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This dissertation presents the computational modeling of high frequency plasma discharges on metamaterial surfaces (metasurface) and its application to plasma assisted combustion.  A metamaterial is an artificial composite assembled with periodic elements smaller than an incident field wavelength. In microwave regime, a surface wave mode known as a spoof surface plasmon polariton (SSPP) can be excited at a corrugated metal surface where the corrugations are defined by an array of rectangular cavities (comb structures) in the metal. Spoof plasmon resonances occurring at each cavity couple with one another to produce localized surface wave structures at the interface of the corrugations and air. The resonance mode of SSPP on a finite metasurface provides sufficient electric field intensification for gas breakdown and plasma formation.

In the first part of the work, a high fidelity parallel-computing simulation tool is developed to investigate the formation of standing waves pertinent to the resonance and subsequent generation of surface plasmas. The second part of the work extends the simulation tool to a coupled multi-physics system involving high frequency plasma and combustion physics. This part of the work investigates the application of SSPP generated plasmas towards generation of an ignition kernel for a lean -air mixture under high pressure conditions. In particular, the effect of the size of a plasma kernel, generated using an SSPP surface wave resonance, on ignition delay characteristics of the gas mixture are discussed.