C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation Modelling, Analysis and SimulationDeviations from the local field approximation in negative streamer heads C. Li, W.J.M. Brok, U. Ebert, J.J.A.M. van der Mullen Deviations from the local field approximation in negative streamer heads ABSTRACT 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 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is <= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), 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 the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field. REPORT MAS-E0706 FEBRUARY 2007 Mathematics Subject Classification: 82D10Keywords and Phrases: streamers; ionization front; particle model; local field approximation Note: This work was carried out under project "Multiscale Modelling and Nonlinear Dynamics"-"Electric discharges and plasma technology". The authors acknowledge support by the Dutch national program Bsik, in the ICT project BRICKS, theme MSV1. arXiv:physics/0702129v1 15 Feb 2007Deviations 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 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is ≤ 50 kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200 kV/(cm bar), 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, ...

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 computational effort and reproduces the results of a pure particle model. 52.80.Mg, 52.65.Kj Streamers generically occur in the initial electric breakdown of long gaps. They are growing filaments of weakly ionized nonstationary plasma; they are produced by a sharp ionization front that propagates into non-ionized matter within a self-enhanced electric field. Streamers are used in industrial applications such as lighting [1], gas and water purification [2,3] or combustion control [4], and they occur in natural processes as well such as lightning [5,6] or transient luminous events in the upper atmosphere [7,8]. Important recent questions concern (i) propagation and branching of streamers [9] and the role of avalanches created by single electrons, (ii) the electron energy distribution in the streamer head and the subsequent gas chemistry that is used in the above applications, as well as (iii) runaway electrons and X-ray generation, possibly in the streamer zone of lightning leaders [8,10]. The present paper deals with the efficient simulation of these problems.Monte Carlo particle simulations [11,12] model these effects as they contain the full microscopic physics; the deterministic electron motion between collisions is calculated and collisions of electrons with neutrals are treated through a Monte Carlo process with appropriate statistical weights. The particle model includes the complete electron velocity and energy distribution as well as the discrete nature of particles. However, a drawback of such models is that the required computation resources grow with the number of particles and eventually exceed the CPU space of any computer. This difficulty is counteracted by using superparticles carrying the charge and the mass of many physical particles, but superparticles in turn create unphysical fluctuations and stochastic heating [13].Streamers are therefore mostly modeled as fluids (see e.g. [14,15,16,17,18]) since a fluid model is computationally much more efficient. In the case of a negative discharge in a pure non-attaching gas like nitrogen, it consists of continuity equations for the densities of electrons n e and positive ions n p coupled to the Poisson equation for the electric field E. The electron mobility µ and diffusion matrix D and the impact ionization rate α are calculated from microscopic scattering and transport Figure 1: (Color online) The streamer ionization front, that here is indicated by th...

No abstract

A model developed for a dielectric barrier discharge (DBD) in helium, used as a new spectroscopic source in analytical chemistry, is presented in this paper. The model is based on the fluid approach and describes the behavior of electrons, He+ and He+2 ions, He metastable atoms, He atoms in higher excited levels, and He2 dimers. The He ground-state atoms are regarded as background gas. The characteristic effect of charging/discharging of the dielectrics which cover both electrodes is also simulated. Typical results of the model include the distribution of potential inside the plasma (and the potential drop across the dielectrics), the electric current and gap voltage as a function of time for a given applied potential profile, the spatial and temporal number-density profiles of the different plasma species, and the relative contributions of the mechanisms of their production and loss.

No abstract