The use of a direct numerical solution of the radiative transfer equation to improve the simulation of streamer discharges

摘要

It is well known that the production of secondary electron by photoionisation and photoemission isvery often necessary to explain the propagation of streamers. Classical integral methods which aregenerally used to calculate the photoionisation source term are computationally very expensive. Itwas shown recently [1], that the treatment of photo ionisation using an improved Eddingtonapproximation, allows very fast and accurate calculations for absorption coefficient values higherthan 50 cm-1. The objective of this work is to employ a direct numerical method of solution of theradiative transfer equation. In this case, there is no limitation on the value of the absorptioncoefficient. The validity of this method is checked with a Gaussian emission source and for adouble-headed streamer in a two-dimensional axisymmetric cylindrical geometry, in air, at atmospheric pressure.