A finite-difference time-domain simulation of high power microwave generated plasma at atmospheric pressures

A finite-difference algorithm was developed to calculate several RF breakdown parameters, for example, the formative delay time that is observed between the initial application of a RF field to a dielectric surface and the formation of 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 finite-difference algorithm provides numerical solutions to partial differential equations with high resolution in the time domain, making it suitable for simulating the time evolving interaction of microwaves with plasma; in lieu of direct particle tracking, a macroscopic electron density is used to model growth and transport. This approach is presented as an alternative to particle-in-cell methods due to its low complexity and runtime leading to more efficient analysis for a simulation of a microsecond scale pulse. The effect and development of the plasma is modeled in the simulation using scaling laws for ionization rates, momentum transfer collision rates, and diffusion coefficients, as a function of electric field, gas type and pressure. The incorporation of plasma material into the simulation involves using the Z-transform to derive a time-domain algorithm from the complex frequency-dependent permittivity of plasma. Therefore, the effect of the developing plasma on the instantaneous microwave field is calculated. Simulation results are compared with power measurements using an apparatus designed to facilitate surface flashover across a polycarbonate boundary in a controlled N ₂, air, or argon environment at pressures exceeding 50 Torr.