Modeling Errors in Microwave Plasma Diagnostics Employing the Reflection Coefficient

The use of the complex reflection coefficient, R, at microwave frequencies as a plasma diagnostic tool in the high electron density range (1012 electrons/cm3) has been reported by several authors. A common assumption is that at microwave frequencies the boundary between free space and a stationary plasma is best described as a step function in electron density. Actually, many practical boundaries consist of a finite-width region wherein the electron density has a finite gradient. The complex reflection coefficient is derived for the finite width boundary and comparisons are made with an assumed sharp boundary. It is shown that improper modeling of the plasma boundary can result in significant error in electron density measurements when R is used as a diagnostic tool.