1. Introduction Inductively coupled (electrodeless) discharges hold much promise as plasma sources for electrical discharge light ing and plasma processing. Since they do not depend upon large voltages to drive displacement current through the powered RF sheaths, ion energies in inductive discharges are considerably lower than those found in capacitively coupled RF discharges (especially at high power density). Relatively low ion energies in inductive discharges result in a decrease in ion-wall interactions (e.g. sputtering, etching and a variety of energetic ion- induced chemical reactions). In many instances, in vely coupled discharges efficiently provide a high density plasma with relatively small ion power loss in the sheaths. Moreover, plasma generation and ion accelera tion processes can be independently controlled for in ductive discharges in plasma processing reactors through RF biasing of the remote substrate, resulting in independ ent control of the ion energy Inductively coupled discharges have been known for over a century [1,2] and many authors have analysed their operation. A short concise literature review dealing with modelling low-pressure, collisional discharges main tained by an RF current applied to an induction coil is contained in recent papers by Lister and Cox C3] and by Denneman [4]. In these works the spatial distribution of uhe a RF field and the current density are numeri cally calculated by solving a coupled set of Maxwell equations for an internal [3] (referenced to the plasma) and an external [4] inductor coil. Assuming diffusion controlled plasma density profiles (one with zero bound d ary values) for cylindrical and coaxial plasmas and