Topic/Type: 1. Plasma Simulation, Invited
Centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands
Applied Physics, Eindhoven University of Technology, The Netherlands
Streamer discharges are the fundamental mode of primary electric breakdown of most gasses; streamer-like phenomena also occur in liquids and solids. They appear equally in nature, laboratory and technology, over lengths of (tens of) centimetres at normal density, and over lengths of tens of kilometres as so-called sprite discharges at 40 to 90 km altitude in our atmosphere .
Even a single streamer has a complex structure: it contains a thin ionization and space charge layer at the channel tip that enhances the electric field ahead of the extending plasma channel. In this field, electrons are extremely far from equilibrium and can even run away. These electrons are very efficient in exciting molecules; therefore streamers are used for chemical processing, disinfection and sterilization and many other applications. Furthermore, streamers appear in trees and groups and interact with each other and with external electric circuits.
Clearly, not the whole range of scales from (i) single electron dynamics through (ii) space charge and ionization fronts at the channel tip to (iii) the whole discharge channel and (iv) the interaction of several channels in 3D can presently be implemented in one simulation tool. We focus on the following recent results:
1. 3D hybrid simulations for streamers where a PIC-MCC description in the high field region is coupled to a fluid description in the low field region . The studies indicate short-comings of the fluid approximation in high background fields . They will be used to study run-away electrons and hard X-ray emissions as well as particle fluctuation effects.
2. Streamer simulations in fluid approximation with adaptive grid refinement to study the interaction of two streamers , and the interaction of emerging sprite streamers with lightning stroke and ionosphere .
3. Reduced electrodynamic models for streamer properties like diameter, velocity, ionization density etc. [6,7].
 For a review of phenomena, see cluster issue on 'Streamers, Sprites and Lightning' in J. Phys. D: Appl. Phys. 41, no. 23 (dec. 2008), eds.: U. Ebert, D.D. Sentman.
 C. Li, U. Ebert, W. Hundsdorfer, http://arxiv.org/abs/0907.0555
 C. Li, U. Ebert, W. Hundsdorfer, http://arxiv.org/abs/0904.2968
 A. Luque, U. Ebert, and W. Hundsdorfer, Phys. Rev. Lett. 101, 075005 (2008).
 A. Luque, U. Ebert, revised for Nature Geoscience.
 A. Luque, F. Brau, U. Ebert, Phys. Rev. E 78, 016206 (2008).
 A. Luque, V. Ratushnaya, U. Ebert, J. Phys. D: Appl. Phys. 41, 234005 (2008).