C Chao Li

3D hybrid computations for streamer discharges and production of runaway electrons

We introduce a 3D hybrid model for streamer discharges that follows the dynamics of single electrons in the region with strong field enhancement at the streamer tip while approximating the many electrons in the streamer interior as densities. We explain the method and present first results for negative streamers in nitrogen. We focus on the high electron energies observed in the simulation.

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a one-dimensional setting, allowing reasonable run time and memory consumption and high numerical accuracy without introducing superparticles. If the reduced electric field immediately before the front is ⩽50kV∕(cmbar), solutions of fluid and particle model agree very well. If the field increases up to 200kV∕(cmbar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in th...

Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts

Streamers are the first stage of sparks and lightning; they grow due to a strongly enhanced electric field at their tips; this field is created by a thin curved space charge layer. These multiple scales are already challenging when the electrons are approximated by densities. However, electron density fluctuations in the leading edge of the front and non-thermal stretched tails of the electron energy distribution (as a cause of X-ray emissions) require a particle model to follow the electron motion. But present computers cannot deal with all electrons in a fully developed streamer. Therefore, super-particle have to be introduced, which leads to wrong statistics and numerical artifacts. The method of choice is a hybrid computation in space where individual electrons are followed in the region of high electric field and low density while the bulk of the electrons is approximated by densities (or fluids). We here develop the hybrid coupling for planar fronts. First, to obtain a consistent flux at the interface between particle and fluid model in the hybrid computation, the widely used classical fluid model is replaced by an extended fluid model. Then the coupling algorithm and the numerical implementation of the spatially hybrid model are presented in detail, in particular, the position of the model interface and the construction of the buffer region. The method carries generic features of pulled fronts that can be applied to similar problems like large deviations in the leading edge of population fronts, etc.

Spatially hybrid computations for streamer discharges: II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air. Future applications of the hybrid model lie in effects of electron density fluctuations on inception, propagation and branching of streamers, and in accurate calculations of electron energies at and of electron run-away from the streamer head. The last is relevant for hard radiation from streamer-leader systems and possibly for Terrestrial Gamma-Ray Flashes.

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.

Spatial coupling of particle and fluid models for streamers : where nonlocality matters

Particle models for streamer ionization fronts contain correct electron energy distributions, runaway effects and single electron statistics. Conventional fluid models are computationally much more efficient for large particle numbers, but create too low ionization densities in high fields. To combine their respective advantages, we here show how to couple both models in space. We confirm that the discrepancies between particle and fluid fronts arise from the steep electron density gradients in the leading edge of the fronts. We find the optimal position for the interface between models that minimizes the computational effort and reproduces the results of a pure particle model.

Avalanche-to-Streamer Transition in Particle Simulations

The avalanche-to-streamer transition is studied and illustrated in a particle model. The results are similar to those of fluid models. However, when superparticles are introduced, numerical artifacts become visible. This underscores the need of models that are hybrid in space.

PPPS-2013: Particle and hybrid modeling of NS pulsed discharges: Discharge structures and electron energies

Summary form only given. ICCD photographs with nanosecond resolution of nanosecond pulsed discharges from a pointed electrode show a characteristic sequence of evolution: first the formation of an ionization cloud around the electrode, and then an expanding spherical ionization front that eventually breaks up into streamers, if the pulse duration permits [1,2].