Transformer ratio saturation in a beam-driven wakefield accelerator

We show that for beam-driven wakefield acceleration, the linearly ramped, equally spaced train of bunches typically considered to optimise the transformer ratio only works for flat-top bunches. Through theory and simulation, we explain that this behaviour is due to the unique properties of the plasma response to a flat-top density profile. Calculations of the optimal scaling for a train of Gaussian bunches show diminishing returns with increasing bunch number, tending towards saturation. For a periodic bunch train, a transformer ratio of 23 was achieved for 50 bunches, rising to 40 for a fully optimised beam.