Booster conceptual design of the southern advance photon source

The Southern Advanced Photon Source is a proposed diffraction-limited storage ring operating at middle energy. A candidate injector includes a low energy Linac and a full energy booster. In the paper, we present the concept design of the booster, which is a high intensity synchrotron accelerator. An impedance model has been obtained and the instability threshold has been predicted.


Introduction
The Southern Advanced Photon Source (SAPS) is a diffraction-limited storage ring with energy of 3.5 GeV which will be built neighbouring the China Spallation Neutron Source (CSNS) in Guangdong Province, the south of China [1].This photon source, together with the CSNS, is expected to benefit multi-discipline scientific researches in the south of China.
Several candidate lattices for the SAPS storage ring have already been designed [2].And the current one has a circumference of 810 m and the nominal emittance of about 30 pm.rad.The extremely small emittance of the storage ring leads to a small dynamic aperture which makes it difficult for the injection, so novel on-axis swap-out injection scheme in the transverse plane and the longitudinal accumulation injection scheme are considered [3].For the injector, two candidate options are being compared, i.e., booster with pre-injector Linac and a full energy Linac [4].The injector option of a low energy Linac and a booster has been adopted by many synchrotron photon facilities [5][6][7][8][9][10] due to its robustness and lower cost, so it is the primary option.The pre-injector Linac has also been conceptually designed [11].We have compared several candidate lattices of booster, finally the FODO lattice of the booster has been selected and the conceptual design is presented in the paper.

The booster lattices
The component of the booster will be installed in a separate-tunnel neighboured the storage ring.In the current design, the booster is a three-fold symmetric structure with the circumference of 233.4 m, a classical FODO lattice.The layouts and the optical parameters of one super-period are shown in Fig. 1.Each super-period is composed of eight standard cells and two matching cells, which forms two straight sections and an arc section with a maximal dispersion of 0.55 meters in horizontal plane.This design provides three 8 m long dispersion-free section to accommodate injection, extraction and RF components.There are 60 dipoles, 81 quadrupoles, 57 sextupoles, 49 correctors, and 2 pulsed magnets in the booster.The main parameters of the booster are listed in Table 1.The beam is injected into the booster at 250 MeV and extracted at 3.5 GeV.The extracted beam emittance is as small as 35.4 nm.rad and the bunch length is about 11 mm.The nominal tune is (12.42,7.17) with natural chromaticity of (-19.9, -10.8).The beam is injected into the booster through a single-turn injection scheme in vertical plane, so a Lambertson magnet and a vertical kicker downstream of the Lambertson are used.After accelerating, Due to the manufacture and installation errors, the real machine may be different from the design.Therefore, beam-based alignment is necessary to mitigate the impact of misalignment.By utilizing 49 steer magnets and 42 beam position monitors (BPM), the closed orbit distortions can be corrected to less than 1.5 mm.
Sextupoles are utilized around the lattice to address nonlinear effects.Two sextupoles, one focusing and one defocusing, are implemented in each unit cell to correct chromaticity.Additionally, one family of harmonic sextupoles is utilized in the dispersion-free straight section to optimize nonlinear driving terms.The sextupole strength is optimized using the Acceleration Toolbox (AT) [12].The dynamic aperture (DA) at the injection point and the frequency map of the bare lattice are displayed in Fig. 2. The results demonstrate that the dynamic acceptance exceeds the physical aperture (~11 mm), while the transverse momentum acceptance is closed to 8%.

Longitudinal beam dynamic design
The ramping curve of longitudinal parameters in the booster are illustrated in Fig. 3.The beam energy is boosted from 250 MeV to 3.5 GeV over a period of 220 ms.The RF voltage is set at 2 MV during injection and 3.0 MV during extraction.The synchrotron tune is changed from about 0.06 at injection to 0.02 at extraction and the bucket height is shrunk from 4 % to 1.06 %.Beam energy spread and emittance evolution with energy ramping can be calculated according to the formula of Ref [13].The results are shown in Fig. 4. When the energy exceeds approximately 2 GeV, the emittance and energy spread reach a balanced state due to radiation damping and quantum excitation.
A ramping cycle is displayed in Fig. 5, which has benefited from the ramping experience of the High Energy Photon Source (HEPS) booster [14,15].The cycle consists of a 60 ms flat bottom to accumulate the injected beam, followed by an equal-length flat top to extract the accelerated beam.To enhance ramping accuracy, a sinusoidal curve is utilized at low and high energy stages, while a mostly linear curve is employed at middle energy stages.The induced eddy current in the dipole vacuum chamber produces an additional sextupole field, and the induced sextupole strength during ramping is estimated [16] as shown in Fig. 6.The maximum chromaticity shift due to this effect is about 2, and the perturbation should be compensated for by the sextupole magnet.

Impedance and high intensity test
During the conceptual design stage, building an accurate impedance model can be challenging.However, critical components contributing to the impedance can be obtained from other real machines.Here, we choose the impedance of the booster of the High Energy Photon Source (HEPS) project, which has been treated in detail by Tian [17,18].Based on these results, the impedance model of the SAPS booster was obtained as shown in Fig. 7.The 5-cell copper cavity will be adopted, which is responsible for the Higher order modes (HOM) in the impedance spectrum.It should be noted that the fundamental mode at about 500 MHz of longitudinal impedance is also included.The booster is required to produce 3.5 GeV bunches at a repetition rate of 2 Hz.The bunch charge in the booster is 4.2 nC which corresponds to an average beam current of 5 mA.For the bare lattice, the threshold charge is simulated by using ELEGANT [19] as shown in Fig. 8.The head-tail instability is observed in the simulation for large bunch charge.However, this result shows that the instability threshold is significantly higher than the injected bunch charge of 4.2 nC.The booster is filled four bunches, and the beam current is approximately 20 mA.The transverse coupled bunch instability (TCBI) is mainly caused by two sources: the higher-order modes (HOM) of the RF cavity and the resistive wall impedance.The HOM impedance is larger than the threshold impedance [20].In order to avoid longitudinal and transverse coupled-bunch instabilities, the HOM must be well damped.For the resistive wall impedance, the stainless-steel round chamber is considered in the booster with the radius of 11 mm.The growth time in vertical plane can be calculated [21] and it is 0.78 ms at injection and 11 ms at extraction, respectively.We find that the TCBI growth time at the extraction energy is larger than the damping time (6.3 ms), effectively taming the instability.However, at injection energy, the beam is unstable due to the excessively long damping time.Therefore, a dampening scheme should be implemented in the booster.

Summary
The physics design of the FODO lattice is introduced in the paper and the dynamic in longitudinal plane is also presented.The impedance model is built with all essential vacuum components.The instability threshold is examined to estimate the limitations of beam current intensity and the damp scheme should be implemented in the booster, particularly during the injection energy stage.

Figure 1 .
Figure 1.Booster layouts and the optical parameters of one super-period.

14th
International Particle Accelerator Conference Journal of Physics: Conference Series 2687 (2024) 032003 IOP Publishing doi:10.1088/1742-6596/2687/3/0320033 the beam is also extracted from the booster in vertical plane.The extraction system consists of a Lambertson magnet, 4 bumper magnets and a kicker located upstream to the extraction point.

Figure 2 .
Figure 2. The DA and chromaticity curve of the bare lattice at injection point.

Figure 4 .
Figure 4.The ramping process of the booster.

Figure 5 .
Figure 5. Ramping cycle in the booster.

Figure 8 .
Figure 8.The threshold charge in the booster.

Table 1 .
The main parameters of the booster