Alejandro Luque

Positive and negative streamers in ambient air : modelling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. First, double-headed streamers in homogeneous electric fields of 50 kV cm^(−1) are briefly studied, and then we analyse streamers that emerge from needle electrodes with voltages of 10–20 kV in more detail. The streamer velocity at a given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamer evolution by length, velocity, head radius, head charge and maximal field enhancement. We show that the velocity of positive streamers is determined mainly by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Initially it is puzzling that negative streamers can be slower than positive ones under similar conditions, both in experiment and in simulation, as negative streamer fronts always move at least with the electron drift velocity in the local field. We argue that this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.

Probing photo-ionization: simulations of positive streamers in varying N2 : O2-mixtures

Photo-ionization is the accepted mechanism for the propagation of positive streamers in air though the parameters are not very well known; the efficiency of this mechanism largely depends on the presence of both nitrogen and oxygen. But experiments show that streamer propagation is amazingly robust against changes of the gas composition; even for pure nitrogen with impurity levels below 1 ppm streamers propagate essentially with the same velocity as in air, but their minimal diameter is smaller, and they branch more frequently. Additionally, they move more in a zigzag fashion and sometimes exhibit a feathery structure. In our simulations, we test the relative importance of photo-ionization and of the background ionization from pulsed repetitive discharges, in air as well as in nitrogen with 1 ppm O2 .W e also test reasonable parameter changes of the photo-ionization model. We find that photo-ionization dominates streamer propagation in air for repetition frequencies of at least 1 kHz, while in nitrogen with 1 ppm O2 the effect of the repetition frequency has to be included above 1 Hz. Finally, we explain the feather-like structures around streamer channels that are observed in experiments in high purity nitrogen, but not in air. (Some figures in this article are in colour only in the electronic version)

Interaction of Streamer Discharges in Air and Other Oxygen-Nitrogen Mixtures

The interaction of streamers in nitrogen-oxygen mixtures such as air is studied. First, an efficient method for fully three-dimensional streamer simulations in multiprocessor machines is introduced. With its help, we find two competing mechanisms how two adjacent streamers can interact: through electrostatic repulsion and through attraction due to nonlocal photoionization. The nonintuitive effects of pressure and of the nitrogen-oxygen ratio are discussed. As photoionization is experimentally difficult to access, we finally suggest to measure it indirectly through streamer interactions.

Quantum corrected electron holes

Abstract The theory of electron holes is extended into the quantum regime. The Wigner–Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude and to increase the number of deeply trapped electrons. They, hence, tend to bring this extreme non-equilibrium state closer to thermodynamic equilibrium, an effect which can be attributed to the tunneling of particles in this mixed state system.

Density models for streamer discharges: Beyond cylindrical symmetry and homogeneous media

Streamer electrical discharges are often investigated with computer simulations of density models (also called reaction-drift-diffusion models). We review these models, detailing their physical foundations, their range of validity and the most relevant numerical algorithms employed in solving them. We focus particularly on schemes of adaptive refinement, used to resolve the multiple length scales in a streamer discharge without a high computational cost. We then report recent results from these models, emphasizing developments that go beyond cylindrically symmetrical streamers propagating in homogeneous media. These include interacting streamers, branching streamers and sprite streamers in inhomogeneous media.

Kinetic theory of periodic hole and double layer equilibria in pair plasmas

The existence of manifestly nonlinear electrostatic modes in pair plasmas is shown analytically by means of the quasi-potential method applied to the Vlasov?Poisson system. These modes owe their existence to the trapping of particles in the potential trough(s) and are typically characterized by a notch in the particle distribution functions at resonant velocity, forming vortices in phase space. Both entities, wave structure ?(x) and phase velocity v0, are uniquely characterized by two parameters, the periodicity parameter k0 and the spectral parameter B. Whereas k0 = 0 describes double layers, with a phase velocity in the thermal range, k0 ? 0 represents a periodic wave train which can propagate with two rather distinct phase velocities. One is related to the fast plasma wave, the other one to the slow acoustic mode.

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

Branching is an essential element of streamer discharge dynamics. We review the current state of theoretical understanding and recall that branching requires a finite perturbation. We argue that, in current laboratory experiments in ambient or artificial air, these perturbations can only be inherited from the initial state, or they can be due to intrinsic electron-density fluctuations owing to the discreteness of electrons. We incorporate these electron-density fluctuations into fully three-dimensional simulations of a positive streamer in air at standard temperature and pressure. We derive a quantitative estimate for the ratio of branching length to streamer diameter that agrees within a factor of 2 with experimental measurements. As branching without this noise would occur considerably later, if at all, we conclude that the intrinsic stochastic particle noise triggers branching of positive streamers in air at atmospheric pressure.

Multiple scales in streamer discharges, with an emphasis on moving boundary approximations

Streamer discharges determine the very first stage of sparks or lightning, and they govern the evolution of huge sprite discharges above thunderclouds as well as the operation of corona reactors in plasma technology. Streamers are nonlinear structures with multiple inner scales. After briefly reviewing basic observations, experiments and the microphysics, we start from density models for streamers, i.e. from reaction–drift–diffusion equations for charged-particle densities coupled to the Poisson equation of electrostatics, and focus on derivation and solution of moving boundary approximations for the density models. We recall that so-called negative streamers are linearly stable against branching (and we conjecture this for positive streamers as well), and that streamer groups in two dimensions are well approximated by the classical Saffman–Taylor finger of two fluid flow. We draw conclusions on streamer physics, and we identify open problems in the moving boundary approximations.

Nonlinear instability and saturation of linearly stable current-carrying pair plasmas

The nonlinear instability of current-carrying pair plasmas is investigated with a Vlasov–Poisson model for the two-particle species. It is shown that linearly stable configurations are unstable against small incoherent perturbations of the particle distribution functions. The instability gives rise to a self-acceleration and growth of phase-space holes. After the growth of the phase-space holes, the instability reaches a chaotic saturation where the finite-amplitude holes interact and merge, and after a long time, the system attains a stable equilibrium state with a smaller drift and a larger temperature than the initial one, and where a few stable phase-space holes are present.

Theory of negative energy holes in current carrying plasmas

The theory of hole structures or phase-space vortices in a one-dimensional current-carrying plasma is extended, focusing on the energy of trapped-particle modes in comparison to a homogeneous plasma. It is shown how the energy expression presented in [J.-M. Griesmeier and H. Schamel, Phys. Plasmas 9, 2462 (2002)] is obtained for small amplitude structures. Parameter regimes admitting negative energy solutions are given. It is demonstrated how negative energy structures can be found analytically for the case of a generalized solitary electron hole (where ion trapping is shown to further lower the critical drift velocity), for a generalized solitary ion hole (where the influence of electron trapping increases the critical drift velocity) and for a harmonic (monochromatic) structure. Consequently, a plasma may become nonlinearly unstable well below linear threshold already for infinitesimal wave amplitudes.