Centrum Wiskunde & Informatica, Amsterdam Propagation mechanisms of positive streamers in different N2:O2 mixtures Gideon Wormeester Centrum Wiskunde & Informatica, Amsterdam Amsterdam, 27-10-2010 In cooperation with: S Pancheshnyi, A Luque, S Nijdam & U Ebert

Outline Main questions Model Numerical results In air In N2 + 1 ppm O2 Feather-like structures Conclusions and outlook

Main questions Main questions fueled by experiments: What mechanism drives propagation of positive streamers? Why do streamers seem insensitive to gas-composition? What is the influence of repetition frequency? Why do feather-like structures appear in N2, but not in air?

Model Model contains: Fluid model for particle densities Computational domain (rectangle) and electrode configuration Model contains: Fluid model for particle densities Impact ionization, attachment, detachment, recombination Photo-ionization using Zhelezniak model “Background ionization” means a uniform initial density of O2- and O2+/N2+ Parameters: 12 kV or 24 kV potential p = 1 bar, T = 300 K 4mm or 8mm gap between electrodes Only positive streamers are investigated

Results in air Position of streamerhead Level of background ionization has small effect on velocity. Background ionization gives rise to narrower streamers and higher fields.

Results in air Both photo-ionization and background ionization are real processes. Comparing them separately in air is not physical. Only at 1011 cm-3 of O2-, the influence of background ionization becomes visible. Experimentally, this can be reproduced by repeated discharges at very high (>kHz) frequencies. In all other cases, the photo-ionization mechanism dominates. Velocities of streamers with photo-ionization

Electron density on axis, compared with air Results in N2 + 1 ppm O2 Electron density on axis, compared with air Position of streamerhead Absorbtion length of ionizing photons 5 orders of magnitude longer than air (260 m instead of 1.3 mm) Velocities less than 1 order of magnitude lower than those in air. Low amount of electrons in front of streamer head yields steeper density profiles. Streamers in N2 branch under these circumstances, while those in air did not (Experiments: Streamers in N2 branch more than those in air)

Position of streamer head Results in N2 + 1 ppm O2 Photo-ionization and varying levels of O2- background ionization in near-pure N2 Position of streamer head In N2 with only 1 ppm of O2, the effect of background ionization becomes noticeable at much lower levels than in air: ~1 Hz repetition frequency is the “threshold value”. In rough agreement with experimental results by Nijdam et al.

Feather-like structures Electron density for streamer in air Electron density on streamer axis Air: High electron densities where E > Ebreakdown (105 mm-3). Many avalanches that will overlap. No distinct hairs visible. N2 + 1 ppm O2 Electron densities much lower than in air (102 mm-3) Number of avalanches will be low, stochastic effects will be present. Avalanches visible as distinct hairs. Need a particle or hybrid model to fully study formation of feathers. Area where E > Ebreakdown

Conclusions and outlook Propagation speeds do not differ by orders of magnitude even if source-parameters do and background ionization alone yields propagating positive streamers in air at [O2-] = 105 cm-3 and above. Streamers appear to have a “self-correction” mechanism: Less source electrons results in narrower streamers, which results in higher fields, which makes better use of the electrons available (more and faster ionization). Photo-ionization is the dominant process up to a threshold level of background ionization, this level changes with gas composition. These effects were also observed experimentally. Future work: Use more accurate transport data – cooperation with Sasa Dujko. Explore other gases, planetary atmospheres – cooperation with Daria Dubrovin. Explain the “self-correction” mechanism by providing an analytical model for the streamer head. Results in: “Probing Photo-ionization: Simulations of positive streamers in various N2:O2-mixtures”, Wormeester, Pancheshnyi, Luque, Nijdam, Ebert – Accepted for J. Phys. D