Spark formation: Experiments and modeling of discharge trees
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Dielectric breakdown patterns emerge from a Laplacian growth process and resemble diffusion limited aggregation; this has inspired the phenomenological dielectric breakdown model for the fractal growth of spark patterns. However, recent experiments on the initial breakdown of ambient air between a needle and a planar electrode over the distance of several centimetres (the so-called streamer process) are an incentive to reconsider and reconstruct such macroscopic models starting from microscopic mechanisms.
First we report several breakthroughs in the experimental characterization of streamer breakdown patterns:
1. Pictures with intensified CCD cameras allow snapshots with high quantum efficiency and nanosecond resolution. They visualize the full dynamics of the growing and branching streamer tree including local velocities 1.
2. Streamers can have quite different widths. The width of positive streamers in air can vary from a minimal width of 0.2 mm up to 2.5 mm when the voltage applied to the streamer emitting needle increases from 15 up to 60 kV. Wide initial streamers break up into more narrow ones 2. This effect can be observed only with modern high voltage switches that increase the voltage to its full amplitude within few nanoseconds before the discharge starts. Many earlier experiments are hampered by interplay of voltage rise and streamer development.
3. It is known that positive or negative discharges form different structures. Here we report that the macroscopic branching trees of streamers in nitrogen or air show characteristic differences as well.
Second, this experimental situation requires a build-up of macroscopic theory from microscopic mechanisms.
We review the ladder of multiscale models from microscopic mechanisms (ionization by electron impact and by photons and space charge effects) up to macroscopic branched structures. (i) Microscopic Monte Carlo particle models and coarse grained continuum model are treated by C. Li et al. contribution at this conference. (ii) We present numerical solutions of the continuum model with adaptive grid refinement showing the emergence of a thin charge layer that can undergo a Laplacian instability to finger branching 3. (iii) The charge layer can be treated as a moving boundary comparable to viscous fingering or solidification by F. Brau et al. contribution at this conference.
1) U. Ebert et al., Plasma Sources Sci. Technology 15, S118 (2006).\\
2) T. Briels, J. Kos, E.M. van Veldhuizen and U. Ebert, J. Phys. D: Appl. Phys. 39, 5201 (2006).\\
3) M. Arrayas et al., Phys. Rev. Lett. 88, 174502 (2002); C. Montijn et al., J. Comp. Phys. 209, 801 (2006); C. Montijn et al., Phys. Rev. E 73, 065401 (2006); A. Luque et al., Appl. Phys. Lett. 90, 081501 (2007).