Microwave Reflectometry to Characterize the Time-Varying Plasma Generated in the Shock Tube

To investigate the behavior of plasma generated in the shock tube, microwave reflectometry is proposed to extract the permittivity $\epsilon _{r}$ of plasma. To remove the influence of parasitic reflections caused by the surroundings, a calibration process is introduced and the unknown calibration coefficients are determined by utilizing microwave interferometry as the reference technique. The shock tube is modeled as a three-layered medium to calculate the reflection coefficient. A time-dependent reconstruction algorithm is applied and theoretically validated to eliminate the multiple solutions in the inverse problem. By comparing the permittivities extracted with microwave reflectometry and interferometry, the effects of plasma diffusion are demonstrated with a modified analytical model in the beginning time region of experiments. In addition, the nonuniform flow in the generated plasma located near the end time region is also observed. The determination of the effective time region for electron density $N_{e}$ and collision frequency $v_{e}$ extraction is discussed as well. Finally, the differences between microwave reflectometry and interferometry in terms of averaged $N_{e}$ $1{\times }10^{17} m^{-3}$ and averaged $v_{e}$ $1.5{\times }10^{9} s^{-1}$ are investigated in the effective time region