Spin-Orbital momentum decomposition and helicity exchange in a set of non-null knotted electromagnetic fields

We calculate analytically the spin-orbital decomposition of the angular momentum using completely non-paraxial fields that have certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behaviour of the local angular momentum density is rather different. By taking cases with constant and non-constant electric and magnetic helicities, we show that the total angular momentum density present different characteristics during time evolution

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

The onset of tree-like patterns in negative streamers

We present the first analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully 3-D case. This model follows from fundamental considerations on charge production by impact ionization and balance laws, and leads to an equation for the evolution of the interface between ionized and non-ionized regions. We compare some experimental patterns with the numerically simulated ones, and give an explicit expression for the growth rate of harmonic modes associated with the perturbation of a symmetrically expanding discharge. By means of full numerical simulation, the splitting and formation of characteristic tree-like patterns of electric discharges is observed and described

Contour dynamics model for electric discharges

A contour dynamics model for electrical discharges is obtained and analyzed. The model is deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion. The dispersion relation for a non planar 2-D discharge is calculated. The development and propagation of finger-like patterns are studied and their main features quantified.Comment: 4 pages, 2 fi

Spontaneous branching of anode-directed streamers between planar electrodes

Non-ionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to Firsov's limit of ``ideal conductivity''. Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism

Electric discharge contour dynamics model: the effects of curvature and finite conductivity

In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron diffusion is small. It consists of two integro-differential equations defined at the boundary of the plasma region: one for the motion and a second equation for the net charge density at the interface. We have computed explicit solutions with cylindrical symmetry and found the dispersion relation for small symmetry-breaking perturbations in the case of finite resistivity. We implement a numerical procedure to solve our model in general situations. As a result we compute the dispersion relation for the cylindrical case and compare it with the analytical predictions. Comparisons with experimental data for a 2-D positive streamers discharge are provided and predictions confirmed.Comment: 23 pages, 3 figure