  We show that an all-optical configuration of the laser-electron collision in
the $\lambda^{3}$ configuration based on 10 PW-class lasers presents a viable
platform for reaching the range of parameters where a perturbative QED in
strong external electromagnetic field breaks. This case is contingently
referred to as a case of the nonperturbative QED; and this range of parameters
is the intriguing goal from an experimental point of view because of a possible
manifestation of a new physics of the interaction of a highly radiating
particle with a strong electromagnetic field. We show that the strong field
region can be reached by the electrons having the initial energy higher than 50
GeV. Our theoretical considerations are in agreement with three-dimensional
particle-in-cell simulations. While increasing of the electron energy raises
the number of electrons experiencing the strong field region, the observable
signature of photon emission radiative correction in the strong field is
expected to fade out when the electron energy surpasses the optimal value. This
threshold of electron energy is identified and the parameters for achieving the
nonperturbative limit of QED are provided.
