Formation and stabilisation of single current filaments in planar dielectric barrier discharge

In the experimental part we report on a typical bifurcation scenario of the current distribution in the discharge plane of a planar dielectric barrier discharge system. Increasing the amplitude \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat U$\end{document} of the sinusoidal driving voltage after breakdown a large number of dynamic solitary filaments is observed and the subsequent decrease of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat U$\end{document} results in a pronounced hysteresis with decreasing number of filaments. In this way isolated single stationary filaments can be generated. In the theoretical part the latter are modeled by a reaction-drift-diffusion equation that is solved in three dimensional space numerically without any fitting procedure. As a result we obtain well defined stationary filaments of which size an shape essentially are independent of the initial conditions and having a width and an amplitude that agree with experiment rather well. On the basis of the numerical results we consider mechanisms of filament stabilisation. This includes the discussion of the well known surface charges as well as an additional focusing effect of volume charges.