Micro-discharges are specific cold filamentary plasma that are generated at atmospheric pressure between electrodes stressed by high voltage. As cold plasma or non-thermal plasma, we suggest that the energy of electrons inside the conductive plasma is much higher than the energy of the heaviest particles (molecules and ions). In such kind of plasma, the temperature of the gas remains cold (i.e. more or less equal to the ambient temperature) unlike in the field of thermal plasmas where the gas temperature can reach some thousands of Kelvin. This high level of temperature can be measured for example in plasma torch or in lightning. The conductive channels of micro-discharges are very thin. Their diameters are estimated around some tens of micrometers. This specificity explains their name: micro-discharge. Another of their characteristic is their very fast development. In fact, micro-discharges propagate at velocity that can attain some tens of millimetres per nanosecond i.e. some 107 cm.s-1. This very fast velocity is due to the propagation of space charge dominated streamer heads. The space charge inside the streamer head creates a very high electric field in which the electrons are accelerated like in an electron gun. These electrons interact with the gas and create mainly ions and radicals. In fact, the energy distribution of electrons inside streamer heads favours the chemical electron-molecule reactions rather than the elastic electron-molecule collisions. Therefore, micro-discharges are mainly used in order to activate chemical reactions either in the gas volume or on a surface (Penetrante & Schultheis, 1993, Urashima &Chang, 2010, Foest et al. 2005, Clement, 2001). Several designs of plasma reactors are able to generate micro-discharges. The most convenient and the well known is probably the corona discharge reactor (Loeb, 1961&1965, Winands, 2006, Ono & Oda a, 2004, van Veldhuizen & Rutgers, 2002, Briels et al., 2006 ). Corona micro-discharges reactor has at least two asymmetric electrodes i.e. with one of them presenting a low curvature that introduces a pin effect where the geometric electric field is enhanced. The corona micro-discharges are initiated from this high geometric field area. Some samples of corona reactor geometries are shown in Fig. 1. The transient character and the small dimensions make some micro-discharges parameters, like charged and radical densities, electron energy or electric field strength, difficult to be accessible to measurements. Therefore, the complete simulation of the discharge reactor, in complement to experimental study can lead to a better understanding of the physico-