Statistical and numerical analysis of secondary electron avalanches with ion-induced electron emission in air

Statistical and numerical analyses of secondary electron avalanches with ion-induced electron emission and multielectron initiation in air is carried out. Statistical analysis is based on the negative binomial distribution (NBD) and its mixtures and the mean number of electrons in avalanches is determined. The development of successive secondary electron avalanches for ion-induced electron emission from the cathode (${\gamma }_i$ process) in air is simulated by the fluid model. The statistics of secondary avalanches is described by a mixture of NBDs, and it is found that the mixing weights $a_j$ are positively correlated with ${\mu }^j$ for the contribution of secondary avalanche of $j$th generation, where $\mu ={\gamma }_i[\exp (\alpha d)-1]$ is the avalanche regeneration factor. Gaussian continual approximations for the discrete negative binomial distribution are also applied to the experimental data and the mixing weights are determined. Our models can explain a deviation of the electron number distribution from exponential due to influence of ion feedback processes.