Work

On the importance of slow ions in the kinetic Bohm criterion

Year: 2024

Type: article

Abstract: Between a plasma and a solid target lies a positively charged sheath of several Debye lengths $\lambda _{D}$ width, typically much smaller than the characteristic length scale $L$ of the main plasma. This scale separation implies that the asymptotic limit $\epsilon = \lambda _{D} / L \rightarrow 0$ is useful to solve for the plasma-sheath system. In this limit, the Bohm criterion must be satisfied at the sheath entrance. A new derivation of the kinetic criterion, admitting a general ion velocity distribution, is presented. It is proven that, for $\epsilon \rightarrow 0$ , the distribution of the velocity component normal to the target, $v_x$ , and its first derivative must vanish for $|v_x| \rightarrow 0$ at the sheath entrance. These two conditions can be subsumed into a third integral one after it is integrated by parts twice. A subsequent interchange of the limits $\epsilon \rightarrow 0$ and $|v_x| \rightarrow 0$ is invalid, leading to a divergence which underlies the misconception that the criterion gives undue importance to slow ions.

Source: Journal of Plasma Physics

DOI: 10.1017/s0022377824001387

Authors: Alessandro Geraldini, Stephan Brunner

Institution: École Polytechnique Fédérale de Lausanne

Language: English

Topic: Plasma Diagnostics and Applications

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: EUROfusion