Plasma photocathode wakefield acceleration combines energy gains of tens of GeV m^-1 with generation of ultralow emittance electron bunches, and opens a path towards 5D-brightness orders of magnitude larger than state-of-the-art. This holds great promise for compact accelerator building blocks and advanced light sources. However, an intrinsic by-product of the enormous electric field gradients inherent to plasma accelerators is substantial correlated energy spread-an obstacle for key applications such as free-electron-lasers. Here we show that by releasing an additional tailored escort electron beam at a later phase of the acceleration, when the witness bunch is relativistically stable, the plasma wave can be locally overloaded without compromising the witness bunch normalized emittance. This reverses the effective accelerating gradient, and counter-rotates the accumulated negative longitudinal phase space chirp of the witness bunch. Thereby, the energy spread is reduced by an order of magnitude, thus enabling the production of ultrahigh 6D-brightness beams.

Synchronized, independently tunable and focused $\mu$J-class laser pulses are used to release multiple electron populations via photo-ionization inside an electron-beam driven plasma wave. By varying the laser foci in the laboratory frame and the position of the underdense photocathodes in the co-moving frame, the delays between the produced bunches and their energies are adjusted. The resulting multibunches have ultra-high quality and brightness, allowing for hitherto impossible bunch configurations such as spatially overlapping bunch populations with strictly separated energies, which opens up a new regime for light sources such as free-electron-lasers.

The 'Trojan Horse' underdense plasma photocathode scheme applied to electron beam-driven plasma wakefield acceleration has opened up a path which promises high controllability and tunability and to reach extremely good quality as regards emittance and five-dimensional beam brightness. This combination has the potential to improve the state-of-the-art in accelerator technology significantly. In this paper, we review the basic concepts of the Trojan Horse scheme and present advanced methods for tailoring both the injector laser pulses and the witness electron bunches and combine them with the Trojan Horse scheme. These new approaches will further enhance the beam qualities, such as transverse emittance and longitudinal energy spread, and may allow, for the first time, to produce ultrahigh six-dimensional brightness electron bunches, which is a necessary requirement for driving advanced radiation sources. This article is part of the Theo Murphy meeting issue 'Directions in particle beam-driven plasma wakefield acceleration'.

This is the working summary of the Accelerator Science working group of the Computing Frontier of the Snowmass meeting 2013. It summarizes the computing requirements to support accelerator technology in both Energy and Intensity Frontiers.