A Finite-Difference time-domain simulation of formative delay times of plasma at high RF electric fields in gases

A Finite Difference (FD) algorithm was developed to calculate the formative delay time between the application of an RF field to a dielectric surface and the formation of a field-induced plasma interrupting the RF power flow. The analysis is focused on the surface being exposed to a background gas pressure above 50 torr. The FD-algorithm is chosen over particle-in-cell methods due to its higher computational speed and its ease of being ported to commercial electromagnetics solvers. The dynamic frequency-dependent permittivity of the plasma is mapped to the time domain of the FD algorithm using the Z transform. Therefore, together with the electron density, the effect of the developing plasma on the instantaneous microwave field is calculated. The high observed value of absorption, up to 60 %, is a result of the momentum transfer collision frequencies in the developing plasma being much larger than the microwave frequency. As a result, the electron density increases to values well beyond the density calculated from setting a plasma frequency equal to the microwave frequency. In the experiment, flashover is induced across a Lucite window by a 4 MW S-band magnetron operating at 2.85 GHz with ~50 ns rise time. The results of the FD simulation are compared with experimental data obtained from flashover with background gases such as nitrogen, air, and argon all at pressures exceeding 50 Torr.