  We consider interaction of a high-energy electron beam with two
counterpropagating femtosecond laser pulses. Nonlinear Compton scattering and
electron-positron pair production by the emitted photons result in development
of an electromagnetic "shower-type" cascade, which however collapses rather
quickly due to energy losses by secondary particles. Nevertheless, the laser
field accelerates the low-energy electrons and positrons trapped in the focal
region, thus giving rise to development of electromagnetic cascade of another
type ("avalanche-type"). This effect of cascade collapse and revival can be
observed at the electron beam energy of the order of several GeV and intensity
of the colliding laser pulses of the level of $10^{24}$W/cm$^2$. This means
that it can be readily observed at the novel laser facilities which are either
planned for the nearest future, or are already under construction. The proposed
experimental setup provides the most realistic and promissory way to observe
the "avalanche-type" cascades.
