Pierre Ségur

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

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 (SP3) 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 S´ egur 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 O2 R< 150 Torr cm, where pO2 is the partial pressure of molecular oxygen in air in units of Torr (pO2 = 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, SP3 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.

Application of photoionization models based on radiative transfer and the Helmholtz equations to studies of streamers in weak electric fields

Recent advances in development of photoionization models in air based on radiative transfer and Helmholtz equations open new perspectives for efficient solution of nonthermal gas discharge problems involving complex geometries. Many practical applications require accurate modeling of streamer discharges developing in weak electric fields, in which the photoionization process significantly contributes to discharge dynamics. This paper (1) reports original studies, which demonstrate the validity and accuracy of the recently proposed photoionization models for studies of streamers in weak electric fields, and (2) introduces efficient boundary conditions for the photoinization models based on radiative transfer theory.

The use of the ghost fluid method for Poisson's equation to simulate streamer propagation in point-to-plane and point-to-point geometries

This paper presents the application of the ghost fluid method (GFM) to solve Poissons equation for streamer discharge simulations between electrodes of complex geometries. This approach allows one to use a simple rectilinear grid and nevertheless take into account the influence of the exact shape of the electrode on the calculation of the potential and the electric field. First, the validity of the GFM approach concerning the computation of the electric field is demonstrated by performing direct comparisons in a point-to-plane geometry of the Laplacian potential and electric field calculated with this method and given by the analytical solution. Second, the GFM is applied to the simulation of a positive streamer propagation in a hyperboloid-to-plane configuration studied by Kulikovsky (1998 Phys. Rev. E 57 7066–74). Very good agreement is obtained with the results of Kulikovsky (1998) on all positive streamer characteristics during its propagation in the interelectrode gap. Then the GFM is applied to simulate the discharge in preheated air at atmospheric pressure in point-to-point geometry. The propagation of positive and negative streamers from both point electrodes is observed. After the interaction of both discharges, the very rapid propagation of the positive streamer towards the cathode in the volume pre-ionized by the negative streamer is presented. This structure of the discharge is in qualitative agreement with the experiment.

Physics and applications of atmospheric non-thermal air plasma with reference to environment

Since air is a natural part of our environment, special attention is given to the study of plasmas in air at atmospheric pressure and their applications. This fact promoted the study of electrical conduction in air-like mixtures, i.e. mixtures containing an electronegative gas component. If the ionization growth is not limited its temporal evolution leads to spark formation, i.e. a thermal plasma of several thousand kelvins in a quasi-local thermodynamic equilibrium state. But before reaching such a thermal state, a plasma sets up where the electrons increase their energy characterized by an electron temperature Te much higher than that of heavy species T or T+ for the ions. Since the plasma is no longer characterized by only one temperature T , it is said to be in a nonthermal plasma (NTP) state. Practical ways are listed to prevent electron ionization from going beyond the NTP states. Much understanding of such NTP may be gathered from the study of the simple paradigmatic case of a discharge induced between a sharp positively stressed point electrode facing a grounded negative plane electrode. Some physical properties will be gathered from such configurations and links underlined between these properties and some associated applications, mostly environmental. Aerosol filtration and electrostatic precipitators, pollution control by removal of hazardous species contained in flue gas exhaust, sterilization applications for medical purposes and triggering fuel combustion in vehicle motors are among such applications nowadays.

Numerical simulation of filamentary discharges with parallel adaptive mesh refinement

Direct simulation of filamentary gas discharges like streamers or dielectric barrier micro-discharges requires the use of an adaptive mesh. The objective of this paper is to develop a strategy which can use a set of grids with suitable local refinements for the continuity equations and Poissons equation in 2D and 3D geometries with a high-order discretization. The advantages of this approach are presented with a filamentary discharge simulation in plane-plane geometry in nitrogen within the diffusion-drift approximation.

A new one-dimensional moving mesh method applied to the simulation of streamer discharges

Streamer front propagation involves steep gradients in charge density and electric field. Since the front has to be meshed with a sufficient number of points, adaptive meshing is essential for fast and accurate numerical simulations. In this paper a one-dimensional (1D) moving mesh method recently developed by Tang and Tang (2003 SIAM J. Numer. Anal. 41 487–515) is successfully applied to the simulation of streamer discharge. One-and-half (1.5D) and two-dimensional (2D) simulations of streamer discharges in nitrogen at atmospheric pressure are presented. The moving mesh method is combined with the third order ULTIMATE QUICKEST scheme (Leonard 1991 Comput. Math. Appl. Mech. Eng. 88 17–74) to solve the advection part of the plasma continuity equations in a selection of classical problems in streamer simulation: point-to-plane and plane-to-plane electrode systems. The combination of the 1D moving mesh method and the high order scheme increases the accuracy of numerical solutions and reduces the computational time.

Photoionization and Optical Emission Effects of Positive Streamers in Air at Ground Pressure

A positive streamer in a weak electric field in air at ground pressure is investigated by utilizing a recently developed photoionization model based on the radiative transfer theory. The modeling results on the streamer emissions demonstrate that blue emissions of the second positive band system of N2 dominate the streamer spectra, in contrast to streamers in predominately red sprite discharges observed at low air pressures at high altitudes in the Earths atmosphere.

The finite volume method solution of the radiative transfer equation for photon transport in non-thermal gas discharges: application to the calculation of photoionization in streamer discharges

This paper presents the development of a direct accurate numerical method to solve the monochromatic radiative transfer equation (RTE) based on a finite volume method (FVM) and its application to the simulation of streamer propagation. The validity of the developed model is demonstrated by performing direct comparisons with results obtained using the classic integral model. Comparisons with approximate solutions of the RTE (Eddington and SP3 models) are also carried out. Specific validation comparisons are presented for an artificial source of radiation with a Gaussian shape. The reported results demonstrate that whatever the value of the absorption coefficient, the results obtained using the direct FVM are in excellent agreement with the reference integral model with a significantly reduced computation time. When the absorption coefficient is high enough, the Eddington and SP3 methods are as accurate and become faster than the FVM. However, when the absorption coefficient decreases, approximate methods become less accurate and more computationally expensive than the FVM. Then the direct finite volume and the SP3 models have been applied to the calculation of photoionization in a double-headed streamer at ground pressure. For high values of the absorption coefficient, positive and negative streamers calculated using the SP3 model and the FVM for the photoionization source term are in excellent agreement. As the value of the absorption coefficient decreases, discrepancies between the results obtained with the finite volume and the SP3 models increase, and these differences increase as the streamers advance. For low values of the absorption coefficient, the use of the SP3 model overestimates the electron density and underestimates the photoionization source term in both streamers in comparison with the FVM. As a consequence, for low values of the absorption coefficient, positive and negative streamers calculated using the SP3 model for the photoionization source term propagate more slowly than those calculated using the FVM.