A simple analysis of an inductive RF discharge

The electrical properties of an inductive low pressure RF discharge have been analysed by considering the discharge to be a one-turn secondary of an air-core transformer. Expressions for spatially averaged quantities representing familiar discharge parameters such as the voltage, current and electric field have been determined as functions of measured electrical parameters of the primary circuit. Based on an analytical expression relating the coupling between the electrical characteristics of the primary coil and the plasma load, scaling laws for plasma parameters and the RF power distribution between the inductor coil and the discharge have been determined. The analysis developed here was applied to a collisionally dominated inductive RF discharge in a mercury-rare gas mixture. It may also be applied as a practical design and optimization tool for a plasma processing source based on an inductive discharge.