# Current Filaments in Asymmetric Surface Dielectric Barrier Discharge
## 6 Conclusions  
We have reported results on the statistical properties of asymmetric surface dielectric barrier discharges with an exposed metal electrode, and the other fully isolated from air, both glued onto a dielectric surface. We study the charge, current, and duration of the individual discharge events composing the two active phases of the SDBD, denoted as forward and backward strokes (FS and BS), respectively. A strong asymmetry between the two strokes has been found. For the BS, the mean charge carried by a burst is about \(0.3\,\mathrm{nC}\), the mean current  
Figure 21: Distribution of delays between bursts in the forward (stars) and backward (o) strokes.  
is 35 mA and the duration is 15 ns, while for the FS, the corresponding values are smaller in magnitude--that is, \(-0.1\) nc, \(-20\) mA and 11 ns, respectively.  
We have studied temporal correlations between two successive backward strokes, by building the random walk profiles resulting from differences in current discharges evaluated at the same time within the BS cycle. We applied a fluctuation analysis to extract the scaling behavior of the profiles at different times scales. We found a well defined power-law of fluctuations, for 6 ns \(<\ t<\) 200 ns, characterized by a Hurst exponent \(H\sim 2/3\), suggesting the presence of persistent (positive) correlations between consecutive BS. At times \(t<\) 6 ns, the correlation is maximal, leading to \(H=1\). The correlations found at intermediate times are a result of non-trivial phenomena related to the interaction between discharges and plasma. These findings should be useful for better assessing the models attempting to describe this complex behaviour.  
We have also measured the optical emission of discharges using a photomultiplier to further study spatial correlation patterns. The optical emission is produced by electron impact excitations due to the ionizing wave propagation igniting the discharge. In particular, we have measured the spreading rate of the ionizing wave associated to microdischarges for BS. The wave moves, mostly perpendicularly, away from the edge of the exposed electrode towards the dielectric surface, roughly corresponding to the direction of the electric field determined by the instantaneous voltage level applied to the insulated electrode, but opposite to the electron drift motion. This is also the direction of the produced ionic wind. Both the order of magnitude and the direction of the ionizing wave velocity are compatible with a cathode directed streamer mechanism. However, the absence of a corresponding propagation for the microdischarges for FS points towards the presence of a different mechanism acting in this opposite phase.  
Conceptualization, C.R. and C.P.; methodology, C.R., R.B., C.P; software, R.B.; validation, C.P., R.B.; formal analysis, C.P., R.B., H.E.R.; investigation, C.P.; resources, C.R.; data curation, C.P.; writing--original draft preparation, C.P., R.B., H.E.R.; writing--review and editing, C.P., H.E.R.; visualization, C.P.; supervision, C.R.; project administration, C.R.; funding acquisition, C.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
We gratefully acknowledge the technical support of [PERSON] in the device development and experiment execution. The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
DBD Dielectric barrier discharge  
SDBD Surface dielectric barrier discharge  
UV Ultraviolet  
FS Forward stroke  
BS Backward stroke  
AC Alternating current  
HV High voltage  
DC Direct current  
FFT Fast Fourier transform  
OES Optical emission spectroscopy  
PMT Photomultiplier tube  
RW Random walk