%0 Book Section %1 statphys23_0635 %A Li, C. %A Brok, W.J.M. %A Ebert, U. %A Hundsdorfer, W. %A Mullen, J.J.A.M. Van Der %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K approximation field front ionization local model montecarlo particle statphys23 streamers topic-3 %T Spark forming ionization fronts: particle, continuum and hybrid computations %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=635 %X The formation of spark channels (known as the ``streamer'' process) in electric breakdown is a phenomenon with multiple scales 1,2. Here we investigate the inner structure of the ionization front that creates a discharge finger, and compare Monte Carlo particle models with continuum approximations. The investigation is driven by three challenges: 1) inclusion of particle density and energy fluctuations into the previous continuum approximation, 2) explanation of differences between breakdown patterns in different gases, and 3) understanding of X-ray emission from early stages of lightning channels. While continuous ``fluid'' models are computationally efficient in regions with large particle densities like the ionized interior of a channel, Monte Carlo particle models contain the full microscopic scattering physics with its fluctuations and are appropriate for regions with low densities and for particles in the tail of the energy distribution. A particle model should be used at least in the leading edge of a ``pulled'' 2,3 ionization front where few single particles can create fluctuations of velocity and ionization rate and might trigger inherent instabilities. The goal of the project is therefore to develop a computation scheme that is hybrid in space as shown in the figure. We derive the parameter functions for the continuum model from the particle model with its correct microscopic physics. Then planar fronts can be studied both in the particle and in the continuum model with reasonable run-time and memory-consumption, while the strong spatio-temporal gradients of the front are retained. We find that the ionization density behind the particle front is much higher than behind the continuum front, in particular, when the electric field ahead of the front is high. Furthermore, the electron energies in the leading edge of the ionization front are higher in the particle model than in the continuum model. These higher electron energies in the ionization front lead to higher ionization rates, and consecutively to a higher ionization density behind the front (as can be proven by an analytical bound). The discrepancy between particle and continuum model is not due to the assumption that parameters of the continuum model depend on the local electric field (``local field approximation''), but to the strong density gradients in the leading edge of the ionization front 4. Work on hybrid spatial coupling of particle and continuum models as indicated in the figure is in progress. 1) U. Ebert $et$ $al$., Plasma Sources Sci. Technology 15, S118 (2006). 2 C. Montijn $et$ $al$., J. Comp. Phys. 209, 801 (2006); A. Luque $et$ $al$., Appl. Phys. Lett. 90, 081501 (2007). 3 U. Ebert, W. van Saarloos, Physica D 146, 1 - 99 (2000) 4 Chao Li $et$ $al$., arxiv 0702129, submitted to J. Appl. Phys.

@incollection{statphys23_0635, abstract = {The formation of spark channels (known as the ``streamer'' process) in electric breakdown is a phenomenon with multiple scales [1,2]. Here we investigate the inner structure of the ionization front that creates a discharge finger, and compare Monte Carlo particle models with continuum approximations. The investigation is driven by three challenges: 1) inclusion of particle density and energy fluctuations into the previous continuum approximation, 2) explanation of differences between breakdown patterns in different gases, and 3) understanding of X-ray emission from early stages of lightning channels. While continuous ``fluid'' models are computationally efficient in regions with large particle densities like the ionized interior of a channel, Monte Carlo particle models contain the full microscopic scattering physics with its fluctuations and are appropriate for regions with low densities and for particles in the tail of the energy distribution. A particle model should be used at least in the leading edge of a ``pulled'' [2,3] ionization front where few single particles can create fluctuations of velocity and ionization rate and might trigger inherent instabilities. The goal of the project is therefore to develop a computation scheme that is hybrid in space as shown in the figure. We derive the parameter functions for the continuum model from the particle model with its correct microscopic physics. Then planar fronts can be studied both in the particle and in the continuum model with reasonable run-time and memory-consumption, while the strong spatio-temporal gradients of the front are retained. We find that the ionization density behind the particle front is much higher than behind the continuum front, in particular, when the electric field ahead of the front is high. Furthermore, the electron energies in the leading edge of the ionization front are higher in the particle model than in the continuum model. These higher electron energies in the ionization front lead to higher ionization rates, and consecutively to a higher ionization density behind the front (as can be proven by an analytical bound). The discrepancy between particle and continuum model is not due to the assumption that parameters of the continuum model depend on the local electric field (``local field approximation''), but to the strong density gradients in the leading edge of the ionization front [4]. Work on hybrid spatial coupling of particle and continuum models as indicated in the figure is in progress. 1) U. Ebert $et$ $al$., Plasma Sources Sci. Technology {\bf 15}, S118 (2006). [2] C. Montijn $et$ $al$., J. Comp. Phys. {\bf 209}, 801 (2006); A. Luque $et$ $al$., Appl. Phys. Lett. {\bf 90}, 081501 (2007). [3] U. Ebert, W. van Saarloos, Physica D {\bf 146}, 1 - 99 (2000) [4] Chao Li $et$ $al$., arxiv 0702129, submitted to J. Appl. Phys.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Li, C. and Brok, W.J.M. and Ebert, U. and Hundsdorfer, W. and Mullen, J.J.A.M. Van Der}, biburl = {https://www.bibsonomy.org/bibtex/20812fd197f972da199b0547fa76866d8/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {3f616f80b1a3983ef084e0ffbbdb4fda}, intrahash = {0812fd197f972da199b0547fa76866d8}, keywords = {approximation field front ionization local model montecarlo particle statphys23 streamers topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:25.000+0200}, title = {Spark forming ionization fronts: particle, continuum and hybrid computations}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=635}, year = 2007 }