Abstract
The sheath-edge electric field ( Es ) is an important parameter to patch the quasi-neutral pre-sheath and non-neutral sheath regions. The choice of Es significantly influences the theoretically estimated values of the sheath width, potential, and ion density distribution inside the sheath, as determined by the Poisson equation. The precise nature of Es has been a persistent subject of investigation, giving rise to the question of whether it should be zero or possess a finite value, as proposed by various authors. In this study, we determine the values of Es by solving Poisson’s equation as a boundary-value problem, utilizing experimentally determined values of sheath radius from a DC-biased hairpin probe. The obtained values of Es are found to be finite and closely align with the analytical expressions presented by Riemann (1991 J. Phys. D: Appl. Phys. 24 493) and Kaganovich (2002 Phys. Plasmas 9 4788). Additionally, the impact of electron-penetrating sheaths and interacting sheaths on the applicability of the hairpin probe in low-pressure plasmas is briefly discussed.
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