Honeycomb hexagon pattern in dielectric barrier discharge

We report on a honeycomb hexagon pattern in dielectric barrier discharge. It bifurcates from a square pattern as the applied voltage is increased. A phase diagram of the pattern types as a function of the gas component and applied voltage is presented. The spatial Fourier spectrum of the honeycomb hexagon pattern is a hexagonal superstructure with three wave vectors <(k(1)(h))over right arrow>, <(k(2)(s))over right arrow> and <(k(3)(s))over right arrow> at least, demonstrating that the pattern is a superlattice pattern. Measurements of the correlation between discharge filaments indicate that the honeycomb hexagon pattern is an interleaving of three different transient hexagonal sublattices, whose spatial wave vectors are exactly equal to <(k(1)(h))over right arrow>, <(k(2)(s))over right arrow> and <(k(3)(s))over right arrow>, respectively. These three wave modes fulfill a triad resonance condition <(k(3)(s))over right arrow>-<(k(2)(s))over right arrow>=<(k(1)(h))over right arrow>.