Propagation of super-high-speed ionizing waves in long shielded tubes

A generalization of our old model that is based on the averaging of the two-dimensional equations over the cross section of the tube and on using a local relationship between an electrical potential and an electrical charge and that describes the propagation of the ionizing waves near to light velocity in long shielded tubes is given. The numerical modelling and the analytical self-similar solutions of the problem of high-speed ionizing wave (FIW) propagation in long shielded tubes are presented. Within the framework of the new self-similar solution obtained using analytical formulae it is possible to explain many experimental facts: dependence of the velocity of the high-speed ionizing waves on the amplitude of the high-voltage potential and on the building-up time of the high-voltage potential, on the effective permeability of surrounding matter and, mainly, on the pressures of gases. The analytical self-similar solution is obtained with an accuracy to only one constant, that is the ionization threshold field. This constant is inferred from fitting of the analytical dependence of the FIW's velocity on the gas pressure to the experimental results of one point for each gas. The results obtained correlate quantitatively with experimental results within the accuracy of the experiments. The influence of the condensed particles on the propagation of the high-speed ionizing waves is analysed, these results may be useful for the problem of high-speed ionizing wave propagation in specially produced channels in free atmosphere.