Simulations of the Collisional Bohm Criterion and Edge-to-Center Density Ratio Over a Range of Gas Pressure

Abstract

The flux of plasma into the sheath is the product of the ion velocity and density at the sheath edge Γ=n se V se . When ionneutral collisions are rare Bohm's criterion relates the sheath edge flux to bulk parameters Γ=h l n 0 c s , where h l is the edge-tocenter density ratio and c s is the sound speed. However, when the gas pressure increases and the ion-neutral mean free path approaches the electron Debye length the ions are not expected to reach c s , but instead a collisional Bohm criterion a l c s where 0<a l <1. Here we use particle-in-cell simulations to test if the ions are slowed at the sheath edge and model how the collisional Bohm criterion impacts current predictions of the edge-to-center density ratio. We find that ions satisfy a collisional Bohm criterion and that the edge-to-center density ratio is higher than predicted by previous models. In addition, the collisional Bohm criterion is used to predict the plasma potential in collisional plasmas.