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P: Plasmaphysik
P 10: Poster II
P 10.5: Poster
Dienstag, 18. März 2003, 17:30–19:15, Foyer
Spontaneous branching of discharge streamers: conformal mapping approach — •Bernard Meulenbroek1, Andrea Rocco1, and Ute Ebert1,2 — 1Center for Math. and Comp. Science, Amsterdam, NL — 2Dept. Physics, TU Eindhoven, NL
Numerical solutions [1-3] of the minimal streamer model show that in high fields, a discharge streamer can approach such a high conductivity that the ionization front is almost equipotential. At this stage, the streamer can branch spontaneously.
We analyze this instability analytically: the limit of an equipotential ionization front around the streamer head is equivalent to an “ideally conducting” streamer, as suggested by Lozansky and Firsov in the 1970’ies. However, the predictions of this model were not seriously investigated.
Conformal mapping techniques are an elegant way to study this nonlinear problem of moving boundaries in 2D. We show how to apply this technique to an insolated streamer in a constant far field. With the simplifying approximation that the velocity of the edges of the streamer is proportional to the local field, the moving boundary problem can be reduced to a set of ordinary differential equations for the amplitudes of Fourier modes. The solutions demonstrate spontaneous branching.
[1] M. Arrayás, U. Ebert, W. Hundsdorfer, PRL 88, 174502 (2002).
[2] A. Rocco, U. Ebert, W. Hundsdorfer, PRE 66, 035102(R) (2002).
[3] see also talk Ebert and poster Montijn, Hundsdorfer, Rocco, Ebert.