A one-dimensional fluid model of the microwave electron cyclotron resonance (ECR) discharge, which includes the inhomogeneity effects of the external magnetic field, is developed. The plasma and sheath are modelled seperately, and appropriate plasma-sheath boundary conditions are utilized. Microwave is represented by an energy flow, and treated by a ray tracing technique.
An 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 (TCP) 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 discharge condition.