# Characteristics of Photon Beam and Preservation of Coherence in Fourth-Generation Light Sources
## 1 Introduction  
The synchrotron radiation (SR) from storage rings has a wide range of applications, including surface science [1], magnetic materials [2], materials chemistry [3], environmental sciences [4], protein crystallography [5], bio-microscopy [6], and chemical dynamics [7]. The SR from storage rings has many notable characteristics including high brilliance and flux, wavelength tunability, beam size tunability, (partially) coherent radiation, polarization, and time structure. In addition, the SR is very stable in energy, intensity, position, and size. The brightness of SR from storage rings has been increased by more than seven orders of magnitude from first-generation to third-generation storage rings (3 GSRs; Figure 1). To increase brightness, operation electron beam current has been increased to 400 mA or higher, and the undulator has been successfully operated to realize a dramatic increase in brightness. At the same time, efforts have been made to increase brightness by reducing electron-beam emittance.  
Figure 1: The progress of average brightness.  
The natural emittance in an electron storage ring is given by  
\[\varepsilon_{0}=C_{q}\gamma^{2}\frac{\langle H/\big{|}\rho^{3}\big{|}\rangle}{j_{x }\langle 1/\rho^{2}\rangle}, \tag{1}\]  
where \(C_{q}\cong 3.832\times 10^{-13}\) m, \(\gamma\) is the relativistic factor for a particle, \(H\cong 1/\rho^{2}\) (where \(\rho\) is the unit-cell bending angle) and \(j_{x}\) is the horizontal damping partition number [8; 9; 10]. The natural emittance scales with \(1/\rho^{3}\), so the multi-bend achromat lattice concept [11] enables an emittance reduction by one to two orders of magnitude compared with 3 GSRs.  
The Heisenberg uncertainty principle (\(\Delta\)x\(\Delta\)\(p_{x}\)\(\geq\)\(\hbar/2\)) sets a lower limit for the emittance of radiation. In storage rings, the altered relation for SR is given by  
\[\Delta\)x\(\Delta\)x\({}^{\prime}\)\(\geq\)\(\lambda/4 \tag{2}\]  
where \(\Delta\)x, \(\Delta\)x\({}^{\prime}\) and \(\lambda\) are the position, divergence and wavelength of SR, respectively. If both the horizontal and vertical emittance of the beam are less than \(\lambda/(4\pi)\), then the emitted radiation is fully coherent and the source is diffraction-limited. Here, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. In a storage ring, coherence is an important parameter in some experiments, such as photon correlation spectroscopy, X-ray holography, and imaging.  
Storage rings that exploit the multi-bend achromat (MBA) lattice concept are emerging as part of a worldwide push to move beyond the brightness and coherence reached by present 3 GSRs. The first MBA machine was MAX-IV, which began user operations in 2017. SIRIUS [12] and ESRF-EBS [13] are also currently in operation, and several new projects worldwide are exploiting these new concepts, either targeting new light sources such as HEPS, or replacing existing sources; upgrades of APS [14], ALS-U [15], SLS and PETRA-IV are already in progress, and those of DIAMOND, ELETTRA, SOLEIL and others are in a planning phase. The upgraded lattice designs for these facilities have reduced the beam emittance to a few hundred picometers, or even \(\leq\)100 pm. Therefore, 4 GSRs can produce coherent beams up to 1 keV X-ray and higher-coherent-fraction X-ray beams \(>\) 1 keV. In this paper, we address this new era of SR, introduce the parameter of Korea-4 GSR to represent 4 GSR, and describe the coherent characteristics of SR from 4 GSRs.