On a sheath between a plasma and a conducting surface

Abstract

The influence of plasma inertia and temperature and wall polarity on the formation of a stationary charged sheath between the plasma and a conducting wall was considered. A criterion for stationary sheath existence for both negative and positive wall polarities was formulated and applied to several special cases. It was shown, in particular, that a sheath is not formed in a two-beam plasma with cold electrons and cold or warm supersonic ions. The formation of a discontinuity-like a shock wave at a thermal singularity was analyzed. Consideration of special cases showed that conditions for the steady sheath are compatible with the condition for shock wave formation (supersonic ions) only in the case of positive wall potential, hot electrons and warm ions, moving to the wall with velocity greater then the ion-sound velocity. The determined maximum wall positive potential at which no discontinuity forms is φc=[ZTe−Ti ln(1+(ZTe/Ti))]/2Ze, where Te is the electron temperature, and Ti and Ze are the ion temperature and charge.