Technique for estimating space-charge densities in systems containing air ions

Abstract

The exact analysis of electrified systems containing air ions is difficult because of the interdependence between the system electric-field and space-charge distributions. A technique is described in this paper for estimating space-charge densities in unipolar and bipolar systems of air ions. A formula is introduced for systems containing only one ionic species which relates the space-charge density at a point P to the space-charge density at the ionic source and the transit time required for an ion to move from this source to P. In systems where air flow determines ionic velocities, transit times can be directly estimated. For other systems, a lower bound for the ionic transit time is derived and used to set an upper bound on the ionic space-charge density. Two general results are derived for systems containing several species of ions during steady-state zero-wind conditions: the conversion of only a relatively few small ions into large ions, through collisions with condensation nucleii, results in dramatic reductions in small-ion space-charge densities; many bipolar systems may be broken into subsystems which can be analyzed using unipolar methods.