Streamers, sprites, leaders, lightning: from micro- to macroscales

‘Streamers, sprites, leaders, lightning: from micro- to macroscales’ was the theme of a workshop in October 2007 in Leiden, The Netherlands; it brought together researchers from plasma physics, electrical engineering and industry, geophysics and space physics, computational science and nonlinear dynamics around the common topic of generation, structure and products of streamer-like electric breakdown. The present cluster issue collects relevant papers within this area; most of them were presented during the workshop. We here briefly discuss the research questions and very shortly review the papers in the cluster issue, and we also refer to a few recent papers in this and other journals

Stability of negative ionization fronts: regularization by electric screening?

We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length. For a fixed value of the electric field ahead of the front we calculate the dispersion relation numerically. These results guide the derivation of analytical asymptotes for arbitrary fields: for small wave-vector k, the growth rate s(k) grows linearly with k, for large k, it saturates at some positive plateau value. We include a physical interpretation of these results

Stability of negative ionization fronts: regularization by electric screening?

We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length. For a fixed value of the electric field ahead of the front we calculate the dispersion relation numerically. These results guide the derivation of analytical asymptotes for arbitrary fields: for small wave-vector k, the growth rate s(k) grows linearly with k, for large k, it saturates at some positive plateau value. We give a physical interpretation of these results.Comment: 11 pages, 2 figure

Front propagation into unstable states : universal algebraic convergence towards uniformly translating pulled fronts

Depending on the nonlinear equation of motion and on the initial conditions, different regions of a front may dominate the propagation mechanism. The most familiar case is the so-called pushed front, whose speed is determined by the nonlinearities in the front region itself. Pushed dynamics is always found for fronts invading a linearly stable state. A pushed front relaxes exponentially in time towards its asymptotic shape and velocity, as can be derived by linear stability analysis. To calculate its response to perturbations, solvability analysis can be used. We discuss, why these methods and results in general do not apply to fronts, whose dynamics is dominated by the leading edge of the front. This can happen, if the invaded state is unstable. Leading edge dominated dynamics can occur in two cases: The first possibility is that the initial conditions are 'flat', i.e., decaying slower in space than e^{-lambda^* x for $xto infty$ with $lambda^*$ defined below. The second and more important case is the one in which the initial conditions are 'steep', i.e., decay faster then e^{-lambda^* x. In this case, which is known as ``pulling'' or ``linear marginal stability'', it is as if the spreading leading edge is pulling the front along. In the central part of this paper, we analyze the convergence towards uniformly translating pulled fronts. We show, that when such fronts evolve from steep initial conditions, they have a universal relaxation behavior as time $ttoinfty$, which can be viewed as a general center manifold result for pulled front propagation. In particular, the velocity of a pulled front always relaxes algebraically like v(t)=v^*-3/(2lambda^*t); left(1-sqrt{pi/big((lambda^*)^2Dtbig)right)+O(1/t^2), where the parameters $v^*$, $lambda^*$, and $D$ are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state. This front velocity is independent of the precise value of the amplitude which one tracks to measure the front velocity. The interior of the front is essentially slaved to the leading edge, and develops universally as phi(x,t)=Phi_{v(t)left(x-int^t dtau ;v(tau)right)+O(1/t^2), where Phi_{v(x-vt) is a uniformly translating front solution with velocity $v$. We first derive our results in detail for the well known nonlinear diffusion equation of type $partial_t phi =partial_x^2phi+phi-phi^3$, where the invaded unstable state is $phi=0$, and then generalize our results to more general (sets of) partial differential equations with higher spatial or temporal derivatives, to {em p.d.e.'s with memory kernels, and also to difference equations occuring, e.g., in numerical finite difference codes. Our {it universal result for pulled fronts thus also implies independence of the precise nonlinearities, independence of the precise form of the dynamical equation, and independence of the precise initial conditions, as long as they are sufficiently steep. The only remaind

Electron density fluctuations accelerate the branching of positive streamer discharges in air

Branching is an essential element of streamer discharge dynamics but today it is understood only qualitatively. The variability and irregularity observed in branched streamer trees suggest that stochastic terms are relevant for the description of streamer branching. We here consider electron density fluctuations due to the discrete particle number as a source of stochasticity in positive streamers in air at standard temperature and pressure. We derive a quantitative estimate for the branching distance that agrees within a factor of 2 with experimental values. As branching without noise would occur later, if at all, we conclude that stochastic particle noise is relevant for streamer branching in air at atmospheric pressure.Comment: 5 pages, 4 figure

Cross sections and modelling results for TGF- and positron spectrum produced by a negative stepped lightning leader

We model the energy resolved angular distribution of TGFs and of positrons produced by a negative lightning leader stepping upwards in a thundercloud. First we present our new results for doubly differential cross sections for Bremsstrahlung and pair production based on the triply differential cross-sections of Bethe and Heitler. Other cross sections in literature and databases do not cover the appropriate energy range or do not apply to the small atomic numbers of nitrogen and oxygen or do not resolve both energies and emission angles of emitted photons or positrons. Second we have extended the Monte Carlo model of Chao Li towards relativistic electron energies, and we have included the new cross sections as well as Compton scattering of photons and photo ionization. We will present the angular resolved spectrum of TGFs and positrons of stepped negative leaders and compare it with results of other authors