Analytical fit of the I–V probe characteristic for finite ion temperature values: Justification of the radial model applicability

Abstract

This article deals with an extension of the radial model for the sheath that surrounds a cylindrical or spherical Langmuir probe immersed in a plasma in which positive ion thermal motion is taken into account. The dependence of the electric potential profile and of the I–V characteristic on the positive ion temperature is obtained. Moreover, a different parameterization is established from a numerical fit of the I–V characteristic as a function of the probe radius, the biasing potential, and the ratio between the positive ion temperature and the electron temperature. This parameterization allows us to obtain an analytical approximation to the potential profile and the sheath edge. Finally, it also gives us a means of justifying under what conditions the radial model can be applied in plasmas with finite positive ion temperature.