Electromagnetic cascades and the depletion of intense fields.*

The interaction of electrons, positrons, and photons with intense electromagnetic fields gives rise to multi-photon Compton and Breit-Wheeler processes.~It is shown that electrons and/or positrons undergo a cascade-type process involving multiple~emissions of photons. These photons can consequently convert into electron-positron pairs. As a result charged~particles quickly lose their energy developing an exponentially decaying energy distribution. Moreover the multi-photon nature of~Compton and Breit-Wheeler processes implies the absorption of a significant number of photons. As a result, the interaction of a highly charged electron bunch with an intense laser pulse can lead to a significant depletion of the laser pulse energy, thus rendering the external field approximation invalid. The relevance of these results to the proposed BELLA-i beamline at BELLA center at LBNL is discussed.