Extensions and applications of the Bohm criterion

Abstract

Abstract.The generalized Bohm criterion is revisited in the context of incorporating kinetic effects of the electron and ion distribution functions into the theory. The underlying assumptions and results of two different approaches are compared: The conventional 'kinetic Bohm criterion' and a fluid-moment hierarchy approach. The former is based on the asymptotic limit of an infinitely thin sheath (λ D /l = 0), whereas the latter is based on a perturbative expansion of a sheath that is thin compared to the plasma (λ D /l 1). Here λ D is the Debye length, which characterizes the sheath length scale, and l is a measure of the plasma or presheath length scale. The consequences of these assumptions are discussed in terms of how they restrict the class of distribution functions to which the resulting criteria can be applied. Two examples are considered to provide concrete comparisons between the two approaches. The first is a TonksLangmuir model including a warm ion source [Robertson 2009 Phys. Plasmas 16 103503]. This highlights a substantial difference between the conventional kinetic theory, which predicts slow ions dominate at the sheath edge, and the fluid moment approach, which predicts slow ions have little influence. The second example considers planar electrostatic probes biased near the plasma potential using model equations and particle-in-cell simulations. This demonstrates a situation where electron kinetic effects alter the Bohm criterion, leading to a subsonic ion flow at the sheath edge.

Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs

“…The figure also shows that flow speed of ions at the sheath edge is sonic near the wall, but subsonic near the electrode. A comparison of the simulated speed was found to be consistent with the prediction of equation (32) [155].…”

“…This work also shows consistency with measured IVDFs. The predictions of equation (32) have also been tested using PIC simulations of biased electrodes [155,161]. In this case, the modification from the fluid Bohm criterion arises due to the non-local kinetic character of the electron distribution.…”

Two-fluid solutions for Langmuir probes in collisionless and isothermal plasma, over all space and bias potential

“…The Bohm criterion 5 u i0 ≥ u Bohm = √ qTe mi is recovered for cold ions (T i = 0) and negligible electron inertia (m e = 0). Persson's 23 expression is obtained when ion temperature is accounted for, and the complete expression (16) of Baalrud et al 46 is recovered when electron inertia is also included. Note that criterion (15) implies a general coupling between ion and electron initial velocities for all bias potentials.…”

Concepts, Capabilities, and Limitations of Global Models: A Review

“…Extensions exist for multiple ion species, [34] including negative ions, [35] but the classical result will be used in this model. Although the Bohm velocity is a widely known result in low temperature plasma physics, the applicability of it to any system that deviates from the strict conditions from which it is derived is a topic of ongoing contention, [36][37][38][39][40][41] and researchers should use caution when using a value for the Bohm velocity for anything but the most basic of plasmas.…”