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

TL;DR

This paper evaluates various noninvasive frequency domain methods, including Gerchberg-Saxton, for reconstructing electron bunch profiles, providing insights into their accuracy and suitability for plasma accelerators and free electron lasers.

Contribution

It offers a comprehensive statistical comparison of reconstruction techniques, highlighting the effectiveness of the Gerchberg-Saxton algorithm for longitudinal profile recovery.

Findings

Gerchberg-Saxton algorithm shows high accuracy in profile reconstruction

Kramers-Kronig based methods are effective but less precise

Statistical analysis guides the choice of reconstruction technique

Abstract

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.