Calculation of the propagation constant in a rectangular waveguide containing an inhomogeneous longitudinally magnetized plasma

An experiment is currently being conducted to monitor breakdown phenomena in nitrogen (G. Hays, 1100 Quarterly Report Solid State Sciences, July to September 1984, Sandia National Laboratories). The motivation is provided by current interest in atmospheric propagation of large amplitude short rise time electromagnetic fields. The gas sample in the experiment is contained within a quartz cell in a rectangular waveguide. The sample is also biased by a longitudinal magnetostatic field to help increase absorption. A small amplitude interferometer is then used to monitor the electron density in the cell. This report summarizes an analysis done in support of this experiment. Standard perturbation is used to calculate the propagation constant in the gas sample making it possible to relate the electron density in the sample to the phase shift measured by the interferometer. The effects of the quartz cell are also determined.