  The design of a primary electron beam facility at CERN is described. The
study has been carried out within the framework of the wider Physics Beyond
Colliders study. It re-enables the Super Proton Synchrotron (SPS) as an
electron accelerator, and leverages the development invested in Compact Linear
Collider (CLIC) technology for its injector and as an accelerator research and
development infrastructure. The facility would be relevant for several of the
key priorities in the 2020 update of the European Strategy for Particle
Physics, such as an electron-positron Higgs factory, accelerator R\&D, dark
sector physics, and neutrino physics. In addition, it could serve experiments
in nuclear physics. The electron beam delivered by this facility would provide
access to light dark matter production significantly beyond the targets
predicted by a thermal dark matter origin, and for natures of dark matter
particles that are not accessible by direct detection experiments. It would
also enable electro-nuclear measurements crucial for precise modelling the
energy dependence of neutrino-nucleus interactions, which is needed to
precisely measure neutrino oscillations as a function of energy. The
implementation of the facility is the natural next step in the development of
X-band high-gradient acceleration technology, a key technology for compact and
cost-effective electron/positron linacs. It would also become the only facility
with multi-GeV drive bunches and truly independent electron witness bunches for
plasma wakefield acceleration. A second phase capable to deliver positron
witness bunches would make it a complete facility for plasma wakefield collider
studies. [...]
