Microwave Measurements of High Electron Densities Using the Complex Reflection Coefficient

The determination of electron densities in the high density range has become increasingly important in recent years and the use of the complex reflection coefficient at microwave frequencies as a plasma diagnostic tool has been reported by several authors. However, the sensitivity of the reflected phase to the electron density profile composing the boundary of the plasma reduces the effectiveness of the sharply bounded uniform slab as a plasma model. Since this model finds frequent use, the resultant errors should be considered. Indeed, even when the width of the electron-gradient boundary zone is very small, serious error in the determination of the plasma number density can occur when the reflection coefficient is used. This paper suggests a method by which electron-gradient-induced errors in number density calculations can be overcome. Briefly, it is shown that if measurements of the complex reflection coefficient can be made at several frequencies, the data can be extrapolated to find the electron density in a uniform plasma region regardless of the width of the boundary zone of the plasma or the associated plasma density profile. The region where ωP>ω is emphasized.