Reconstructions from randomly generated longitudinal electron bunch profiles with Gaussian envelopes using the Gerchberg–Saxton algorithm

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