# Lattice Design of an Intermediate-Energy Electron Storage Ring Dedicated to Materials Research
## 2 Linear Optics Design  
In order to achieve a low natural emittance while maintaining a high straight section ratio, we adopted the double double-bend achromat (DDBA) lattice [26], which has four bending magnets per cell and provides an additional straight section in the middle of the arc. The storage ring has an energy of 3 GeV and a circumference of 288 m, with a total of 12 cells. Each cell contains a long straight section (LSS) of 6.20 m and a short  
Figure 2: Schematic diagram of the MBA lattice structure (assuming M = 7, M represents the number of bending magnets in one cell) and dispersion function (green line) trend of (**a**) hybrid 7 BA and (**b**) HOA 7 BA. The blue rectangles in the figure represent the dipoles, the red polygons represent quadrupoles, and the green polygons represent sextupoles.  
straight section (SSS) of 1.86 m, allowing for the accommodation of more insertion devices (IDs). A standard 24 m cell contains main magnetic elements including four dipoles, ten quadrupoles and ten sextupoles. Six sextupoles are located within the dispersion bump for chromaticity correction and four harmonic sextupoles are located in the dispersion-free region to optimize its nonlinear performance. Figure 3 shows the linear optics of the DDBA cell, and the main parameters of the storage ring are presented in Table 1.  
There is only one family of combined dipole in the storage ring, with a dipole magnetic field of 0.87 T and a combined quadrupole field gradient of \(-5.27\) T/m. There are five families of quadrupoles used for focusing, with the maximum quadrupole strength being 24.33 T/m. The maximum sextupoles strength is 824.57 T/m\({}^{2}\). The specifications of these magnets can be found in Table 2. The magnetic field strengths of these magnets are almost at the level of third-generation light source, and the requirements for the bore diameter of  
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Beam energy & 3 GeV \\ Circumference & 288 m \\ Lattice type & 12 \(\times\) DBA \\ Tunes & 21.17, 7.23 \\ Horizontal emittance & 2.57 nm rad \\ Energy spread & 8.64 \(\times\) 10\({}^{-4}\) \\ Natural chromaticity & \(-\)51.60, \(-\)30.45 \\ Corrected chromaticity & 1.0, 1.0 \\ Momentum compaction factor & 8.23 \(\times\) 10\({}^{-4}\) \\ Energy loss per turn & 0.625 MeV \\ Damping partition numbers & 1.46, 1.1, 54 \\ Damping time & 6.33 ms, 9.22 ms, 5.97 ms \\ Long straight section & 12 \(\times\) 6.20 m \\ Short straight section & 12 \(\times\) 1.86 m \\ Twiss at LSS (betax, betay, etax) & 18.0 m, 3.20 m, 0 m \\ Twiss at SSS (betax, betay, etax) & 3.41 m, 2.85 m, 0.065 m \\ RF frequency & 499.654 MHz \\ Harmonic number & 480 \\ RF voltage & 4.0 MV \\ RF bucket height & 4.06\% \\ RMS bunch length & 3.58 mm \\ \hline \end{tabular}
\end{table}
Table 1: Ring parameters.  
Figure 3: Optical functions of one DDBA cell.  
the magnets are much less stringent than for the DLSR. Therefore, the vacuum chamber of this DDBA ring can be made very large, which is conducive to reducing the impedance and provides very favorable conditions for the storage ring to achieve a high beam current, while the straight section of this DDBA lattice occupies a relatively high ratio, which facilitates the installation of a larger number of IDs.