The properties of plasma sheath containing the primary electrons with a Cairns-distribution

We study the properties of plasma sheath containing the cold positive ions, the secondary electrons, and the primary electrons with a Cairns-distribution (a non-thermal velocity-distribution). We derive the generalized Bohm criterion and Bohm speed, the new floating potential at the wall, and the new critical secondary electron emission coefficient. We show that these properties of the plasma sheath depend significantly on the a-parameter in the non-thermal a-distribution, and so they are generally different from those of the plasma sheath if the primary electrons were assumed to be a Maxwellian distribution.