution function. We explain the limitations of the q-exponential function, where the experimental data V > Vp needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the q-Weibull function is introduced as a natural generalization to the q-exponential distribution, and it has greater flexibility in order to represent the concavity change around Vp. We apply this procedure to analyze the measurements corresponding to a nitrogen N2 cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the q parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.