Effects of energy spread on brightness and coherence of undulator sources

Abstract

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free-electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single-electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction-limited rings with ultralow emittance coming on-line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.

Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

“…In a recent paper by Geloni et al (2018), energy spread effects on brightness and coherence were carefully analysed using directly equation (24) with an account of energy spread effects. For the far-field distribution of the electric field emitted by an electron with the energy deviating from the resonant photon energy of the undulator radiation harmonic, the following expression was used in equation (24)…”

“…Strictly speaking, this expression is valid only for a Gaussian approximation of the electron-beam source parameters and natural single electron radiation with emittance values " ph x;y defined in equation (28) (see, for discussion, Geloni et al, 2018). We will introduce the coherent fraction as…”

“…It was first outlined by Tanaka & Kitamura (2009) that energy spread effects may affect the brightness of the X-ray storage rings. In a recent paper by Geloni et al (2018), energy spread effects on brightness and coherence were carefully analysed for the low-emittance storage rings using an analytical approach. As a result of this analysis, it was shown that the brightness of diffraction-limited sources with small but finite emittance only slightly depends on the energy spread effects; the same is valid for the coherence function centred at the optical axis of the undulator with stronger effects at off-axis values.…”

Undulator radiation brightness and coherence near the diffraction limit

“…The aim of this paper is to investigate how closely one can approach the diffraction limit when the effects of electron beam emittance and energy spread are included and also to explore the validity of the commonly used Gaussian approximation (GA). We will also shed further light on the recently highlighted "paradox" that energy spread by itself does not influence the peak brightness but does degrade the transverse coherence off axis [4].…”

“…In particular, as the emittance becomes very small, it becomes increasingly important to understand the influence of the energy spread of the electron beam [4], which has been ignored in many of the early studies of brightness and coherence.…”