## 6 An Equivalent Gas Conductivity for RIC Phenomenon
The lower slope trend was considered to be representative of the average behavior of the gas, while the higher slope trend is considered as a deviation from the average, which is a reasonable assumption when \(S\) is not too high since regions of the computational domain where ions' concentration is considerably higher than the average are kept to a small percentage of the total gas domain. From this procedure, a relation between \(\sigma_{G}\) and \(S\) can be obtained as follows:  
\[\sigma_{G}=\kappa S+\sigma_{0} \tag{18}\]  
where \(\sigma_{0}\) is the conductivity of the non-irradiated gas (set to \(10^{-19}\) S/m), and a constant \(\kappa\) [Sm\({}^{2}\)s] was found by this process to describe this linear dependence accurately. It is worth explaining that this behavior was found to be independent of the model geometry. Additionally, during the data analysis conducted to derive the given relation, a phenomenon was identified that helps explain the discrepancy between the results obtained from this relation and those from DDR simulations at high values of \(S\). Indeed, as the generation rate grows, data points start to cluster not only around the line described by Equation (18), but the emergence of points populations following alternative regimes, i.e., clustering around straight lines with different slopes, can be observed. This is explained by the fact that ions are not uniformly spread inside the gas but concentrate in specific regions due to the effect of the electric field. Then, if the concentration of ions is low enough at low generation rates to allow an average description of gas conductivity via a single value, the presence of regions with a high ion concentration at high radiation levels, following a different \(J\)-\(E\) relation with respect to medium concentration regions, is not negligible anymore. Thus, the observed alternative conductivity regimes become important, preventing the application of a single value of \(\sigma_{G}\) to all the computational domains. Considering this aspect and the range of applicability of the proposed method, data obtained from the described simulations seem to suggest its validity for \(S\), ranging from \(10^{7}\) to \(10^{9}\) m\({}^{-3}\) s\({}^{-1}\). However, it is important to notice that this range could be strongly linked to the amount of gas taken into account during the simulation and to the specific geometry considered, since the presence of a larger volume available for ion motion can lower their tendency to cluster inside large high-concentration regions (where the proposed linear model is not a good approximation of gas conductivity due to the phenomena described above), thus keeping the majority of the computational domain to average concentration level and allowing an accurate application of the linear dependence of conductivity to \(S\). Nevertheless, the existence of several regions, identified by their ionic concentration, where conductivity follows different specific trends, shows the need to obtain a relation for gas conductivity characterized by an explicit dependence on both ion-pair generation rate and electric field intensity (thus indirectly taking into account ions' concentration levels), which is left to future work.