The self-focusing of a pulsed high-intensity electron beam in a gas declines in the intermediate pressure region owing to gas breakdown. The degree of the self-focusing of a beam from a Febetron 706 in monatomic gases increases by increasing the breakdown time (tB), which is defined as the time when the plasma conductivity becomes 10 mho/cm. Secondary electrons are consumed appreciably in polyatomic gases after tB through their reactions with ions and neutral molecules. Therefore, in such gases, the amount of the consumption must be estimated to analyze the self-focusing. For the estimation of the consumption, we must remark that the mean energy of secondary electrons is quite different between before and after tB because of the different strength of induced longitudinal electric field. As a result of the numerical analyses, we obtain the equation tB−tN =12/w (α−η) (tN is neutralization time, w is electron drift velocity, α is the first Townsend ionization coefficient, and η is the electron attachment coefficient). Since η is usually negligibly small before tB and tN is also negligibly small above a certain pressure, tB is approximately inversely proportional to wα. The tB in polyatomic gases, however, must be corrected for the consumption described above.