Analysis of the Transition from Hexagon to Square Pattern in Dielectric Barrier Discharge

Several spatiotemporal patterns: random spots, hexagon pattern, coexistences of hexagon and square pattern, and square pattern are obtained in dielectric barrier discharge system while increasing the voltage with other parameters fixed. By using image processing including spatial correlation function and Fourier spectrum, the structures of patterns and the bifurcation scenario are studied. It is shown that the structures of hexagon and square patterns are both perfect, and the spatial periodicity increases with the voltage increasing, whereas the mean distance between the neighboring filaments decreases. Moreover, the development of the modes excited from the system in this transition is investigated in detail. Both the two methods are in agreement with each other.