One-dimensional solution for electron heating in an inductively coupled plasma discharge

A one-dimensional analytic solution, which is valid for general collision frequencies and device lengths, has been obtained for plasma heating in a planar-type inductively coupled plasma (ICP) discharge. The analytic solution agrees with a particle simulation result based on the particle in cell method, and it indicates the existence of an optimum chamber length. An exact analytic solution for the surface impedance is obtained in the form of a series expansion. It is also shown that a simplified approximate form may be used for high-density ICP discharges. \textcopyright{} 1996 The American Physical Society.