Generalized Sheath Criterion for Multi-species Weakly Ionized Plasmas

The problem of sheath formation in glow discharges close to surfaces has been well-studied since 1949 (Bohm, 1949). Since electrons are more mobile than the ions, the surfaces exposed to plasma charge up negatively.   The potential drop from the plasma to the surface is screened over a region determined by the Debye length.    The “Bohm Criterion” determines the sheath formation and its stability for collisionless steady plasmas. This requires that the ions enter the sheath with a directed velocity greater than or equal to the ion acoustic velocity.   This criterion has been consistently used for systems in which the assumption of collisionless plasmas is valid (Riemann, 1991). In the current work, this criterion has been extended to systems with multiple species including effects such as electron inertia and electrical fields.  The analysis further shows that for discharges with multiple species this criteria leads to a symmetric and elegant condition. The resulting conditions simplifies to the "Bohm Criterion” for collisionless plasmas with Boltzmann distribution for electrons.  The generalized criterion is also consistent with experimental results that in the presence of multiple species, the ions do not reach sheath edge as determined by this criterion (Severn, 2003, 2007).

 

1. Bohm, D., 1949. Minimum ionic kinetic energy for a stable sheath. The characteristics of electrical discharges in magnetic fields, pp.77-86.
   
   Riemann, K.U., 1991. The Bohm criterion and sheath formation. Journal of Physics D: Applied Physics, 24(4), p.493.
   
   Severn, G.D., Wang, X., Ko, E. and Hershkowitz, N., 2003. Experimental studies of the Bohm criterion in a two-ion-species plasma using laser-induced fluorescence. Physical review letters, 90(14), p.145001.
   
   Severn, G.D., 2007. A note on the plasma sheath and the Bohm criterion. American Journal of Physics, 75(1), pp.92-94.