Comment on The plasmasheath transition in low temperature plasmas: on the existence of a collisionally modified Bohm criterion

R N Franklin (1)

1 Oxford Research Unit

In a recent Rapid Communication Brinkmann [ 1 ] claims to have discovered a collisionally-modified Bohm Criterion. He introduces a new local variable length λ defined by λ = n i dx/dn i, where n i is the ion density, this has the effect of locally compressing the natural length scale where n i is rapidly varying and has maximum effect near the point of inflexion in n i (x). This point he calls the Bohm point and the ion speed there is given the name the collisionally-modified Bohm Criterion - let us call it c s *, with c s being the ion sound speed. It can readily be shown that d 2 n i /dx 2 = (1 - dλ/dx).n i /λ 2. There is no doubt that the spatial distributions of both ions and electrons have a point of inflexion somewhere between the centre of the plasma and the wall in a real active plasma, but it is difficult to see how such a point can be given the significance suggested when its location is a function of the plasma size L, the ion mean free path λ i, and the Debye length λ D based on the plasma density at the centre n 0. c s * is likewise a function of these three variables. For specific gas and a finite plasma one needs to include the ionization rate by electron impact Z, and this varies with the nature of the gas, and not just the ion mass. Thus for a given situation it is possible to write the plasma balance equation as - (Z(Z+ ν i) 1/2 L/c s = K(ν i /Z, λ D /L) where K is a number of the order of 1, and depends on the geometry, albeit plane or cylindrical, ν i is the ion collision frequency for momentum transfer. While the ion sound speed enters here unmodified, one could devise a modified expression for c s * = c s N(v i /Z, λ D /L), N being a number between 1 and 0 with limiting values N = 1 for v i /Z  0, and N  0 for v i /Z >> 1.. I cannot see how such a two-dimensional plot, even when for λ D /L  0, N has known values given in my book [ 2 ], gives additional physical insight. All of this was fully explored in my Topical Review [ 3 ], which was not acknowledged by Brinkmann. References [ 1 ] Brinkmann R.P. 2011 J. Phys D: Appl. Phys. 44 042002. [ 2 ] Franklin R. N 1976. Plasma Phenomena in Gas Discharges (Oxford: Oxford University Press). [ 3 ] Franklin 2003 J. Phys. D: Appl. Phys. 36 R309-R320.

Mots clés: Physical Sciences

R N Franklin. Comment on The plasmasheath transition in low temperature plasmas: on the existence of a collisionally modified Bohm criterion. Journal of Physics D: Applied Physics, 2011, 44 (15), pp.158001. ⟨10.1088/0022-3727/44/15/158001⟩. ⟨hal-00613265⟩