Simple approximate treatment of unipolar space-charge-dominated coronas: The Warburg law and the saturation current

Abstract

Unipolar space‐charge distribution ρ(t) drifting with constant ion mobility μ in gas under time and space dependent electric fields will evolve according to the unipolar charge drift formula [1/ρ(t)]−[1/ρ(t₀)] = (μ/ε₀)(t−t₀), neglecting diffusion effects. This general formula is especially useful as a starting point for approximate treatment of space‐charge effects, both in ion drift and diffusion experiments, and in electrical coronas. A first simple derivation of an equivalent of the Warburg cos⁵ϑ current‐density distribution for point‐to‐plane coronas is given, together with a formula for the maximum possible unipolar ion current (the unipolar saturation current) I_s ≊2με₀ V²/d, for a given corona voltage V and point‐to‐plane distance d. It is demonstrated that corona currents in excess of this limit always involve free electron or bipolar conduction phenomena, like streamers.