Bohm Criterion in a Magnetized Plasma Sheath

Abstract

Bohm criterion in a magnetized plasma sheath is investigated with a fluid model.The upper and lower limits for the sheath criterion in different states of applied magnetic field are studied. The results from numerical simulation reveal that the magnetic field affects significantly the ion Mach number. The variation of the ion Mach number with the incident angle of the ions is also presented.

Examining the range of validity of the Bohm criterion

“…But the new Bohm criterion corresponds to a misinterpretation of sheath model according to the mathematical structure of boundary layer when the non-neutrality parameter q → 0. According to Liu et al (2003); ; El Kaouini et al (2011); Ghomi and Khoramabadi (2011);Ji et al (2011);and Hatami and Shokri (2012), for an electropositive plasma in collisional regime (β → ∞), with cold ions and no ionizations (q c = q and q i → 0), the velocity of positive ions at the sheath edge (u 0 = v +s /c s ) must be bounded by: (3.20b) or in the pre-sheath representation:…”

“…But the new Bohm criterion corresponds to a misinterpretation of sheath model according to the mathematical structure of boundary layer when the non-neutrality parameter q → 0. According to Liu et al (2003); ; ; El Kaouini et al 2011; Ghomi and Khoramabadi (2011); Ji et al (2011); and Hatami and Shokri (2012), for an electropositive plasma in collisional regime (β → ∞), with cold ions and no ionizations (q c = q and q i → 0), the velocity of positive ions at the sheath edge (u 0 = v +s /c s ) must be bounded by: (3.20b) or in the pre-sheath representation: β, q) and η s = η (ξ s ; β, q) being the electric field at the sheath edge when q = 0. The problem is that to obtain these relations, the authors assume that the point S belongs to the exact solution when q = 0 and does not consider the dependence of η (orẏ) with the non-neutrality parameter q.…”

“…In recent years, in particular, there are some authors that claim that there is a specific Bohm criterion when collisions are taken into account. According to their work, the speed of positive ions in the sheath edge must be bounded by minimum and maximum values El Kaouini et al 2011;Ghomi and Khoramabadi 2011;Ji et al 2011;Hatami and Shokri 2012). These studies were based on the results of the pioneering work by Liu et al (2003).…”

Kinetic-theory-based investigation of electronegative plasma–wall transition with two populations of electrons

“…Besides these, it is crucial in the understanding of the Earthʼs ionosphere [16] and astrophysical plasmas [17]. In the past few decades, many works have been devoted to the study of plasma-sheath characteristics with two or more populations of negatively charged particles (e.g., two groups of electrons, or those containing negative ions) and this is still an attractive subject in plasma physics [18][19][20][21][22]. Sheridan et al [10] experimentally observed the existence of two-temperature groups: hot and cold electrons in magnetron sputtering plasma.…”

Sheath Criterion for an Electronegative Plasma Sheath in an Oblique Magnetic Field

“…They researched the effect of negative ions on sheath structure and Bohm criterion. We [19] studied the Bohm criterion in a magnetized plasma sheath taking collision into account, and presented the effects of an external magnetic field and the incident angle of the ions on Bohm criterion in 2011. In the same year, Ghomi [20] examined the effect of negative ion parameters on sheath formation criterion in electronegative plasmas without considering magnetic field.…”