Moving boundary approximation for curved streamer ionization fronts: Solvability analysis

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dc.creatorBrau, Fabian
dc.creatorDavidovitch, Benny
dc.creatorEbert, Ute
dc.date2008-07-29
dc.date.accessioned2026-07-07T10:19:58Z
dc.date.available2026-07-07T10:19:58Z
dc.descriptionThe minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.
dc.description22 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0807.4614
dc.identifierhttp://arxiv.org/abs/0807.4614
dc.identifierPhys. Rev. E 78, 056212 (2008)
dc.identifierdoi:10.1103/PhysRevE.78.056212
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174704
dc.subjectPlasma Physics
dc.titleMoving boundary approximation for curved streamer ionization fronts: Solvability analysis
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