The propagation of the transverse microwave E(x) E(y) into electron cyclotron resonance (ECR) plasmas is studied (with simplified plasma dynamics), emphasizing that plasma dimensions and wavelength lambda are comparable, which is the case with most ion sources. The coupling to the E(z) field is included. A simple system of coupled equations is found and a closed fourth-order differential equation is obtained. Nonpropagating modes are easily solved. Numerical solutions are shown for propagating modes applied to the ECR Alice dimension (radius 3 cm, lambda congruent to 2 cm). A simplified formula for the cavity admittance is given, involving the matching of the guide to cavity, where each mode contribution is weighted; weights are computed for the circular waveguide case. (C) 1996 American Institute of Physics.
