4 research outputs found
A moving boundary model motivated by electric breakdown: II. Initial value problem
An interfacial approximation of the streamer stage in the evolution of sparks
and lightning can be formulated as a Laplacian growth model regularized by a
'kinetic undercooling' boundary condition. Using this model we study both the
linearized and the full nonlinear evolution of small perturbations of a
uniformly translating circle. Within the linear approximation analytical and
numerical results show that perturbations are advected to the back of the
circle, where they decay. An initially analytic interface stays analytic for
all finite times, but singularities from outside the physical region approach
the interface for , which results in some anomalous relaxation at
the back of the circle. For the nonlinear evolution numerical results indicate
that the circle is the asymptotic attractor for small perturbations, but larger
perturbations may lead to branching. We also present results for more general
initial shapes, which demonstrate that regularization by kinetic undercooling
cannot guarantee smooth interfaces globally in time.Comment: 44 pages, 18 figures, paper submitted to Physica
Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures
Positive streamers are thought to propagate by photo-ionization whose
parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in
nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in
pure oxygen and argon. Our new experimental set-up guarantees contamination of
the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to
measure as they emit considerably less light in the sensitivity range of our
fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all
nitrogen/oxygen mixtures look generally similar, but become somewhat thinner
and branch more with decreasing oxygen content. In pure nitrogen the streamers
can branch so much that they resemble feathers. This feature is even more
pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the
feathers at 200 mbar; this density could be interpreted as the free electron
density creating avalanches towards the streamer stem. It is remarkable that
the streamer velocity is essentially the same for similar voltage and pressure
in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen
concentration and therefore the photo-ionization lengths vary by more than five
orders of magnitude. Streamers in argon have essentially the same velocity as
well. The physical similarity of streamers at different pressures is confirmed
in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and
spectra removed - subsection regarding effects of repetition frequency added
- many more smaller change