Description
Plasma-based accelerators offer high accelerating gradients and scalability through staging or long plasma sources, which makes them possible candidates for future accelerator and collider concepts. Proton-driven accelerators in particular have the potential to bring particles to high energy in a single stage. In the quasilinear regime - where the plasma wake is only partially evacuated - a witness bunch of electrons drives a self-blowout, which acts to preserve the emittance of the portion of the witness within the cavitated region. In the case of a misalignment between the driver and witness, this behaviour can persist, but its effectiveness is reduced. Here we study transverse witness dynamics in this regime, and develop analytical models to describe the witness motion. We find that the degree of emittance preservation can be characterised by a single function of the witness parameters and offset. Particle in cell simulations using the AWAKE Run 2c baseline parameters show excellent agreement with models developed. This work allows alignment constraints to be set both for the AWAKE experiment and other wakefield acceleration schemes operating in the quasilinear regime.