  Recent simulations have shown that a high-energy proton bunch can excite
strong plasma wakefields and accelerate a bunch of electrons to the energy
frontier in a single stage of acceleration. This scheme could lead to a future
$ep$ collider using the LHC for the proton beam and a compact electron
accelerator of length 170 m, producing electrons of energy up to 100 GeV. The
parameters of such a collider are discussed as well as conceptual layouts
within the CERN accelerator complex. The physics of plasma wakefield
acceleration will also be introduced, with the AWAKE experiment, a proof of
principle demonstration of proton-driven plasma wakefield acceleration, briefly
reviewed, as well as the physics possibilities of such an $ep$ collider.
