Collider design issues based on proton-driven plasma wakefield acceleration

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. It therefore paves the way towards a compact future collider design using the proton beams from existing high-energy proton machines, e.g. Tevatron or the LHC. This paper addresses some key issues in designing a compact electron-positron linear collider and an electron-proton collider based on the existing CERN accelerator infrastructure.