Floating Sheath Potentials in Non-Maxwellian Plasmas

Abstract

The floating sheath potential in a plasma having a Maxwellian electron distribution function is eϕ>s = -kTe 1n (a/b)/2 where Te is the electron temperature, a is the ratio of electron temperature to ion temperature, and b is the ratio of electron mass to ion mass. This expression is derived by equating the flux of electrons and ions to a surface in the plasma. Only electrons initially having an energy greater than -eϕs flow to the surface. These electrons are in the tail of the distribution, a region that differs significantly from a Maxwellian in many plasmas. An analysis is performed where the sheath potential is solved for using a two-temperature model for the electron distribution function. The two-temperature model accurately describes the distortion from a Maxwellian in the tail of the distribution function. The magnitude of the sheath potential calculated with the two-temperature distribution is significantly smaller than that obtained using a Maxwellian distribution, a result of the reduction in the relative abundance of energetic electrons in the tail of the distribution.