Electron inertia effects on the planar plasma sheath problem

The steady one-dimensional planar plasma sheath problem, originally considered by Tonks and Langmuir, is revisited. Assuming continuously generated free-falling ions and isothermal electrons and taking into account electron inertia, it is possible to describe the problem in terms of three coupled integro-differential equations that can be numerically integrated. 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), is also shown.