Bohm criterion generalized to multicomponent electronegative plasmas

This study investigates how different assumptions about the velocity distribution of negative ions in electronegative plasmas influence the Bohm criterion and the resulting Bohm velocities at the sheath edge. An expression for the Bohm criterion is derived for a multicomponent electronegative plasma with non-collisional sheaths, generalized for electron and negative ion velocity distribution functions of the form f(v)=A exp(−Bv2ξ), where ξ is a positive real number greater than 0.5. Additionally, a method is presented for computing the Bohm criterion for any given negative ion velocity distribution function f(v). For a simple three-component plasma consisting of electrons, positive ions, and negative ions, it is shown that if the ion velocity distribution is convex (ξi>1.0), the Bohm velocity is lower than the Maxwellian prediction, whereas for a concave distribution (0.5<ξi<1.0), the Bohm velocity is higher. These results indicate that both the electronegativity and the shape of the velocity distribution contribute to deviations from the conventional Bohm velocity.