Effect of dust grains size distribution on the Bohm sheath criterion in plasmas

Abstract

Taking into account the dust grain size distribution, the Bohm criterion is revisited by means of a one-dimensional, stationary, and non-magnetized theoretical model. An argon plasma is considered where the electrons are characterized by the Boltzmann distribution; however, the other species are described by the fluid equations. The dust grain charge number is described by the orbit motion limited model and their size is modeled by a Gaussian law. The generalized Bohm criterion has been calculated by using the Sagdeev's pseudo-potential approach. The numerical results show that the Bohm velocity values are greater than those of the classical model where the dust grains are absent, and they exhibit a peak. Moreover, by taking into account the dust size distribution, the obtained Bohm velocity values are practically comparable to those found in the mono-size model for a mean radius of the dust grains. Furthermore, it is found that the presence of mono-energetic electrons increases the Bohm velocity values. The dust grain surface potential at equilibrium is also calculated and discussed.