Time-dependent behavior of a Debye sheath: Lengthening and establishment of the stationary state

Abstract

After solving the time-dependent Boltzmann–Vlasov kinetic equation and finding the corresponding particle distribution functions [realized by Tskhakaya et al., Phys. Plasmas 27(1), 023517 (2020)], there is an opportunity to consider various non-stationary-plasma problems. Using these distribution functions, the time evolution of a one-dimensional Debye sheath is investigated. The time dependence of the sheath's lengthening is described, while the characteristic time to establish a stationary Debye sheath is estimated. We show that the sheath's potential reaches a stationary state only when the floating potential condition is fulfilled.