Modeling Gas Breakdown in High Quality-Factor Resonators at GHz to THz Frequencies

Recently, there has been an effort to explore and incorporate plasmas into electromagnetically resonating components, for applications in plasma generation, wave control, and sensing, among other things. High quality factor (High-Q) resonators are desirable for gas breakdown because they operator with relatively low input power. Gas breakdown in a resonator is highly dependent upon the operating frequency and the geometry of the resonator. An important characterization of high-Q resonators is the frequency response generated by numerical simulation. However, in order to resolve a high-Q resonance, the number of simulated wave periods must be greater than Q. As the Q-factor is not known a priori, this can lead to very long simulation times of greater than 10^6 wave periods. Considering that the computation mesh must also resolve small geometrical features, the problem can become unwieldy quickly. We present a method of numerical simulation based on the Finite-Difference Time-Domain (FDTD) method that reduces the computational cost of simulating gas breakdown. We demonstrate the technique of using a time-step operator representation of the electromagnetic simulation to obtain the steady-state plasma response under a diffusive flux assumption.