The aim of current investigation is to evaluate by means of analytic and kinetic modeling the characteristics of the microwave (MW) breakdown filament. Separate MW breakdown domain passes through several phases in its development and as a result of it the discharge plasmoid is not homogeneous, but have an internal structure. Inside relatively uniform bulk main domain of plasmoid, there may appear very thin hot channel, or filament. An attempt is made to construct analytic solution for this stage which is characterized by interconnection of electrodynamic, gas dynamic, kinetic processes and is strongly non-linear. The finite-time explosive analytic solution, as well as characteristic time of the process is obtained. The solution describes collapse-like creation of channel(s) with high electron and energy concentration. Also optical emission spectra obtained from MW discharge in supersonic flows of air and nitrogen has shown that along with the second positive nitrogen system bands, the first negative system bands of the positive nitrogen molecule ion are definitely observed. Gas temperatures defined by processing of the rotational spectra bands of each system turned out to differ strongly. This fact let us suppose that light emission from nitrogen molecules and ions is coming from different spatial domains - the second positive nitrogen system is lightening from the relatively cold bulk hallo, whereas the first negative - from the hot breakdown filament. Comparison of the results of kinetic modeling with experimental ones let us determine the minimal electron concentration in the filament as 10¹⁶ cm^-3 under 70Torr air pressure and its dimension as less than 10^-2 cm.