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P: Fachverband Plasmaphysik
P 21: Low Pressure Plasmas and their Application II
P 21.1: Hauptvortrag
Donnerstag, 29. Februar 2024, 14:00–14:30, ELP 6: HS 3
The collisionally modified Bohm criterion: Insight or illusion? — •Ralf Peter Brinkmann — Ruhr-Universität Bochum
In low pressure plasmas, where the Debye length
λD
is much smaller than the mean free path λ, the transition from the quasineutral
plasma to the electron-depleted sheath is governed by the Bohm criterion [1]:
Ions exit the plasma into the sheath with a speed vB= √Te/mi.
(Te denotes the electron temperature and mi the mass of the ions.)
Long-standing debates surround the application of the Bohm criterion in plasmas where the λD/λ ratio is not small, prompting questions about the necessity of adjusting the critical velocity.
This contribution investigates a stationary model of a plasma-sheath transition where the electrons are in Boltzmann equilibrium and the ion motion is governed by the ambipolar field, the space-charge field, collisional friction, and inertia. Within the quasi-neutral presheath,
the ambipolar field prevails over friction,
while in the sheath, the space charge field balances the
inertia.
The mathematical description of this scenario results in a differential
equation for the ion speed vi
as a function of a transformed spatial coordinate q.
A removable singularity at a specific ion speed resembles a collisionally modified Bohm criterion [2].
The presentation will explore the physical significance of this feature, examining whether it truly reflects system characteristics (insight) or simply arises as a mathematical artifact (illusion).
[1] D. Bohm, in The Characteristics of Electrical Discharges in Magnetic Fields, A. Guthry and R.K. Wakerling (eds.) New York (1949)
[2] R.P. Brinkmann J. Phys. D: Appl. Phys. 44, 042002 (2011)
Keywords: Plasma sheath transition; Collisionally modified Bohm criterion