Accounting for Debye sheath expansion for proud Langmuir probes in magnetic confinement fusion plasmas.

Abstract

A Child-Langmuir law-based method for accounting for Debye sheath expansion while fitting the current-voltage I-V characteristic of proud Langmuir probes (electrodes that extend into the volume of the plasma) is described. For Langmuir probes of a typical size used in tokamak plasmas, these new estimates of electron temperature and ion saturation current density values decreased by up to 60% compared to methods that did not account for sheath expansion. Changes to the collection area are modeled using the Child-Langmuir law and effective expansion perimeter lp, and the model is thus referred to as the "perimeter sheath expansion method." lp is determined solely from electrode geometry, so the method may be employed without prior measurement of the magnitude of the sheath expansion effects for a given Langmuir probe and can be used for electrodes of different geometries. This method correctly predicts the non-saturating ΔI/ΔV slope for cold, low-density plasmas where sheath-expansion effects are strong, as well as for hot plasmas where ΔI/ΔV ∼ 0, though it is shown that the sheath can still significantly affect the collection area in these hot conditions. The perimeter sheath expansion method has several advantages compared to methods where the non-saturating current is fitted: (1) It is more resilient to scatter in the I-V characteristics observed in turbulent plasmas. (2) It is able to separate the contributions to the ΔI/ΔV slope from sheath expansion to that of the high energy electron tail in high Te conditions. (3) It calculates the change in the collection area due to the Debye sheath for conditions where ΔI/ΔV ∼ 0 and for V = Vf.