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Microcavity plasma arrays of inverse pyramidal cavities fabricated on p-Si wafers act as localized dielectric barrier discharges. When operated at atmospheric pressure in argon and excited with high voltage at 10 kHz, a strong interaction between individual cavities is observed leading to wave-like optical emission propagating along the surface of the array. This phenomenon is numerically investigated. The computed ionization wave propagates with a speed of 5 km/s, which agrees well with experiments. The wave propagation is due to the sequential drift of electrons followed by drift of ions between cavities seeded by photoemission of electrons by the plasma in adjacent cavities.