Theory of a cooled spherical electrostatic probe in a continuum gas

The idealized problem of a cooled spherical electrostatic probe in a quiescent continuum slightly ionized chemically frozen gas has been investigated. The electron temperature is described by two limiting models; either the electrons are assumed to be at local thermal equilibrium, or they are assumed frozen at the ambient temperature far from the probe. From numerical solutions of the governing equations, it has been found that with the frozen electron temperature assumption, the probe characteristics for a cold probe are only slightly altered from those of an adiabatic probe. With the electrons at thermal equilibrium, the probe characteristic is only slightly altered when the bias potential is large, but significant changes in the probe characteristic do occur when the bias potential is small, including a significant shift in the floating potential.