Microwave harmonic generation in a plasma capacitor

Abstract

Microwave harmonic generation in a plasma capacitor is investigated both theoretically and experimentally. Deficiencies of previous harmonic generation theories are pointed out and a nonlinear one-dimensional mathematical model, which includes the reactive nonlinearities due to the spatial variation of E, is developed. This nonlinear plasma capacitor model indicates that under certain electron-density and capacitor-plate spacing conditions strong harmonic resonances and an antiresonance are present. The antiresonance occurs when n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</inf> = ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> and the resonances occur when n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</inf> ≳ ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> , where ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> =plasma frequency, ω= the fundamental frequency, and n is the harmonic number. Harmonic generation in a number of gases is investigated experimentally in a coaxial discharge structure. Third-harmonic (9-GHz) efficiencies of up to 13 percent, and third-harmonic output power in excess of 600 mW are reported. Double-probe and microwave-scattering measurements show that enhanced harmonic generation occurs at the above resonances and, hence, substantiate the non-linear plasma capacitor theory. In order to explain the harmonic output power variations that occur with pressure variation and gas type, a graphical method of analysis based on experimental fact and pressure-collision frequency-electron energy curves is presented. This method of analysis not only yields results that compare qualitatively with experimental observations, but it may also possibly be used to design and predict the performance of future plasma frequency multipliers.