Energy flow through a nonambipolar Langmuir sheath

Abstract

When electrons travel through the sheath toward a plasma-facing surface, they lose a part of their kinetic energy due to the negative work of the electric field in the sheath. What happens to this energy? Does it need to be accounted for if one needs to calculate an energy flux to a wall? In this note, the above questions are answered for three different cases of the boundary conditions: (a) electrically isolated surface charged to a steady-state value corresponding to a floating potential; (b) an isolated wall not yet charged to the floating potential; and (c) biased electrode conducting a steady-state current. The answers are found to be different in each case, but the general conclusion is that to evaluate surface power deposition due to particle bombardment, electron and ion energy fluxes need to be calculated at the wall, and not in the quasineutral plasma.