Laplacian instability of planar streamer ionization fronts-An example of pulled front analysis
Derks, G, Ebert, U and Meulenbroek, B (2008) Laplacian instability of planar streamer ionization fronts-An example of pulled front analysis Journal of Nonlinear Science, 18 (5). pp. 551-590.
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Streamer ionization fronts are pulled fronts that propagate into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long-time attractor out of a continuous family. A stability analysis for perturbations in the transverse direction has to take these features into account. In this paper we show how to apply the Evans function in a weighted space for this stability analysis. Zeros of the Evans function indicate the intersection of the stable and unstable manifolds; they are used to determine the eigenvalues. Within this Evans function framework, we define a numerical dynamical systems method for the calculation of the dispersion relation as an eigenvalue problem. We also derive dispersion curves for different values of the electron diffusion constant and of the electric field ahead of the front. Numerical solutions of the initial value problem confirm the eigenvalue calculations. The numerical work is complemented with an analysis of the Evans function leading to analytical expressions for the dispersion relation in the limit of small and large wave numbers. The paper concludes with a fit formula for intermediate wave numbers. This empirical fit supports the conjecture that the smallest unstable wave length of the Laplacian instability is proportional to the diffusion length that characterizes the leading edge of the pulled ionization front. © 2008 Springer Science+Business Media, LLC.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||October 2008|
|Identification Number :||10.1007/s00332-008-9023-0|
|Additional Information :||The original publication is available at http://www.springerlink.com|
|Depositing User :||Symplectic Elements|
|Date Deposited :||14 Aug 2013 10:20|
|Last Modified :||23 Sep 2013 20:13|
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