Time-dependent kinetic theory of the plasma-wall transition layer in a weakly ionized plasma

Abstract

An analytic solution of the time-dependent Boltzmann kinetic equation is found for the first time. The plasma-wall transition (PWT) layer is analyzed using time-dependent velocity distribution functions for electrons and ions. The process of wall charging by electrons is described and estimated. For states close to the time-independent (stationary) state, for which the time dependence of the PWT parameters is weak, (i) the potential shapes in the pre-sheath (PS) and the Debye sheath (DS) are analyzed and (ii) the intermediate region, which bridges the PS and DS sublayers, is defined and its characteristic length is determined. The ion kinetics are dominated by charge exchange with cold neutrals and electron-impact ionization collisions of neutrals. The charge-exchange mean free path λcx is assumed to be constant and much larger than the electron Debye length λDe. The detailed time dependence of the PS sublayer's approach of the stationary state is found. It is proved that the stationary state can be realized only if the floating-potential condition is fulfilled.