Toward a plasma-based accelerator at high beam energy with high beam charge and high beam quality

From plasma-wakefield acceleration as a physics experiment toward a plasma-based accelerator as a user facility, the beam physics issues remaining to be solved are still numerous. Providing beams with high energy, charge, and quality simultaneously, not only within the plasma but also at the user doorstep itself, is the main concern. Despite its tremendous efficiency in particle acceleration, the wakefield displays a complex 3D profile which, associated to the beam-loading field induced by the accelerated beam itself, makes the acceleration of high charge to high energy often incompatible with high beam quality. Beam extraction from the plasma without quality degradation for a transfer either to the next plasma stage or to the user application is another difficulty to consider. This article presents the substantial studies carried out and the different innovative methods employed for tackling all these different issues. Efforts focused on achieving the challenging beam parameters targeted by the EuPRAXIA accelerator facility project. The lessons learned at the end of these in-depth simulations and optimizations are highlighted. The sensitivity to different error sources is also estimated to point out the critical components of such an accelerator. Finally, the needs in terms of laser and plasma parameters are provided.