Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

Abstract

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP 3 ) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by Ségur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 < p O 2 R < 150 Torr cm, where p O 2 is the partial pressure of molecular oxygen in air in units of Torr (p O 2 = 150 Torr at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP 3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of boundary conditions represents an important task needed for a successful extension of the proposed formulations to two-and three-dimensional physical systems with obstacles of complex geometry (i.e. electrodes, dust particles, aerosols, etc), which are opaque for the photoionizing UV photons.

Plasma irregularities in the D-region ionosphere in association with sprite streamer initiation

“…Note that, although included, the effect of detachment in our simulations is negligible over a B2 ms time scale. Photoionization processes are included using the three-group SP 3 model 28 . The motion of charged species is simulated by solving the drift-diffusion equations for electrons and ions coupled with Poisson's equation 19 .…”

Vibrational kinetics of air plasmas induced by sprites

“…Another important assumption of the kinetic model is related to the exclusion of photochemistry processes occurring in sprites. Some photochemical mechanisms, like photoionization, might impact the propagation and branching of sprite streamers [Liu and Pasko, 2004;Bourdon et al, 2007] but with an indirect or minor influence on the non-equilibrium chemistry of the streamer plasma.…”

Surface charge deposition inside a capillary glass tube by an atmospheric pressure discharge in air

“…Transport parameters and reaction rates are taken from [16]. For the photoionization source term, the three-group SP 3 model is used [17] with boundary conditions given in [18]. In Eq.…”