Langmuir-probe characteristic in the presence of drifting electrons

The electron current to a negatively biased, cylindrical Langmuir probe is computed for the case of drifting, Maxwellian electrons in a low-pressure discharge. The degree of drift is characterized by ${\mathit{v}}_{\mathit{d}}$/${\mathit{v}}_{\mathrm{th}}$, where ${\mathit{v}}_{\mathit{d}}$ and ${\mathit{v}}_{\mathrm{th}}$ are the electron drift and thermal speeds, respectively. We find that the inflection point of the characteristic underestimates the plasma potential, for ${\mathit{v}}_{\mathit{d}}$/${\mathit{v}}_{\mathrm{th}}$>1.25. Further, for ${\mathit{v}}_{\mathit{d}}$/${\mathit{v}}_{\mathrm{th}}$ greater than about 0.1, an analysis assuming stationary electrons computes an erroneously high temperature. Probe data from a sputtering magnetron discharge are fitted with the drifting model, giving a concrete example of its use.