The collisionally modified Bohm criterion: Insight or illusion?

In low-pressure plasmas, where the Debye length λ_D 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: ions exit the plasma into the sheath with a speed v_B = √T_e/m_i (T_e is the electron temperature and m_i the ion mass). There are ongoing debates about the Bohm criterion's application in plasmas where the λ_D/λ ratio is not small, raising questions about the necessity of adjusting the critical velocity.

This study examines a stationary model of a plasma-sheath transition where electrons are in Boltzmann equilibrium, and ion motion is governed by the ambipolar field, space-charge field, collisional friction, and inertia. In the quasineutral presheath, the ambipolar field dominates friction, while in the sheath, the space-charge field balances inertia. The mathematical description results in a differential equation for 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.

The presentation will discuss the physical significance of this feature, exploring whether it reflects system characteristics (insight) or is 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)