Scaling laws of design parameters for plasma wakefield accelerators

Simple scaling laws for the design parameters of plasma wakefield accelerators were obtained using a theoretical model, which were confirmed via particle simulation studies. It was found that the acceleration length was given by Δx=0.804λp/(1−βg), where λp is the plasma wavelength and βgc the propagation velocity of the ion cavity. The acceleration energy can also be given by ΔE=(γm−1)mc²=2.645mc²/(1−βg), where m is the electron rest mass. As expected, the acceleration length and energy increase drastically as βg approached unity. These simple scaling laws can be very instrumental in the design of better-performing plasma wakefield accelerators.