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. -- Highlights: ► Simple scaling laws for the design parameters of laser wakefield accelerators were obtained using a theoretical model. ► The scaling laws for acceleration length and acceleration energy were compared with particle-in-cell simulation results. ► The acceleration length and the energy increase drastically as βg approaches unity. ► These simple scaling laws can be very instrumental in the design of laser wakefield accelerators.