High order fluid model for streamer discharges. II. Numerical solution and investigation of planar fronts

TL;DR

This paper presents a validated high order fluid model for negative planar streamer fronts in nitrogen, demonstrating its accuracy over first order models and highlighting the importance of energy flux terms in simulations.

Contribution

The paper introduces and validates a high order fluid model for streamer discharges, improving accuracy over traditional models and analyzing the effects of energy flux terms.

Findings

High order fluid model agrees with PIC/MC simulations up to 1000 Townsend.

First order models show significant deviations from high order results.

Energy flux term is crucial for accurate streamer discharge modeling.

Abstract

The high order fluid model developed in the preceding paper is employed here to study the propagation of negative planar streamer fronts in pure nitrogen. The model consists of the balance equations for electron density, average electron velocity, average electron energy and average electron energy flux. These balance equations have been obtained as velocity moments of Boltzmann's equation and are here coupled to the Poisson equation for the space charge electric field. Here the results of simulations with the high order model, with a PIC/MC (Particle in cell/Monte Carlo) model and with the first order fluid model based on the hydrodynamic drift-diffusion approximation are presented and compared. The comparison with the MC model clearly validates our high order fluid model, thus supporting its correct theoretical derivation and numerical implementation. The results of the first order fluid model with local field approximation, as usually used for streamer discharges, show considerable deviations. Furthermore, we study the inaccuracies of simulation results caused by an inconsistent implementation of transport data into our high order fluid model. We also demonstrate the importance of the energy flux term in the high order model by comparing with results where this term is neglected. Finally, results with an approximation for the high order tensor in the energy flux equation is found to agree well with the PIC/MC results for reduced electric fields up to 1000 Townsend, as considered in this work.