  The interaction of charged particles and photons with intense electromagnetic
fields gives rise to multi-photon Compton and Breit-Wheeler processes. These
are usually described in the framework of the external field approximation,
where the electromagnetic field is assumed to have infinite energy. However,
the multi-photon nature of these processes implies the absorption of a
significant number of photons, which scales as the external field amplitude
cubed. As a result, the interaction of a highly charged electron bunch with an
intense laser pulse can lead to significant depletion of the laser pulse
energy, thus rendering the external field approximation invalid. We provide
relevant estimates for this depletion and find it to become important in the
interaction between fields of amplitude $a_0 \sim 10^3$ and electron bunches
with charges of the order of 10 nC.
