Formation of kagome-white-eye-honeycomb hexagonal superlattice pattern in dielectric barrier discharge

A kagome-white-eye-honeycomb hexagonal superlattice pattern is observed in dielectric barrier discharge and studied by two photomultipliers, an intensified charge-coupled device, and a spectrograph. It consists of four sublattices, which are kagome structure, halos of white-eye hexagon, honeycomb frame, and central spots hexagon. As an unconventional symmetry sublattice, the kagome structure results in amazing sublattice discharge order. Based on the consideration that any discharge is related to all previous discharges, a mapping matrix which governs self-organization of the pattern is proposed. These results will promote the development of the pattern dynamics.

Figure 1

Schematic diagram of the experimental setup.

Figure 2

Evolution of patterns with increasing voltage. (a) Random filaments, $U=3.04\mathrm{kV}$; (b) honeycomb pattern, $U=3.52\mathrm{kV}$; (c) kagome-white-eye-honeycomb hexagonal superlattice pattern $U=4.88\mathrm{kV}$; (d) chaos, $U=5.36\mathrm{kV}$. Other experimental parameters: gas pressure $p=30$ kPa, air, driven frequency $f=54$ kHz, gas gap $d=2$ mm, exposure time of the pictures $t=25\mathrm{ms}$.

Figure 3

(a) Waveforms of the voltage and the current. (b)–(d) images exposed corresponding to the current pulse phases denoted by $\mathrm{\Delta }{t}_1, \mathrm{\Delta }{t}_2$, and $\mathrm{\Delta }{t}_3$ in (a), respectively, and the images are integrated for 100 voltage cycles. (e) The frame is the superposition of (b)–(d).

Figure 4

(a) Waveforms of the applied voltage and current of the kagome-white-eye-honeycomb hexagonal superlattice pattern. (b) The halos. (c) The honeycomb frame. The pictures (b), (c) are, respectively, correlated with current pulse phases ($\mathrm{\Delta }{t}_4=1000\mathrm{ns}, \mathrm{\Delta }{t}_5=1320\mathrm{ns}$) in (a) and integrated over 100 voltage cycles to obtain sufficient light signals. (d) The frame is the superposition of (b), (c).

Figure 5

Images of the honeycomb frame. (a)–(d) Images exposed corresponding to the current pulse phases denoted by $\mathrm{\Delta }{t}_3$, and the images are integrated for 1, 30, 50, and 100 voltage cycles, respectively.

Figure 6

Time correlation measurement of the kagome-white-eye-honeycomb hexagonal superlattice pattern. (${\mathrm{a}}_1),({\mathrm{a}}_2$) Kagome-honeycomb-hexagonal superlattice pattern, K stands for kagome structure, C stands for central spots, H stands for the halos, F stands for honeycomb frame. (b) Time correlation measurement of central spots and kagome structure. (c) Time correlation measurement of kagome structure and the halos. (d) Time correlation measurement of the halos and the honeycomb frames. $U$ stands for voltage curve, $I$ stands for current curve.

Figure 7

(a) Emission spectrum in the range of 360–420 nm. (b) The molecular vibration temperatures of different sublattices.

Figure 8

(a) Waveforms of the applied voltage and current of the kagome-white-eye-honeycomb hexagonal superlattice pattern. (b) Schematic diagram of the pattern. (c), (g) The kagome structure. (d), (h) The halos. (e), (i) The honeycomb frame. (f), (j) The central spots. (${\mathrm{c}}_1)–({\mathrm{j}}_1$) The schematic diagram of wall charges at different moments on the positive dielectric surface.