  Research in non-perturbative QED in strong-field backgrounds has gained
interest in recent years, due to advances in high-intensity laser technologies
that make extreme fields accessible in the laboratory. One key signature of
strong-field QED is non-linear Compton scattering in collisions between a
relativistic electron beam and a high-intensity laser pulse. In the vicinity of
strong fields, the electron gains a larger effective mass, which leads to a
laser-intensity-dependent shift of the kinematic Compton edge and the
appearance of higher-order harmonics in the energy spectrum. One of the
challenges of measuring the Compton energy spectrum in laser-electron-beam
collisions is the enormous flux of outgoing Compton-scattered electrons and
photons, ranging from $10^3$ to $10^9$ particles per collision. We present a
combined detector system for high-rate Compton electron detection in the
context of the planned LUXE experiment, consisting of a spatially segmented
gas-filled Cherenkov detector and a scintillator screen imaged by an optical
camera system. The detectors are placed in a forward dipole spectrometer to
resolve the electron energy spectrum. Finally, we discuss techniques to
reconstruct the non-linear Compton electron energy spectrum from the high-rate
electron detection system and to extract the features of non-perturbative QED
from the spectrum.
