Simulations of Langmuir probes in a flowing Plasma

One of the greatest utilities of a Langmuir probe is its relatively small size, a few Debye

lengths or less, which allows for spatially resolved, or flexible, measurements of discharge

parameters. For example, a Langmuir probe may be used to spatially resolve an energetic

beam of ions if the energy of the beam is sufficiently large [1]. However, using a probe in a

region where there is relatively weak plasma flow, as in a presheath or sheath region near a

wall, has not been examined in detail. In fact, recent work on the subject indicates that the

standard analysis of a probe’s IV curve in such a region gives erroneously high electron

densities, leading to incorrect local potential readings [2,3].

Motivated by these shortcomings, we leverage 2D particle-in-cell simulations of a

Langmuir probe in the presheath of a biased electrode to understand where the standard analysis fails.

Notably, the success of the standard analysis is due to its ability to account for sheath

expansion around the probe at different voltages. We find that the sheath expansion is further

increased by the ambient plasma flow of the presheath. The enhanced expansion is nonuniform

and is greater on the downstream side of the probe, where the density is different compared to

the upstream side. Accounting for the increase in the effective collecting area corrects the

current sheath expansion model, allowing for accurate measurements of plasma density near

other sheath regions using a Langmuir probe.

[1] W. Weber et al, J. Appl. Phys. 50 (1979)

[2] P. Li et al, Plasma Sources Sci. Technol. 29 025015 (2020)

[3] G. Severn et al, “Experimental Studies of the difference between electron and ion densities measured by Langmuir probes in the presheath”, APS GEC 2023.