Collapse and revival of electromagnetic cascades in focused intense laser pulses

We consider interaction of a high-energy electron beam with superstrong 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 slowed down electrons and positrons, 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 laser pulses intensity ∼10²⁴ W/cm². 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.