# Coherent modes of X-ray beams emitted by undulators in new storage rings

## TL;DR

This paper analyzes the coherence properties of X-ray beams emitted by undulators in advanced storage rings, using a method based on the cross spectral density to understand their coherent modes and propagation.

## Contribution

It introduces a novel method for analyzing and propagating the coherence properties of synchrotron radiation in new storage ring configurations.

## Key findings

- Coherent modes can be decomposed using the cross spectral density.
- The method allows for statistical analysis of beam coherence.
- Coherence properties are fully described by eigenvalues and modes.

## Abstract

Synchrotron radiation emitted by electrons passing through an undulator placed in a storage ring is decomposed in coherent modes. The case of ultimate storage rings where the electron emittance is comparable to the emittance of the photon fan is analyzed by means of the cross spectral density and the coherent mode spectrum. The proposed method permits naturally the statistical analysis and propagation of the cross spectral density along the beamline optics. The coherence properties of the X-ray beam at any point of the beamline are completely given in terms of the eigenvalues and coherent modes of the cross spectral density.