Comparisons of multidimensional non-equilibrium and equilibrium fluid and Monte Carlo models for streamers

Abstract

The formation of ionizing channels and the propagation of cathode- and anode-directed streamers in nitrogen gas have been examined theoretically by a self-consistent, fully two-dimensional simulation, assuming a cylindrically symmetric geometry. The dynamical model of the electron, considering the photoionization effect, is described by equilibrium (a single-moment equation) and non-equilibrium (a three-moment equation) models. A more accurate flux-corrected transport (MAFCT) technique, which provides a solution for the steep and varying gradient problem, is used to solve the electron fluid equations. This is the first investigation of the gas pre-breakdown based on a non-equilibrium two-dimensional fluid model, which is more accurate than the equilibrium fluid model. The differences in the simulation results of the three- and single-moment fluid models for streamers are found. Moreover, a comparison with a Monte Carlo simulation result (a kinetic model) is used to test the validity of fluid models, and the comparison illustrates that the non-equilibrium fluid model provides a more accurate description from the equilibrium fluid model.

Two-dimensional modelling of positive streamer dynamics in non-uniform electric fields in air

“…where χ is the ratio of the number of emitting ionizing photons to the number of acts of ionization, ν i is the The validity of such an approximation is confirmed both by estimates (see [4]) and by the comparison of the results of streamer simulation obtained using the equilibrium and non-equilibrium fluid models [14].…”

Effects of photoionization on propagation and branching of positive and negative streamers in sprites

“…[8] The continuity equations (1), (2), and (3) effectively represent a fluid description of streamer plasma based on a first moment of the Bolzmann kinetic equation [e.g., Guo and Wu, 1993]. The coefficients of the model are assumed to be functions of the local reduced electric field E/N, where E is the electric field magnitude and N is the air neutral density.…”

“…This implies that the equilibrium electron distribution function is achieved instantaneously in time in response to the applied local electric field E. This assumption is justified as soon as relaxation times of the mean energy and momentum of the electron distribution remain substantially less than the timescales characterizing variations of the electric field. In particular, at ground pressure the energy relaxation timescales are on the order of 10 ps, and 1 ps, for the typical electric field magnitudes in the streamer body, and streamer head, respectively [Vitello et al, 1993;Guo and Wu, 1993]. The local field approximation is therefore justified on typical timescales of streamer development, which are usually measured in nanoseconds.…”

Propagator methods for plasma simulations: application to breakdown

“…There is a considerable literature, for instance, [22][23][24][25][26][27][28][29][30] on the use of flux-corrected transport (FCT) to correct for numerical diffusion (ND). ND, in the sense the term is usually used, does not appear to be the main problem in this work.…”