On the Use of Sweeping Langmuir Probes in Cutting-Arc Plasmas—Part II: Interpretation of the Results

A semiempirical Langmuir probe model is introduced that is particularly adapted to high-energy-density cutting arcs, for which, as we have shown in part I, the ion current collected by negatively biased probes shows no plateau in the ion branch of the current-voltage (I-V) probe characteristic, and the signal amplitude is independent of the probe radius. According to the model, the ion drag due to the high-velocity plasma flow around the probe limits the effectively collecting area to a small fraction of the probe surface. If, according to the experimental evidence, this fraction is made independent of the probe radius, then its value results proportional to the probe bias, and so no plateau is found, at least as long as the collecting area is less than (half) the probe surface, which happens only at rather high probe bias. The model requires the determination of the function relating the electric field (in the region between the unperturbed plasma and the space-charge sheath close to the probe) to the parameters of the problem. Dimensional analysis together with empirical information allow to restrict the form of this function to leave only an auxiliary dimensionless function, which can be argued to be practically constant and whose value can be determined between rather tight bounds. As an example, radial profiles of plasma temperature and density are obtained by applying the proposed model to the experimental values of a I-V probe characteristic obtained in part I. The derived temperature profile is in good agreement with a previous published numerical simulation for a similar cutting torch.