Accelerator Physics Challenges towards a Plasma Accelerator with Usable Beam Quality

Enormous progress in compact plasma accelerators has been demonstrated over the recent years in various experiments. These experiments rely on high power pulsed lasers or short electron bunches to excite ultrastrong wakefields in plasmas. Accelerating gradients have reached several 10 GV/m up to 100 GV/m and the achieved gain in electron energy ranges from several GeV to 42 GeV for the different methods. The principle and potential of plasma accelerators have been proven and its performance is steadily improving. Particle accelerators are powerful tools that are ultimately justified by their applications in science, medicine or industry. The demonstration of useable beam quality remains to be achieved for plasma accelerators. The accelerator physics challenges to arrive at this goal are analysed and discussed.