Injection tolerances for AWAKE Run 2c

Particle acceleration in a quasilinear plasma wake provides access to high acceleration gradients while avoiding self-trapping of the background electrons. However, the plasma response to the externally injected witness bunch leads to a variation of the focussing fields along the bunch length, which can lead to a emittance growth. In order to investigate the impact of this emittance growth on the overall beam quality, we develop a single figure of merit based on a potential high-energy application for the AWAKE experiment at CERN. We show that the development of such a figure of merit naturally gives rise to constraints on both the tunability and stability of the initial witness bunch parameters. It is further shown that the unique physics of the quasilinear wake gives rise to broad tolerances for the witness bunch radius at the injection point, as the plasma wakefields self-match to the witness bunch.