High-order fluid model for streamer discharges: I. Derivation of model and transport data

Abstract

Abstract. Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. The present paper focuses on the derivation of a high order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two term approximation for solving Boltzmann's equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high order fluid model. In the second paper in this sequence, we will discuss the solutions of the high order fluid model for streamers, based on model and input data derived in the present paper.PACS numbers: 52.25. Dy, 52.65.Kj, 52.25.Fi, 52.25.Jm Submitted to: J. Phys. D: Appl. Phys.

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

“…For increasing electric field the discrepancies in the streamer velocity increase further, as illustrated in figure 2. Similar trends have been observed in the preceding paper [31] where planar fronts were modelled with the first-order fluid model. In both models, streamers with bulk data are faster and the electron/ion density is higher in both the streamer head and the streamer channel.…”

“…In our preceding paper [31] we have developed a high-order fluid model for streamer discharges. The balance equations were obtained as velocity moments of the Boltzmann equation while the collisional terms were evaluated using momentum transfer theory.…”

“…The energy flux of the drift motion, however, is included. For more details of the derivation we refer to [31]. The derived model consists of a set of differential equations for the electron density n, for the average electron velocity v, for the average electron energy ε and for the average electron energy flux ξ:…”

“…The steps of derivation of this model were discussed and criticized in our previous paper [31]. The model is based on the hydrodynamic reaction-drift-diffusion approximation…”

“…In the part I [31] we have derived a high-order fluid model, whose predictions for streamer dynamics will be tested in this paper. The high-order fluid model contains equations for the electron density, for the average electron velocity, for the average electron energy and for the average electron energy flux.…”