Plasmas respond nonlinearly to GHz electromagnetic waves, owing to nonlinear interactions described by the electron momentum equation. These nonlinearities are especially important in high field regions of the plasma as is common in resonant structures that generate plasma discharges with intense localized amplification of the incident field. Most models treat the plasma as a linear Drude material that does not capture the nonlinear polarization terms of a plasma. In this work, we couple the nonlinear electron momentum equation to electromagnetic wave simulation in order to explore the nonlinear behavior. We develop a theoretical foundation via perturbation analysis to guide our expectations from numerical simulation. Through numerical simulation of 2D TE-polarized waves incident on a cylindrical plasma, we show that in the presence of electrical field strengths of ∼MV/m and higher, dense microplasmas have second harmonic power conversion efficiency approaching 10−6 at low pressures. The generated harmonic power is shown to arise mostly from the inertial term in the electron momentum equation. Therefore, a significant portion of the harmonic current density is generated at the surfaces of critical electron density for the fundamental frequency.
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