A simple formula for the wall potential in the plasma sheath

B. P. Pandey^1a and S. V. Vladimirov²

¹ Department of Physics & Astronomy, Macquarie University - Sydney, NSW 2109, Australia
² Department of Complex Systems, School of Physics, The University of Sydney - Sydney, NSW 2006, Australia

^a birendra.pandey@mq.edu.au

Received: 8 December 2010
Accepted: 26 April 2011

Abstract

An analytical formula for the plasma wall potential in a planer sheath is presented. It is shown that there is no relative error between the analytical and numerical solutions for the large negative wall potential. Even when the wall potential is not large, the relative error is only 3%. Using this analytical formula in Child's law, we show that the sheath width, d (in the unit of Debye length, λ_D) is proportional to the Mach number M, i.e. d/λ_D=0.5 M. In the low- and high-temperature plasma experiments, the present analytical formula could be utilised to accurately estimate the sheath width.