Plasma-Sheath Transition: Electron Rich Sheath

In a collisonfree sheath charged particle trajectories can be described as those of single particles falling freely under the influence of an external electric potential. In plasma field- driven motion is drift -- as long as friction by electron-ion collisions balances the field force $e$\underline {\textit{E}}. It depends only on local quantities. The transition from field driven electronic drift to free fall resembles run-away and we treat it analogously by a fluid model for a stationary inhomogeneous plasma region in front of a (plane) electrode at positive potential. Ions are described by Boltzmann equilibrium, electrons as drifting Maxwellian (similarly to H. Dreicer, Phys. Rev. \textbf{115} (1959) 238). We present numerical solutions of the fluid equation together with the resp. Poisson equation for initial plasma densities of 10$^{10}$ and 10$^{11}$cm$^{-3}$ at \textit{kT}$_{e}$=1eV and 10eV. Initial condition is set by an initial electron drift $v_{D}$. Solutions exhibit quasineutral plasma followed by a sheath -- the extension of plasma depending strongly on the initial condition. For $v_{D}$= 0.5*10$^{-3}$*$$ for example, we obtain quasineutral plasma with decaying density over several thousand Debye-lengths.