A model for a Langmuir sheath in a stagnating dense plasma with secondary ion formation

This simplified model provides solutions for the current-voltage characteristics of a sheath in a dense flowing plasma when surface chemistry contributes secondary ions. The problem is motivated by the recent discovery that strong transient signals in industrial ion current sensors are caused by chemical reactions with carbon in the steel being cut or welded by oxyfuel processes. The one-dimensional model considers a quasi-uniform dense plasma flowing towards and stagnating on an absorbing surface, above which there is a source of secondary ions. Because the secondary ions are formed directly in the plasma sheath, they have strong impacts on the current-voltage characteristic. With ionic Reynolds number, R, and integral length scale, α, secondary ion formation rate, Ω, and length scale, β, saturation currents are simply R + βΩ until β ≪ 1, at which point, new electrons cannot escape the sheath, and secondary ions have no effect. Floating potential, ϕ _∞, scales like exp ( ϕ ∞ ) ∝ R − 3 / 4 , and secondary ions have little impact unless β ²Ω > 1. Even then, floating potential is only weakly affected by secondary ion formation. The integral length scale, α, is not found to strongly affect the results.