# Characteristics of Photon Beam and Preservation of Coherence in Fourth-Generation Light Sources
## 3 PLS-II and Korea-4 GSR  
This analysis uses parameters (Table 2) of PLS-II [17] to represent 3 GSRs, and of Korea-4 GSR [18] to represent 4 GSRs, to estimate the improvement in coherence in 4 GSRs and compare the characteristics of photon beams of 3 GSRs to those of 4 GSRs. The machine characteristics of PLS-II and Korea-4 GSR will be introduced in this section and the results of the investigation of the coherence and characteristics of photon beams will be described in the next section. The PLS-II lattice has a gradient dipole double-bend achromat structure with 12 super-periods. Each of the 12 super-periods contains two gradient dipole magnets equipped with a FODO cell, which is a lattice period composed of a focusing (F) and a defocusing (D) quadrupole with a drift space (O) arrangement. The critical photon energy from bending magnets is 8.97 keV. The lattice provides a 6.88 m and a 3.69 m straight section per cell for installation of insertion devices. To reduce the beam emittance, a horizontal dispersion of 0.25 m is considered in the long straight section, in which RF cavities are installed. The lattice functions (Figure 3) for the PLS-II illustrate how a compact lattice can be realized to accommodate twenty insertion devices along the 280 m circumference. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Project** & **Energy** & **Emittance** & **Ener. Spr.** & **Beta x/y (m)** & **Reverse Bends** & **ID Source** \\  & **(GeV)** & **(pm)** & **(10\({}^{-4}\))** & **@ Source Point** & **Point Move** \\ \hline ALS-U & 2.0 & 108 & 9.8 & 2.0/2.8 & yes & No \\ ELECTTRA 2 & 2.4 & 212 & 9.3 & 5.7/1.6 & yes & No \\ SLS-II & 2.7 & 157 & 12.0 & 2.5/1.3 & yes & \textless{}70 mm \\ SOLEIL-U & 2.75 & 81 & 9.0 & 1.3/1.3 & yes & \textless{}100 mm \\ SIRIUS & 3 & 250 & 8.5 & 1.5/1.5 & no & n/a \\ Diamond-II & 3.5 & 136 & 9.0 & 6.0/2.5 & yes & No \\ APS-U & 6 & 42 & 13.5 & 4.9/1.9 & yes & No \\ ESRF-EBS & 6 & 135 & 9.3 & 6.9/2.6 & no & No \\ HEPS & 6 & \textless{}60 (35) & 10 & 2.6/2.3 & yes & n/a \\ PETRA-IV & 6 & 20 & 11.2 & 4.0/2.0 & TBD & yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Present ongoing 4 GSR projects [16]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **PLS-II** & **Korea-4 GSR** & **Unit** \\ \hline Beam energy & 3 & 4 & GeV \\ Beam current & 400 & 400 & mA \\ Lattice structure & DBA & Hybrid 7 BA & \\ Superperiods & 12 & 28 & \\ Natural hor. emittance & 5.8 & 0.058 & nm rad \\ Betatron tune & 15.28/9.18 & 67.44/23.17 & \\ RF frequency & 500 & 500 & MHz \\ rms energy spread & 0.1 & 0.1 & \% \\ rms bunch length & 20 & 13 & ps \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Major parameters of the Korea-4 GSR storage ring. The Korea-4 GSR lattice has a hybrid seven-bend achromat (H7 BA) type with a 58 pm horizontal emittance. The ring with an 800 m circumference is composed of 28 symmetric cells. As a result of experience with the PLS-II, the length of the straight section in the Korea 4 GSR is set to 6.5 m to accommodate two SCRF modules. The Korea-4 GSR lattice has a 2-T high field central dipole to create radiation that has a critical energy of 21 keV. The Korea-4 GSR uses ESRF-EBS and APS-U lattices. The dispersion was deliberately magnified between the first and second dipoles and between the sixth and seventh dipoles to make a dispersion bump. Chromatic sextupoles were located in this bump region to control the chromaticity with smaller strength. The betatron phase advances between the two dispersion bumps were adjusted to be \(\Delta\varphi_{\mathrm{x}}\)-3\(\pi\) in the horizontal plane and \(\Delta\varphi_{\mathrm{y}}\)-\(\pi\) in the vertical plane. Consequently, nonchromatic effects generated by the sextupoles are canceled out naturally. Five-step longitudinal gradient bends and reverse dipoles were introduced to further reduce natural emittance. Each super-period in the designed lattice for the Korea-4 GSR is composed of a total of 28 cells (Figure 4).