The positively biased planar Langmuir probe in high-pressure plasma

Abstract

The properties of a positively biased planar (electron) Langmuir probe, immersed in a high-pressure flowing plasma are investigated both theoretically and experimentally. A theoretical model is proposed for a one-dimensional convection supported sheath, which is very similar to the existing model for negatively biased (ion) probes. The latter model is the basis of existing ion probe relations for flush, cylindrical and spherical configurations, which relate probe current to plasma velocity, plasma ionization and probe bias. It is shown that these relations can be converted to electron probe relations if two steps are taken: first, the calculated ion current to the probe must be multiplied by a factor equal to the ratio of the electronic to ionic mobilities and second, an additional velocity-induced electric field in the plasma outside the sheath must be taken into account. Measurements in a flame plasma utilizing a large planar probe specifically designed to generate planar sheaths of measurable thickness (up to 6 mm) show that the sheath thickness, the plasma electric field and the electron-to-ion current ratio are close to the values predicted by the theoretical model. This direct experimental evidence in support of this model reinforces similar recently published conclusions on cylindrical probes. In the case of these new results, however, the theoretical model is more closely replicated by the experiment, the theory is less approximate, and most importantly, systematic measurements of sheath thickness and plasma electric field establish the integrity of the model in a way that was not possible in the earlier work.