Statistical optics methods for generating, simulating, and characterising emission from relativistic electron beams

Abstract

Synchrotron radiation sources and free-electron lasers have revolutionised the study of matter and biological systems by providing unique combinations of radiation pulse characteristics. Although these two types of facilities differ fundamentally in terms of pulses time scales, coherence properties, and (peak) brilliance, each offers an exceptional mix of these features. The combination of coherence, short pulse duration, and high photon flux, characteristic of both types of sources, delivers unparalleled experimental capabilities across a wide range of photon energies. However, these advanced capabilities also introduce new challenges in both the characterisation and numerical modelling of this radiation. Improving our understanding of radiation diagnostics techniques and developing new simulation methods could pave the way for innovative approaches to enhance pulse properties.

I begin my thesis by exploring the potential for developing new theoretical models for describing partially coherent sources, with a particular focus on radiation from relativistic electron beams. To this end, I propose a set of numerically efficient algorithms designed to simulate individual statistical instances of the radiation field. These algorithms are highly versatile and efficient, capable of simulating radiation from a range of sources, from fully incoherent to partially coherent systems, including thermal sources, synchrotron radiation, and even free-electron laser radiation with complicated Wigner function distributions.

In particular, one of the developed algorithms offers a new perspective on synchrotron radiation. Building on this, I propose a method for measuring the coherence length of synchrotron radiation at linear accelerator facilities, such as the European XFEL, using a non-interferometric approach. By detecting radiation directly after monochromatization and employing auto-correlation analysis, the coherence length can be determined without the need for an interference scheme. This measurement also reveals that the monochromatized transverse distribution of synchrotron radiation consists of spikes. In practice, this method serves as a novel diagnostic tool for determining the transverse electron beam size at free-electron laser facilities, leveraging the van Cittert-Zernike theorem to relate the transverse coherence length to the electron beam size.

Next, I focus on the virtual source structure of undulator radiation from a single electron. Although undulator radiation in resonance is typically considered to have a single waist at the virtual source position, closer inspection reveals finer details. There are two characteristic lengths associated with undulator radiation: the overall device length and the period length. These scales correspond to the radiation formation lengths and are directly related to the diffraction size of the radiation. In this part, I examine the less-studied peculiarities of the virtual source associated with the undulator period length.

Finally, I describe a numerical code for simulating synchrotron radiation generation in the presence of waveguide effects. These effects typically arise in the infrared frequency range and are influenced by the metallic elements of the beamlines, which are always present. I conducted various cross-checks of the developed code, comparing it with the Synchrotron Radiation Workshop code for free-space scenarios and with analytical expressions for practical cases involving circular waveguides. This research contributes to the development of radiation beamlines for THz pump -- X-ray probe experiments at free-electron laser facilities. The final part of the thesis includes numerical calculations for an iris waveguide designed for THz radiation transport through the beamlines of free-electron lasers.