Transverse Tolerances of a Multi-Stage Plasma Wakefield Accelerator

Plasma wakefield acceleration (PWFA) provides GeV/m-scale accelerating fields, ideal for applications such as a future linear collider. However, strong focusing fields imply that a transversely offset beam with an energy spread will experience emittance growth from the energy dependent betatron oscillation. We develop an analytic model for estimating tolerances from this effect, as well as an effective simplified simulation tool in Elegant. Estimations for a proposed 1 TeV PWFA linear collider scheme indicate tight tolerances of order 40 nm and 1 μrad in position and angle respectively.