  This Letter of Intent describes LUXE (Laser Und XFEL Experiment), an
experiment that aims to use the high-quality and high-energy electron beam of
the European XFEL and a powerful laser. The scientific objective of the
experiment is to study quantum electrodynamics processes in the regime of
strong fields. High-energy electrons, accelerated by the European XFEL linear
accelerator, and high-energy photons, produced via Bremsstrahlung of those beam
electrons, colliding with a laser beam shall experience an electric field up to
three times larger than the Schwinger critical field (the field at which the
vacuum itself is expected to become unstable and spark with spontaneous
creation of electron-positron pairs) and access a new regime of quantum
physics. The processes to be investigated, which include nonlinear Compton
scattering and nonlinear Breit-Wheeler pair production, are relevant to a
variety of phenomena in Nature, e.g. in the areas of astrophysics and collider
physics and complement recent results in atomic physics. The setup requires in
particular the extraction of a minute fraction of the electron bunches from the
European XFEL accelerator, the installation of a powerful laser with
sophisticated diagnostics, and an array of precision detectors optimised to
measure electrons, positrons and photons. Physics sensitivity projections based
on simulations are also provided.
