The use of an improved Eddington approximation to facilitate the calculation of photoionization in streamer discharges

Abstract

In the simulation of streamer discharge propagation, classical integral methods used to calculate the photoionization source term are computationally very expensive. In this work, a new approach based on the direct solution of an approximate radiative transfer equation is developed. Different approximations of the radiative transfer equation are discussed and tested for typical conditions encountered in streamer discharges. An improved Eddington approximation is shown to be very accurate to calculate the photoionization term for a Gaussian emission source term with a half-width length of the order of 0.02 cm when the absorption coefficient of the gas is higher than or equal to 50 cm −1 . For steeper gradients of the source term, good agreement is obtained for higher values of the absorption coefficient. Furthermore, the computation time of the improved Eddington method is four orders of magnitude less than with the usual integral method. For streamer propagation in air at atmospheric pressure, the absorption coefficient is shown to be of the order of 130 cm −1 which validates the use of the improved Eddington approximation to calculate the photoionization term. Finally, two-dimensional calculations of a positive streamer discharge in air at atmospheric pressure in plane-plane geometry with the improved Eddington approximation are presented.

Interaction of Streamer Discharges in Air and Other Oxygen-Nitrogen Mixtures

“…The photon mediated ionization reaction in air and other nitrogen oxygen mixtures is experimentally not easily accessible, but forms a basic ingredient of the present theory of streamers in air [19,20,21,22,23]; all these simulations are based on the single experimental mea-surement of Penney and Hummert in 1970 [24]. Our theoretical results suggest that this reaction could be deduced from experiments on coalescence or repulsion of adjacent streamers as a function of pressure and gas composition.…”

“…We find that when varying gas composition and pressure, streamers can either repel or attract each other. The transition occurs in an unexpected manner, and is not simply determined by an ionization length.The photon mediated ionization reaction in air and other nitrogen oxygen mixtures is experimentally not easily accessible, but forms a basic ingredient of the present theory of streamers in air [19,20,21,22,23]; all these simulations are based on the single experimental mea- …”

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure

“…The source terms c S represent for each charge specie the chemical processes (like ionization, recombination, attachment, dissociative attachment, among others) as well as the secondary emission processes (like photo-ionisation and photo-emission from the walls (Kulikovsky, 2000, Hallac et al 2003, Segur et al 2006). The transport equations of charged particles are not only strongly coupled through the plasma reactivity but also through the potential and electric field equations.…”

Ion-impact secondary emission in negative corona with photoionization

“…18 Classical integral methods were utilized to calculate the photoionization source term and then an improved Eddington approximation is shown to be very accurate to calculate the photoionization term. [19][20][21][22] However, it is inevitable that these approaches are time consuming. Therefore, Bourdon has developed the improved model by more accurately accounting for the spectral dependence of the photoionization and a set of three Helmholtz differential equations were presented.…”