Electron inertia effect on floating plasma potential

Abstract

The steady one-dimensional planar plasma sheath problem, originally considered by Tonks and Langmuir, is revisited. Two-fluid equations for cold ions and isothermal electrons, including terms for particle generation and electron inertia, have been numerically integrated together with Poisson equation. The inclusion of electron inertia in the model allows us to obtain the value of the plasma floating potential as resulting from an electron density discontinuity at the walls, where the electrons attain sound velocity and the electric potential is continuous. Results from numerical computation are presented in terms of plots for densities, electric potential and particles velocities. Comparison with results from literature, corresponding to electron Maxwell-Boltzmann distribution (neglecting electron inertia), are also shown