Statistical analysis of electron bunch longitudinal profile reconstructions using the Gerchberg-Saxton algorithm

Knowledge of longitudinal electron bunch profiles is vital to optimize the performance of plasma wakefield accelerators and x-ray free electron laser linacs. Because of their importance to these novel applications, noninvasive frequency domain techniques are often employed to reconstruct longitudinal bunch profiles from coherent synchrotron, transition, or undulator radiation measurements. In this paper, we detail several common reconstruction techniques involving the Kramers-Kronig phase relationship and Gerchberg-Saxton algorithm. Through statistical analysis, we draw general conclusions about the accuracy of these reconstruction techniques and the most suitable candidate for longitudinal bunch reconstruction from spectroscopic data.