Adiabatic self-matching of witness bunches in a plasma wakefield accelerator

\nPlasma wakefield acceleration offers high accelerating gradients, making it an interesting candidate for future colliders. However, the large accelerating fields are coupled with large focusing fields, leading to accelerated bunches with extremely high charge density. In these regimes, the electron witness bunch can significantly perturb the plasma ion density. The resulting non-linear focusing field can lead to emittance growth, reducing the beam quality. In this work, we show that by accelerating in a single stage, as would be possible with a high-energy proton driver, the witness bunch can adiabatically match to the focusing fields, greatly reducing the emittance growth. This suggests that many of the constraints for electron acceleration in plasma can be avoided.\n