Numerical Computation of the Electrostatic Sheath Thickness

In this work we have established a one dimensional, stationary and non-magnetized theoretical model that describes the electrostatic sheath formation [M. Moisan, J. Pelletier, Physique des Plasmas Collisionnels, Application aux Décharges Haute Fréquence, EDP Sciences, 2006]. The sheath thickness is assessed. For this, we have assumed that all species are described by fluid equations. Dust grains are considered spherical particles with constant radii. Their charge is modeled by the orbit motion limited model [P.K. Shukla, A.A. Mamun, Introduction to Dusty Plasma Physics, Institute of Physics, Bristol 2001; A. Bouchoule, Dusty Plasmas, Physics, Chemistry and Technological Impacts in Plasma Processing, Wiley, Chichester 1999]. The solution of the obtained set of differential equations is found using the shooting method. The numerical results show that the sheath thickness depends considerably on the solid surface potential, as well as physical parameters, such as particle densities and temperatures, gas pressure, etc. The calculated electrostatic sheath thickness is greater than the thickness predicted by Child-Langmuir law [M.A. Lieberman, A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, Wiley, New York 1994].