Using the following expressions for the electron and ion number densities

in the plasma sheath region formed between an infinite plane and a semi infinite plasma, deduce the differential equation satisfied by the electric potential ϕ(x) in the plasma sheath. Show that this differential equation can be written in the form

where

Assuming that at x = ∞ we have n_e = n_i =n₀, F = 0, and dF/dξ = 0, show that

where ξ₀ is a constant. Denoting the potential at the wall by ϕ_w and assuming that eϕ/kT ≪ 1, show that

Transcribed Image Text:

ne(r) = no exp ni (r) = no exp eo(r) kT ep(r)] kT [-e