Optimum design of a microwave interferometer for plasma density measurements

Theoretical and practical problems arising in the application of microwave interferometry to density measurements on transient plasmas are discussed. The conditions for unambiguous measurements in a density range as wide as possible are analysed. It is shown that the initial zero adjustment of the interferometer bridge recommended in most text books is the worst possible choice of initial conditions when the aim is high initial sensitivity at low densities. The analytical expressions needed for unambiguous evaluation of any phase shift from a few degrees to several times pi (counting fringes) are derived. It is pointed out that, in cases of strong intensity variations of the microwave beam transmitted through the plasma, accurate evaluation of the phase shift is possible only by using the exact analytical expressions instead of approximate formulae. The practical design of the interferometer circuit and its inherent error sources due to reflections and non-ideal component properties are discussed. The results are applied to an interferometer operating at 80 GHz used on a pulsed plasma experiment. Examples of measurements are given and the evaluation of the phase shift and plasma density is discussed in detail. The minimum measurable phase shift is 2 degrees and the range of linear densities that have been measured is integral nedx=3*1015-3*1018 m-2, with L= integral dx//0.1 m approximately=0.1 m.