Optimization of transformer ratio and beam loading in plasma wakefield accelerator(PWFA) with structure-based algorithm

The PWFA has emerged as a promising candidate for the accelerator technology for a future linear collider and/or light source. For the linear collider application, it is essential that the energy transfer from the drive beam to the wake and from the wake to the trailing beam be efficient, and the energy spread of trailing bunch should be kept low. One way to achieve this is to use longitudinally-shaped bunches. In the linear regime there is an analytical formalism to determine the optimal shapes. However, in the nonlinear blowout regime the theoretical framework is not as well defined. We thus utilize an optimization tool developed at ANL, to efficiently find optimized drive beam and witness beam profiles for PWFA. We parametrize the beam currents as a piecewise-linear longitudinal profile and define optimization objectives for the energy spread. The algorithm converges quickly, and it finds witness beam shapes similar to those calculated by a recent multi-sheath model for nonlinear wakefields. We also obtain optimized drive beam profiles that give high transformer ratios with constraint of fixing the total charge that qualitatively agree with predictions from W. Lu et al.