Preamble

Candidate Injector Design for the Southern Advanced Photon Source Based on Linac and Booster

Liang-Sheng Huang,¹,²,† Yan-Liang Han,¹,²,‡ Wei-Hang Liu,¹,² Jian-Liang Chen,¹,² Sheng Wang,¹,² Yi Jiao,¹,§ Xiao Li,¹,²,¶ and Jia-Xin Chen¹,²
¹Key Laboratory of Particle Acceleration Physics and Technology, Institute of High Energy Physics, CAS, Beijing, 100049, China
²Spallation Neutron Source Science Center, Dongguan, 523803, China

The Southern Advanced Photon Source (SAPS) is a diffraction-limited synchrotron light source currently under design that employs longitudinal injection as its primary injection scheme. This injection approach requires the injected beam to have a short bunch length and low emittance. The preferred injector should offer high stability and low cost, which has led to the development of a booster synchrotron-based injector. The proposed injector includes a 250 MeV linac, a booster synchrotron that ramps the beam energy to 3.5 GeV, and two beam transport lines to ensure efficient beam delivery and preservation of beam quality. The linac utilizes a thermionic high-voltage DC gun for reliable operation and features a bunching system with an advanced focusing system to preserve emittance. To meet the injection requirements of SAPS, a comprehensive design for the booster has been conducted. The booster synchrotron employs a three-fold lattice structure incorporating modified theoretical minimum emittance cells with a small momentum compaction factor and high RF voltage to achieve an emittance of 3.98 nm·rad and a bunch length of 4.8 mm. The injector has the potential to deliver high charge, reducing the injection period of the storage ring to less than one minute. Simulations demonstrate expected performance with a transmission efficiency of about 90%, confirming its capability to meet the injection requirements of the SAPS storage ring. This design offers a stable and efficient solution for SAPS.

Keywords: Southern Advanced Photon Source, longitudinal injection, booster synchrotron, emittance, bunch length

Introduction

Diffraction-limited storage rings (DLSRs) represent a new generation of storage-ring-based light sources designed to deliver high-brightness synchrotron radiation by minimizing beam emittance to approach the diffraction limit of X-rays. MAX-IV [1, 2] is the first diffraction-limited light source, and subsequently many DLSRs [3–15] have been launched around the world. To achieve ultra-low beam emittance within a reasonable circumference, DLSR designs typically incorporate a multi-bend achromat (MBA) [16] lattice with a small dynamic aperture. Alternative injection schemes [17–26] with relaxed dynamic aperture requirements have been extensively explored, particularly novel on-axis injection schemes [19–26]. These approaches require a dynamic aperture only a few times larger than the injected beam size. One such on-axis injection method is swap-out injection [19], which has been implemented by several DLSRs [20–22]. Another on-axis injection option is longitudinal injection, where the bunch is injected on-axis transversely but with an energy and/or phase deviation relative to the synchronous particle. Longitudinal injection requires superior beam dynamics performance to accommodate the oscillations of the injected beam, including low emittance and very short bunch lengths.

The horizontal natural emittance of an electron beam in a ring can be written as [27]
$$\epsilon = C_q F(\text{type}) \frac{\gamma^2 J_x N^3}{}$$
where $C_q = 3.83 \times 10^{-13}$ m, $\gamma$ is the Lorentz factor with speed of light $c$, $J_x$ is the damping partition number in the horizontal plane, and $F(\text{type})$ is a dimensionless quantity that depends on the lattice type. For example, $F$ is $1/(12\sqrt{15})$ for a theoretical minimum emittance (TME) unit cell. $N_b$ denotes the number of bending magnets, and increasing $N_b$ effectively decreases emittance. To a certain extent, increasing $N_b$ is equivalent to enlarging the ring circumference. The root mean square (RMS) bunch length $\sigma_L$ is given [28] as
$$\sigma_L = \sqrt{\frac{2\pi h e V}{E |\cos \phi_s|}}$$
where $\sigma_E$ is RMS energy spread, $e$ is the electric charge, $\alpha_p$ is the momentum compaction factor with ring circumference $C$, $h$ is the harmonic number, $V$ is the cavity voltage, and $\phi_s$ is the synchronous phase. It is clear that increasing the voltage, reducing the circumference, and lowering $\alpha_p$ can decrease bunch length. Considering both bunch length and emittance, reducing $\alpha_p$ becomes the primary optimization option in lattice design.

The demand for a high-performance synchrotron light source is gradually increasing in southern China, leading to the proposal of the Southern Advanced Photon Source (SAPS) [29–31]. SAPS is a 3.5 GeV DLSR planned for construction near the China Spallation Neutron Source (CSNS) facility [32]. Together with CSNS, this new light source is expected to significantly enhance multidisciplinary scientific research in southern China. The current storage ring design for SAPS spans 810 meters, provides an emittance of 26 pm·rad, and supports a beam current of 500 mA. To enhance light stability, SAPS employs longitudinal injection as the primary injection scheme [33].

For the injector system, several candidate options have been considered, including a full-energy linac injector [34] and a booster-based injector. The booster-based injector is preferred because it utilizes highly stable and thoroughly validated conventional magnets and acceleration units, which offer superior stability and minimized instrumentation expenses. To further improve stability and operational efficiency, many boosters implement separate tunnels from the storage ring [35–52], a strategy also suggested for SAPS. [FIGURE:1] [35–48, 51] presents key accelerator parameters worldwide where boosters with separate tunnels are employed, including the relationship between storage ring and booster circumferences, booster acceleration energy, and beam emittance and bunch length relative to booster circumference. Specifically, the upper left plot illustrates the circumference relationship, with most light sources exhibiting a ratio of approximately 3:1. The upper right plot summarizes booster acceleration energy, indicating an increase of roughly 2 GeV for every 100 meters of circumference. While the emittance and bunch length relative to circumference are not clearly depicted in the lower plots, these figures highlight the significant advantages in beam performance offered by the SAPS booster design.

To fulfill the requirements for beam quality and efficiency in top-up operation modes of the storage ring, the booster-based injector should deliver electron bunches with high beam quality as summarized in Reference [53] and outlined in [TABLE:1]. With a bunch spacing of 6 ns in the storage ring, longitudinal injection must be precisely executed within this 6 ns period. To prevent disturbances to the circulating beam during injection and reduce the difficulty of injection kickers, the injection phase is set very close to the unstable phase of the bucket, which imposes significant constraints on longitudinal acceptance. Simulations demonstrate that high injection efficiency is achieved for bunch lengths under 5 mm. Moreover, significant energy oscillations during longitudinal injection, with peak energy deviations approaching 4%, reduce the transverse acceptance. Consequently, the horizontal geometric emittance must be kept below 20 nm·rad. For standard longitudinal injection, the bunch charge needs to exceed 0.25 nC, identified as the normal-charge (Norm-Qc) mode.

Once the storage ring is activated, the injection process from zero to full beam current is projected to take less than a minute, enhancing light source utilization. In this mode, each bucket in the ring is filled by a single injected bunch, demanding a bunch charge of 4.2 nC with an injection efficiency of 80%. This operational state is labeled as the high-charge (high-Qc) mode.

As demonstrated by the equations above, minimizing emittance and bunch length can be achieved by increasing the ring circumference and reducing $\alpha_p$. One approach to reduce $\alpha_p$ is the use of combined-function magnets, with optimization algorithms [54, 55] employed to design these lattices. To facilitate selection of optimal lattice structures, we conducted a comparative analysis. The main parameters of these lattices are summarized in [TABLE:2], including a FODO structure with increased circumference, a modified TME structure, and a structure incorporating full combined-function magnets. To meet injection requirements, the circumference of the FODO structure must be increased to approximately 380 meters, significantly enlarging the accelerator and substantially increasing costs. Under equal circumference conditions, the key parameters of the TME structure are similar to those of the full combined-function magnet structure. However, during the design process, optimizing the nonlinear dynamics of full combined-function magnets proved particularly complicated and demanded higher tolerance for magnet errors. Considering both cost and operational reliability, the modified TME structure was ultimately selected.

[FIGURE:2] displays the layout of the booster-based injector. The booster synchrotron-based injector for SAPS consists of a 250 MeV linac, a booster synchrotron that accelerates beams to a full energy of 3.5 GeV for storage in the ring, and two beam transport lines. The paper is organized as follows: Section II describes the preliminary design of the linac, outlining components and their functions. Section III elaborates on the lattice design and beam parameters of the booster synchrotron, closed orbit correction, longitudinal dynamics design, and high-intensity studies. Section IV presents the design of the beam transport lines and booster injection/extraction, explaining their roles in beam delivery and manipulation. Section V introduces simulations of transmission efficiency from the electron gun to the injection point in the storage ring. Section VI discusses the injector design for the longitudinal injection scheme. The concluding section summarizes the findings and proposals, highlighting advancements for the SAPS project.

Linac Design

The 250 MeV linac functions as the pre-injector for the synchrotron light source, delivering electron bunches to the booster synchrotron. The layout of the pre-injector [56] is illustrated in [FIGURE:3]. The system comprises three sections: a DC electron gun, a bunching section, and an accelerating section that includes four S-band accelerating cavities.

As a user facility, the linac should operate with high reliability, which is challenging when employing an RF photo gun equipped with a semiconductor cathode for high bunch charge. Therefore, a thermionic high-voltage DC gun is chosen, capable of providing the required bunch charge to the booster. The total capture efficiency is assumed to be 80%, so this DC gun must provide electron bunches with a charge of 6.5 nC. The software EGUN [57] is utilized for the DC gun design, producing a full-width at half-maximum (FWHM) bunch length of 1.1 ns. For normal-charge mode, this gun can also provide bunches with lower charge by adjusting the bias voltage.

The bunching system compresses the bunch into a single bunch, comprising two subharmonic cavities, a standing-wave S-band pre-buncher, a traveling-wave S-band buncher, and a standard S-band cavity. After passing through this bunching system, over 90% of electrons are confined within a time range of 10 ps, ensuring low energy spread acceleration in the subsequent linac. The entire system is encased in a solenoid focusing channel for transverse focusing and emittance preservation. Our design incorporates 23 solenoids, each with a maximum magnetic field of 0.1 T. The final traveling-wave cavity not only compresses the electron bunch but also provides beam acceleration, achieving a bunch energy of approximately 50 MeV after this section.

The accelerating system comprises four traveling-wave S-band accelerating cavities to increase the bunch energy from 50 MeV to 250 MeV. Two adjacent cavities are grouped together and powered by a klystron. The microwave from the klystron is compressed using SLAC Energy Doubler (SLED) technology [58] to achieve high peak power. The average accelerating gradient of the linac can exceed 20 MV/m. Along the linac cavities, three quadrupole triplets are used to match and focus the beam. The wakefield in the S-band linac is also estimated, and BNS damping [59] is employed to mitigate its effects.

The linac operates in two distinct charge modes: standard-charge mode dedicated to longitudinal injection of the storage ring and a high-charge mode optimized for fast beam accumulation from zero to full current upon storage ring activation. The high-charge mode presents notable challenges to the linac, prompting a focused design approach. Alignment errors for all components are assumed to have RMS standard deviations of 0.1 mm and 0.1 mrad, while cavities and magnets are presumed to exhibit field errors of 0.1%. Following error assessment and correction, optimization and comparison tasks are performed using the ELEGANT [60] and ASTRA [61] codes, with main beam parameters detailed in [TABLE:3]. At the end, the beam energy reaches 250 MeV. The linac achieves a transmission efficiency exceeding 95%, accompanied by normalized emittances of approximately 60 mm·mrad in the transverse plane. A bunch charge of 5.2 nC is required for a booster with 80% transmission efficiency. The transition from high-charge mode to normal-charge mode can be seamlessly accomplished by adjusting the settings of the electron gun, solenoids, and cavities. In this context, the beam emittance and spread are diminished compared to high-charge mode, thereby enhancing injector performance. Nonetheless, a bunch charge of 0.4 nC is maintained with the same transmission efficiency as in high-charge mode.

Booster Synchrotron

Booster Lattice

The separate-tunnel booster features a three-fold structure, with each super-period consisting of 12 modified TME cells and two matching cells. The layout and optical functions of one period are depicted in [FIGURE:4]. The modified TME cell comprises a combined-function dipole magnet and a set of quadrupole magnets. The matching cell, composed of two dipole magnets and powered by five separate power supplies for the quadrupoles, provides flexibility in optimizing the lattice. The lattice includes three long (7.3 m) straight sections with zero dispersion for installation of RF cavities as well as injection and extraction components. The main parameters of the booster are listed in [TABLE:4]. The circumference is shortened to 237 m, comprising 54 dipole magnets, 108 quadrupole magnets, and 51 sextupole magnets. The lattice achieves a sufficiently low horizontal emittance of 3.98 nm·rad at extraction, comparable to that of third-generation storage rings. The bunch length is attained through a small $\alpha_p$ of $1.75 \times 10^{-3}$ and a high voltage of 7.5 MV. The design with low emittance and short bunch length necessitates strong focusing fields, leading to significantly large natural chromaticity. Furthermore, the peak value of the dispersion is below 0.2 meters. Consequently, a sextupole field to correct chromaticity is integrated into the combined-function dipoles to decrease the number of sextupole magnets.

Given the beam parameters for the pre-injector described in Section II, the transverse beam sizes are 1.7 mm × 1.5 mm, respectively. It is assumed that the magnet aperture should be no less than 10 times the beam sizes. In the booster, the maximum strength of dipole magnets is approximately 1 T, with a defocusing strength of 0.542 T/m and sextupole strength of 5.63 T/m². Three types of quadrupole magnets are utilized, with a maximum pole-face strength of 0.72 T. Additionally, one type of sextupole magnet is employed with a maximum pole-face strength of 0.6 T and a length of 0.15 meters.

In addition to the integrated sextupole component in the combined-function magnets, a family of sextupoles distributed in each TME cell is employed for chromaticity correction. Two additional families of sextupoles in the matching cell are utilized to minimize nonlinear driving terms. Independent power supplies for the sextupoles allow separate adjustments of horizontal and vertical chromaticity. Using a 6D code to track particles for 1024 turns, we obtain the dynamic aperture and corresponding frequency map. The sextupole strengths are optimized to achieve a sufficiently large dynamic aperture, with results shown in [FIGURE:5]. The dynamic aperture approximates 15 mm.

Tolerance and Correction

The ring is equipped with 54 BPMs for closed orbit correction, with one BPM positioned in each modified TME cell. It also has 73 dipole correctors, allocated as 38 for the horizontal plane and 35 for the vertical plane. The corrector fields are capable of tracking the energy ramp, ensuring orbit correction at all energy levels. Preliminary evaluations encompass magnet tolerances and the orbit correction system. [TABLE:5] outlines the assumed RMS tolerances for magnet alignment and fields. Another significant source of closed orbit distortion is the stray field from the extraction Lambertson magnet operating in DC mode, which significantly impacts the circulating beam, especially at low energy stages. A local bump has been designed to mitigate this distortion. Tolerances on magnet parameters are developed using analytical estimates, assuming Gaussian-type random errors in all magnets.

In orbit correction simulations, 1000 sets of random seeds are generated. With these BPMs and correctors, the closed orbit distortion due to errors listed in [TABLE:5] can be effectively corrected. The BPM-corrector configuration ensures that the orbit exhibits a maximum deviation of 1.5 mm in each plane after correction, as shown in [FIGURE:6], with average RMS values of 0.23 mm and 0.2 mm in the horizontal and vertical planes, respectively. This requires a maximum corrector strength of 0.5 mrad, simplifying magnet design and fabrication. Furthermore, based on orbit correction, an analysis is conducted to evaluate the impact of magnet alignment errors and field errors on the dynamic aperture. Considering the errors specified in [TABLE:5], the dynamic aperture is reduced to 12 mm, yet it still meets the dynamic aperture requirements for both charge modes.

During operation, the dynamic errors of the power supply are characterized by stability, repeatability, and ripples. To investigate perturbations in the tune, simulations are performed using the ELEGANT code [60]. In these simulations, the total dynamic error for each magnet is modeled using a random 3σ truncated Gaussian distribution. Various RMS error values are scanned, generating 2000 sets of random error seeds for each condition. When the error value is below $4 \times 10^{-4}$, the tune avoids major resonance lines and maintains high transmission efficiency, thus informing power supply design.

Longitudinal Beam Dynamics

The ramp cycle consists of a 60 ms flat bottom for accumulating the injected beam at the beginning, a ramping curve for acceleration, an equally long flat top for extracting the accelerated beam, and a ramping-down period. Reference [62] discusses the impact of various ramping curves on emittance. Given the 60 ms flat top and enhanced ramping accuracy, a comparable sinusoidal curve of energy $E(t)$ is utilized over a duration of 220 ms:
$$E(t) = 1.875 + 1.625\sin(2\pi f t)$$
with $f \approx 2.2727$ Hz and ramping time $t$. The ramping curve and beam evolution in the booster are depicted in [FIGURE:7]. The beam energy increases from 250 MeV to 3.5 GeV in 220 ms. The RF voltage is set to 2 MV at injection and 7.5 MV at extraction. The synchrotron tune shifts from 0.026 at injection to 0.015 at extraction, while the bucket height reduces from 7% to 4%. The evolution of beam energy spread and emittance with energy ramping is detailed in Reference [63] as
$$\frac{dA_i}{dt} = -A_i\left(\frac{2}{\tau_i}\right) + C_q G_i \frac{\dot{E}}{E}$$
with $i = 1$ and $2$. For $i = 1$, $A_1$ denotes the energy spread, $J_1$ is the longitudinal damping partition, and $G_1 = I_3/I_2$ with synchrotron radiation integrals $I_2$ and $I_3$. For $i = 2$, $A_2$ represents horizontal emittance $\epsilon_x$, $J_2$ is the horizontal damping partition $J_x$, and $G_2 = I_5/I_2$ with synchrotron radiation integral $I_5$. $\dot{E}$ is the energy slope at energy $E$ with relativistic energy factor $\gamma$, and $P_\gamma$ is the synchrotron radiation power. When the energy exceeds 2.5 GeV, the emittance and energy spread attain equilibrium as a result of radiation damping and quantum excitation.

Additionally, the induced eddy current in the dipole vacuum chamber produces an extra sextupole field. The induced sextupole strength during ramping [64, 65] is calculated as
$$B_2 = \frac{2F\mu_0\sigma}{h g}$$
where $\sigma$ is the conductivity, $h$ and $g$ are the thickness and height of the vacuum chamber, respectively, $F$ is the chamber form factor, and $\mu_0$ is the magnetic permeability of vacuum. For the specified lattice parameters, the estimated maximum field of the sextupole is 0.3 T/m³ at a repetition rate of 2 Hz. The corresponding chromaticity values are approximately 1.7 for the horizontal plane and -1.3 for the vertical plane, which are significantly smaller than the natural chromaticity and can be easily compensated by ramping up sextupoles.

Estimation of Beam Effects Due to High Intensity

SAPS is in the design phase, making development of an accurate impedance model challenging. However, key components contributing to the impedance can be inferred from other existing accelerators. In this study, we construct a vertical impedance $Z_v$, as depicted on the left side of [FIGURE:8], by scaling the impedance of the HEPS booster [66, 67] as
$$Z_v = Z_{\text{HB}} \frac{C_{\text{HB}}}{C} + N_c Z_{\text{HOM}}$$
where $C_{\text{HB}}$ is the circumference of the HEPS booster [51] and the number of cavities $N_c = 5$. A 5-cell copper cavity will be employed, serving as the source of the higher-order modes (HOM, $Z_{\text{HOM}}$) observed in the impedance spectrum. $Z_{\text{HB}}$ refers to the HEPS booster impedance excluding the cavity impedance.

Instabilities commonly observed in other accelerators [68, 69] are estimated for the booster. For the high-charge mode, the beam current in the booster is approximately 20 mA. The growth time $1/\tau$ of transverse coupled-bunch instability (TCBI), driven by HOMs, is expressed [70] as
$$\frac{1}{\tau} = \frac{f_{\text{rev}} I_b \beta Z_{\text{HOM}}}{2}$$
where $I_b$ is the average beam current with revolution frequency $f_{\text{rev}}$, and $\beta$ is the beta function at the cavity. The growth time in the vertical plane is calculated to be 0.78 ms at injection and 11 ms at extraction. These results indicate that the TCBI growth time at extraction energy exceeds the damping time of 6.3 ms, thereby suppressing the instability. Conversely, the beam remains unstable at injection due to the excessively long damping time. Consequently, a transverse feedback system with a damping time of 0.5 ms is proposed.

Single-bunch effects are simulated utilizing the ELEGANT code [60] for the bare lattice, with threshold charges depicted on the right side of [FIGURE:8]. Head-tail instability is observed at high bunch charges in the simulation. As head-tail effects emerge, both the oscillation amplitude of beam position and the vertical emittance increase. Nevertheless, the results show that the instability threshold charge is around 15 nC, substantially higher than the required charge of 4.2 nC for high-charge mode. Furthermore, a longitudinal impedance model is developed to investigate the dependence of bunch length on bunch charge. The findings reveal that bunch length increases significantly due to microwave instability when the charge exceeds 20 nC. Consequently, bunch lengthening is expected to be negligible in both normal-charge and high-charge modes.

Beam Transport Lines and Booster Injection and Extraction

These references [71–73] serve as the basis for the design considerations of this section. The Linac-to-Booster Transport line (LBT) connects the linac to the booster and must fulfill several functions: beam matching between the linac and booster, and providing space for beam diagnostic elements and momentum collimators. The high-charge mode is considered in the design. The transfer line consists of two doublet bend achromat (DBA) structures, ensuring a dispersion-free condition. It includes 3 dipoles and 12 quadrupoles, with all dipole magnet angles set at 200 mrad. Instrumentation elements are arranged along the 24.4 m transfer line. The maximum beta function is 35 m with maximum dispersions of 0.6 m. The horizontal collimator is positioned in the first DBA structure with a transverse aperture of 16 mm, effectively reducing the energy spread to the required level. The RMS energy spread after collimation is 0.36%. Error studies show that beam emittance does not significantly increase along the transfer line, and beam loss is mainly confined to the collimation section.

The booster injection system is situated in one of the two remaining dispersion-free straight sections and comprises a DC Lambertson magnet and a kicker. It utilizes single-turn on-axis injection, enabling injection of one bunch into the booster RF buckets. The Lambertson has a bend angle of 200 mrad in the horizontal plane, while the kicker has a bend angle of 6.5 mrad in the vertical plane.

The booster extraction system is located in the last dispersion-free straight section and comprises four slow orbit bumpers, a Lambertson magnet, and a kicker. The slow bumpers incrementally shift the orbit of the circulating bunch train toward the extraction Lambertson over several hundred turns. Following this, the extraction kicker directs one bunch into the extraction Lambertson at a vertical angle of zero. The kicker strength is 1.2 mrad, while the Lambertson kick angle is set at 100 mrad. Two of the four bump magnets are positioned in the matching cell, with a maximum bumper strength of 1.3 mrad. Simulations confirm the design, achieving 100% extraction efficiency. Additionally, the beam carrying a charge of 5 nC is tracked from injection to extraction in the booster, with primary results shown in [FIGURE:9]. The injected beam quickly reaches equilibrium after injection in the booster. During the injection plateau phase, these parameters show minimal change, while in the acceleration phase they gradually stabilize and reach equilibrium values. This outcome indicates high beam performance throughout the booster cycle.

The Booster-to-Ring Transport line (BRT) is designed to efficiently convey the booster beam into the storage ring. Due to the low vertical emittance, the beam is vertically injected into the ring to minimize the kick intensity in the storage ring. The BRT consists of 12 dipoles and 19 quadrupoles, extending over a length of 60 m. This transport line is functionally divided into three segments: the extraction matching section, the dispersion-free section, and the injection matching section. The dispersion-free section is allocated for installation of beam diagnostic elements. The magnet aperture is less than 30 mm. The beam transmission efficiency in the BRT is approximately 99%.

Transmission Efficiency Simulation

After completing the physical design of the injector, we studied the overall transmission efficiency, defined as the ratio of charge captured by the storage ring to charge output from the electron gun. Start-to-end simulation is systematically executed to ensure that input parameters at each accelerator stage precisely match the output parameters of the preceding stage, facilitating a seamless acceleration and transmission process. The simulation rigorously tracks the beam from its generation at the electron gun through the linac, the LBT, injection, acceleration, and extraction in the booster, and the BRT, ultimately reaching the injection point in the storage ring. Realistic error margins expected at each accelerator stage are incorporated into the simulation. To evaluate overall performance, we generate 100 random seeds and perform a comprehensive statistical analysis of transmission efficiency and charge accumulated in the storage ring.

First, the high-charge mode is simulated. The results demonstrate exceptional efficiency, with an average transmission efficiency approaching 90%, and most beam loss occurring at the collimator in the LBT. Furthermore, across all simulation scenarios, the accumulated charge in the storage ring exceeded the required charge of 3.33 nC. This indicates that our injector design meets the criteria for efficient injection even when realistic operational errors are considered. To further validate the robustness of the injector design, equivalent simulation studies are performed for the normal-charge mode. Encouragingly, in this mode the transmission efficiency exceeds 90% in every case, providing additional evidence of the design's efficiency and reliability.

Discussion

Synchrotron radiation light sources are undergoing rapid development globally. Selecting an injector with high stability, high beam quality, robustness, and cost-effectiveness is crucial to advancing these facilities. Presently, synchrotron radiation light sources are categorized as high, medium, and low-energy sources based on beam energy. High-energy light sources, exemplified by HEPS [14], operate at energies exceeding 6 GeV and favor booster-based injector schemes for efficient cost management. Low-energy light sources, with energies below 2.5 GeV, can accommodate a full-energy linac injector due to their lower energy requirements, as illustrated by HALF [15]. Medium-energy light sources fall between these extremes and necessitate thorough consideration of various injector options. For instance, SAPS has assessed multiple injector schemes, including full-energy linac, booster-based injection, and innovative injectors, to align with technical requirements, costs, and future expansion applications. Despite the availability of innovative injector schemes and technologies such as laser plasma accelerators, these alternatives often introduce heightened operational risks. Recent studies have shown that booster-based injectors offer significant advantages over other injector types.

The longitudinal injection design of SAPS imposes stringent requirements on injector beam quality, particularly concerning bunch length and beam emittance. Achieving the desired bunch length and emittance while keeping the booster size reasonable presents a major challenge. One strategy involves increasing the RF voltage, but attaining the required beam quality would necessitate increasing the voltage by an order of magnitude, requiring substantial space for RF cavity installation. Another method entails compressing $\alpha_p$, which necessitates strong focusing fields, reducing the dynamic aperture and tightening magnet error tolerances. These challenges escalate not only the cost of the injector but also construction risks, potentially undermining the advantages of a booster-based injector. Balancing these factors, a hybrid approach has been adopted, combining $\alpha_p$ compression and voltage augmentation to preserve the benefits of the booster-based injector. The booster injector offers a promising solution for the longitudinal injection scheme of DLSR storage rings. Considering limitations such as simulation assumptions and the need to incorporate more practical parameters in subsequent optimizations, future work will focus on optimizing design parameters, enhancing system stability, and preparing for actual construction stages. Nevertheless, successful beam commissioning from the HEPS injector [74, 75] offers substantial encouragement for ongoing success.

Summary

A beam with short bunch length and low emittance is vital for storage ring injection in SAPS. This paper presents a detailed overview of the physical design of a booster-based injector engineered to meet these requirements. The injector system comprises a linac, a booster synchrotron, and two beam transport lines. The booster synchrotron accelerates electron beams from 250 MeV to 3.5 GeV at a repetition rate of 2 Hz. The booster synchrotron lattice consists of 54 dipole magnets, 108 quadrupole magnets, and 51 sextupole magnets. The required beam parameters for SAPS injection are achieved by employing a modified TME structure with a small momentum compaction factor and high RF voltage. The resulting beam emittance is 3.98 nm·rad with a bunch length of 4.8 mm. Simulation studies of beam transmission efficiency indicate an overall efficiency of about 90%. Detailed analysis of beam collective effects, based on the current impedance model, shows that the charge stored in the injector significantly exceeds SAPS injection requirements. These findings confirm that the injector meets the injection requirements of the SAPS storage ring. The theoretical and simulation studies of the injector design demonstrate outstanding performance.

Acknowledgements

We would like to thank Yuemei Peng, Cai Meng, Haisheng Xu, and Saike Tian for fruitful discussions and data support. We are also grateful to colleagues from the power supply and magnet groups for their discussions.

References

[1] M. Magnuson, M. Fahlman, R. Uhrberg, et al., MAX IV conceptual design report. Max IV, Lund, Sweden, Rep. CDR, (2006).
[2] P. Tavares, S. Leemann, M. Sjöström, et al., The MAX IV storage ring project. Journal of Synchrotron Radiation 21, pp. 862–877 (2014). doi: 10.1107/S1600577514011503
[3] C. Schroer, I. Agapov, W. Brefeld, et al., PETRA IV: the ultralow-emittance source project at DESY. Journal of Synchrotron Radiation 25, pp. 1277–1290 (2018). doi: 10.1107/S1600577518008858
[4] P. Goslawski, M. Abo-bakr, F. Andreas, et al., BESSY III & MLS II—status of the development of the new photon science facility in Berlin. in Proc. of IPAC'12, Campinas, Brazil, MOPAB126, pp. 451–454 (2021). doi: 10.18429/JACoW-IPAC2021-MOPAB126
[5] Conceptual Design Report for SOLEIL Upgrade, (2021). www.synchrotron-soleil.fr
[6] A. Streun, T. Garvey, L. Rivkin, et al., SLS-2 – the upgrade of the swiss light source. Journal of Synchrotron Radiation 25, pp. 631–641 (2018). doi: 10.1107/S1600577518002722
[7] E. Karantzoulis, A. Fabris, S. Krecic, The ELETTRA 2.0 project. in Proc. of IPAC'22, Bangkok, Thailand, TUPOMS023, pp. 1459-1462 (2022). doi: 10.18429/JACoW-IPAC2022-TUPOMS023
[8] C. Steier, A. Allezy, A. Anders, et al., Status of the conceptual design of ALS-U. in Proc. of IPAC'17, Copenhagen, Denmark, WEPAB104, pp. 2824–2826 (2017).
[9] L. Liu, N. Milas, A. Mukai, et al., The Sirius project. Journal of synchrotron radiation 21, pp. 904–911 (2014). doi: 10.1107/S1600577514011928
[10] SPring-8-II Conceptual Design Report. RIKEN SPring-8 Center, (2014). https://docslib.org/doc/4975580/spring-8-ii-conceptual-design-report
[11] G. S. Jang, S. Shin, M. Yoon, et al., Low emittance lattice design for Korea-4GSR. Nucl. Instrum. Methods Phys. Res. A 1034, 166779 (2022). doi: 10.1016/j.nima.2022.166779
[12] P. Raimondi, N. Carmignani, L. Carver, et al., Commissioning of the hybrid multibend achromat lattice at the European synchrotron radiation facility. Phys. Rev. Accel. Beams 24, 110701 (2021). doi:10.1103/PhysRevAccelBeams.24.110701
[13] Fornek, Thomas E, Advanced Photon Source Upgrade Project Final Design Report, Argonne National Laboratory, United States, (2019). doi: 10.2172/1543138
[14] Y. Jiao, G. Xu, X. Cui, et al., The HEPS project. Journal of Synchrotron Radiation 25, pp. 1611–1618 (2018). doi: 10.1107/S1600577518012110
[15] Z. Bai, G. Liu Gangwen, T. He, et al., Preliminary physics design of the Hefei Advanced Light Facility storage ring. High Power Laser and Particle Beams 34, 104003 (2022). doi: 10.11884/HPLPB202234.220137
[16] D. Einfeld, M. Plesko, J. Schaper, First multi-bend achromat lattice consideration. Journal of Synchrotron Radiation. 21, pp. 856–861 (2014). doi: 10.1107/S160057751401193X
[17] H. Takaki, N. Nakamura, Y. Kobayashi, et al, Beam injection with a pulsed sextupole magnet in an electron storage ring. Phys. Rev. ST Accel. Beams 13, 020705 (2010). doi: 10.1103/PhysRevSTAB.13.020705
[18] Y. Jiao, G. Xu, Pulsed sextupole injection for Beijing Advanced Photon Source with ultralow emittance. Chinese Physics C. 37, 117005 (2013). doi: 10.1088/1674-1137/37/11/117005
[19] M. Borland, A super-bright storage ring alternative to an energy recovery linac. Nucl. Instrum. Methods Phys. Res. A, 557, 230 (2006). doi: 10.1016/j.nima.2005.10.076
[20] A. Xiao, M. Borland, C. Yao, et al. On-axis Injection Scheme for Ultra-Low-Emittance Light Sources. in Proc. of NAPAC'13, Pasadena, CA, pp. 1076–1078 (2013).
[21] C. Steier, A. Anders, T. Luo, et al., On-Axis Swap-Out Injection R+D for ALS-U. in Proc. of IPAC'17, Copenhagen, Denmark, WEPAB103, pp. 2821–2823 (2017).
[22] Z. Duan, J. Chen, Y. Guo, et al., The swap-out injection scheme for the High Energy Photon Source. in Proc. of IPAC'18, Vancouver, BC, Canada, THPMF052, pp. 4178–4181 (2018). doi: 10.18429/JACoW-IPAC2018-THPMF052
[23] M. Aiba, M. Boge, F. Marcellini, et al., Longitudinal injection scheme using short pulse kicker for small aperture electron storage rings. Phys. Rev. ST Accel. Beams 18, 020701 (2015). doi: 10.1103/PhysRevSTAB.18.020701
[24] M. Tordeux, R. Nagaoka, A. Chao, et al., Longitudinal injection into low-emittance ring: a novel scheme for SOLEIL upgrade. in Topical Workshop on Injection, Berlin, pp. 28–30 (2017).
[25] S. Jiang, G. Xu, On-axis injection scheme based on a triple-frequency rf system for diffraction-limited storage rings. Phys. Rev. Accel. Beams 21, 110701 (2018). doi: 10.1103/PhysRevAccelBeams.21.110701
[26] J. Kim, G. Jang, M. Yoon, et al., Injection scheme with deflecting cavity for a fourth-generation storage ring. Phys. Rev. Accel. Beams, 22, 011601 (2019). doi: 10.1103/PhysRevAccelBeams.22.011601
[27] L. C. Teng, Minimizing the emittance in designing the lattice of an electron storage ring. Fermilab Report TM-1269 (1984). doi: 10.2172/6690255
[28] S. Y. Lee, Accelerator Physics, 2nd edn. (World Scientific, Singapore, 2004), p. 251, p. 452.
[29] S. Wang, J. Chen, Y. Han, et al., Proposal of the Southern Advanced Photon Source and Current Physics Design Study. in Proc of IPAC'21, Campinas, SP, Brazil, MOPAB075, pp. 300–303 (2021). doi: 10.18429/JACoW-IPAC2021-MOPAB075
[30] Y. Zhao, Y. Jiao, S. Wang, Design study of APS-U-type hybrid-MBA lattice for mid-energy DLSR. Nucl. Sci. Tech. 32:71, (2021). doi: 10.1007/s41365-021-00902-1
[31] Yu Zhao, Y. Jiao, Z. Li, et al., Improving the MWI threshold of the modified hybrid-7BA lattice design for SAPS. Nucl. Instrum. Methods Phys. Res. A 1056, 168565 (2023). doi: 10.1016/j.nima.2023.168565
[32] S. Wang, S. Fu, H. Qu, et al, Design, Development and Commissioning for High-intensity Proton Accelerator of China Spallation Neutron Source. Atomic energy science and technology, 56:9, 1747–1759 (2022). doi: 10.7538/yzk.2022.youxian.0591
[33] W. Liu, Y. Jiao, Y. Zhao, et al., Multi-objective optimization of longitudinal injection based on a multi-frequency RF system for fourth-generation storage ring-based light sources. Nucl. Instrum. Methods Phys. Res. A 1046, 167712 (2023). doi: 10.1016/j.nima.2022.167712
[34] X. Liu, S. Jiang, W. Liu, et al., Start-to-end simulation of the full energy linac injector for the Southern Advanced Photon Source. in Proc. of IPAC'23, Venice, Italy. TUPL111, pp. 1992–1994 (2023). doi: 10.18429/JACoW-IPAC2023-TUPL111
[35] D. Li, H. Du, H. Li, et al., Status of the SSRF booster. in Proc. of EPAC'08, Genoa, Italy, WEPC083, pp. 2089-2191 (2008).
[36] P. Raimondi, C. Benabderrahmane, P. Berkvens, et al. The Extremely Brilliant Source storage ring of the European Synchrotron Radiation Facility. Commun Phys 6, 82 (2023). doi: 10.1038/s42005-023-01195-z
[37] S. V. Milton, The APS Booster Synchrotron: Commissioning and Operational Experience. Proceedings Particle Accelerator Conference 1, Dallas, TX, USA, pp. 594-596 (1995) doi: 10.1109/PAC.1995.504730
[38] S. Gurov, S. Karnaev, V. Kiselev, et al., Commissioning of NSLS-II booster. in Proc. of IPAC'14, Dresden, Germany, MOPRO088, pp. 295-297 (2014).
[39] F. H. Sa, L. Liu, X. Resende, et al., A new booster synchrotron for the SIRIUS project. in Proc. of IPAC'14, Dresden, Germany, WEPRO009, pp. 1959–1961 (2014). doi: 10.18429/JACoW-IPAC2014-WEPRO009
[40] A. Loulergue, M. Tordeux, A. Dael, et al., The new booster synchrotron for SOLEIL. in Proc. of EPAC'02, Paris, France, pp. 593-595 (2002).
[41] H. C. Chao, J. W. Tsai, H. P. Chang, et al., Conceptual design of booster synchrotron for TPS. in Proc. of EPAC'08, Genoa, Italy, THPC005, pp. 2981–2983 (2008).
[42] G. Benedetti, D. Einfeld, Z. Marti, et al., Optics for the ALBA booster synchrotron. in Proc. of EPAC'08, Genoa, Italy, WEPC067, pp. 2148–2150 (2008).
[43] Charles H. Kim, Commissioning Experiences of the ALS Booster Synchrotron. Conference Record of the 1991 IEEE Particle Accelerator Conference 5, San Francisco, CA, USA, pp. 2691–2693 (1991). doi: 10.1109/PAC.1991.165073
[44] D. Scott, J. Clarke, D. Dykes, et al., A revised DIAMOND booster design. in Proc. of EPAC'02, Paris, France, pp. 617–619 (2002).
[45] G. Zanyan, B. Grigoryan, K. Manukyan, et al., Low emittance booster design for CANDLE storage ring. in Proc. of IPAC'11, San Sebastián, Spain, THPC137, pp. 3209–3211 (2011).
[46] A. Fabris, P. Craievich, C. Pasotti, et al., RF system for the ELETTRA booster synchrotron. in Proc. of EPAC'00, Vienna, Austria, pp. 1957–1959 (2000).
[47] Hung-Chun Chao, Ilya Agapov, Sergey Antipov, Design Considerations of a High Intensity Booster for PETRA IV. in Proc. of IPAC'21, Campinas, SP, Brazil, TUPAB023, pp. 1386–1389 (2021). doi: 10.18429/JACoW-IPAC2021-TUPAB023
[48] M. Tordeux, A. Loulergue, R. Nagaoka et al., A low-emittance booster lattice design for the SOLEIL upgrade. in Proc. of IPAC'21, Campinas, SP, Brazil, MOPAB113, pp. 410–413 (2021). doi: 10.18429/JACoW-IPAC2021-MOPAB113
[49] Y. M. Peng, Y. Jiao, G. Xu, et al., Candidate booster design for the HEPS project. in Proc. of IPAC'16, Busan, Korea, THPMB018, pp. 3263–3265 (2016).
[50] Y. M. Peng, Z. Duan, Y.Y. Guo, et al., The progress of HEPS booster design. in Proc. of IPAC'17, Copenhagen, Denmark, TUPAB065, pp. 1472–1474 (2017). doi: 10.18429/JACoW-IPAC2018-TUPMF062
[51] Y. M. Peng, Z. Duan, Y.Y. Guo, et al., Status of HEPS booster lattice design and physics studies. in Proc. of IPAC'18, Vancouver, BC, Canada, TUPMF06, pp. 1407–1410 (2018). doi: 10.18429/JACoW-IPAC2018-TUPMF062
[52] Cai Meng, Xiang He, Yi Jiao, et al., Physics design of the HEPS LINAC. Radiation Detection Technology and Methods 4, 497–506 (2020). doi: 10.1007/s41605-020-00205-w
[53] W. Liu, injector parameter requirements for SAPS. SAPS Technical Note SAPS-AC-AP-TN-2023-003, (2023)
[54] L. Yang, D. Robin, F. Sannibale et al., Global optimization of an accelerator lattice using multi-objective genetic algorithms. Nucl. Instrum. Methods Phys. Res. A 609, 50–57 (2009). doi: 10.1016/j.nima.2009.08.027
[55] Y. Jiao, G. Xu, Optimizing the lattice design of a diffraction-limited storage ring with a rational combination of particle swarm and genetic algorithms. Chinese Phys. C 41, 027001 (2017). doi: 10.1088/1674-1137/41/2/027001
[56] Y. Han, L. Huang, X. Liu et al., "Design of a 250 MeV linac injector system for the Southern Advanced Photon Source". J. Phys.: Conf. Ser. 2687, 032004 (2024). doi: 10.1088/1742-6596/2687/3/032004
[57] W. Herrmannsfeldt, EGUN - an electron optics and gun design program. SLAC-331, (1988) doi: 10.1016/j.nima.2023.169074
[58] Z. Farkas, H. Hoag, P. Wilson et al., "SLED, a method of doubling SLAC's energy". SLAC-TN-73-15, (1974). https://api.semanticscholar.org/CorpusID:605827
[59] V. Balakin, A. Novokhatsky, V. Smirnov, VLEPP: Transverse beam dynamics. Conf. Proc. C 830811, pp. 119-120 (1983).
[60] M. Borland, "elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation". Advanced Photon Source, no. LS-287, (2000). doi: 10.2172/761286
[61] K. Flottmann, ASTRA User Manual, (2023). http://www.desy.de/mpyflo
[62] Yumi Lee, Eun-San Kim, Ji-Gwang Hwang et al., Beam dynamics in the booster synchrotron of Korea-4GSR project. Nucl. Instrum. Methods Phys. Res. A 1060, 169074 (2024). doi: 10.1016/j.nima.2023.169074
[63] D. Edwards, M. J. Syfers, An introduction to the Physics of High Energy Accelerators. (John Wiley and Sons, Inc., New York, 1993), pp. 110–115
[64] J. Bergstrom, L. Dallin, Effects of Eddy Current Induced Sextupole Moments in the Booster during Ramping. CLS Design Note - 3.2.69.2 Rev. 0, (2000).
[65] Y. M. Peng, J.Y. Li, C. Meng, et al., Study of the ramping process for HEPS booster. in Proc. of IPAC'19, Melbourne, Australia, TUPGW052, pp. 1521–1523 (2019). doi: 10.18429/JACoW-IPAC2019-TUPGW052
[66] Hai-Sheng. Xu, Jing-Ye Xu, Na Wang, Influences of harmonic cavities on single-bunch instabilities in electron storage rings. Nucl. Sci. Tech. 32:98, (2021). doi: 10.1007/s41365-021-00886-y
[67] Saike Tian, (private communication), (2023).
[68] N. Wang, Z. Duan, H. S. Xu, et al., Studies on collective instabilities in HEPS. in Proc. of IPAC'17, Copenhagen, Denmark, THPAB030, pp. 3763–3766 (2017).
[69] Haisheng Xu, Yuemei Peng, Na Wang. Studies of transverse single-bunch instabilities in booster synchrotrons, Nucl. Instrum. Methods Phys. Res. A 940 313—319 (2019). doi: 10.1016/j.nima.2019.06.048
[70] F. Marhauser, E. Weihreter, D. M. Dykes et al., HOM damped 500MHz cavity design for 3rd generation SR sources. in Proc. of PAC'01, Chicago, USA, MPPH033, pp. 846–848 (2001).
[71] PENG Yuemei, Design study of high energy photon source low energy beam transport line, Atom. Ene. Sci. and Tech. 53:9 1702—1705 (2019). doi: 10.7538/yzk.2019.youxian.0140
[72] Y. Y. Guo, J. H. Chen, Z. Duan, et al., The injection and extraction design of the booster for the HEPS projection, in Proc. of IPAC'18, Vancouver, BC, Canada, TUPMF046, pp. 1356–1358 (2018). doi: 10.18429/JACoW-IPAC2018-TUPMF046
[73] Yuanyuan Guo, Yuanyuan Wei, Yuemei Peng, et al., The transfer line design for the HEPS project, Radiation Detection Technology and Methods 4 440—447 (2019). doi: 10.1007/s41605-019-0112-0
[74] C. Meng, X. H. Cui, Z. Duan, et al., Beam commissioning of the HEPS linac, in Proc. of IPAC'23, Venice, Italy, TUPL126, pp. 2023–2026 (2023). doi: 10.18429/JACoW-IPAC-23-TUPL126
[75] Yue-Mei Peng, Jian-She Cao, Jin-Hui Chen, et al., Milestone progress of the HEPS booster commissioning. Nucl. Sci. Tech. 35:16, (2024). doi: 10.1007/s41365-024-01365-w