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Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources

 引用本文: 沈思淇, 田顺强, 张庆磊, 等. 衍射极限环光源纵向束流注入非线性优化[J]. 强激光与粒子束, 2019, 31: 125101.
Shen Siqi, Tian Shunqiang, Zhang Qinglei, et al. Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources[J]. High Power Laser and Particle Beams, 2019, 31: 125101. doi: 10.11884/HPLPB201931.190196
 Citation: Shen Siqi, Tian Shunqiang, Zhang Qinglei, et al. Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources[J]. High Power Laser and Particle Beams, 2019, 31: 125101.

• 中图分类号: TL501

## Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources

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###### Author Bio: Shen Siqi (1991—), male, PhD student, majors in accelerator physics; shensiqi@sinap.ac.cn
• 摘要: 下一代同步辐射光源储存环动力学孔径较小，因而束流注入困难，可以通过纵向束流注入解决这一问题。为了使用更长的kicker脉冲，有必要降低高频频率以增加注入束流到储存束流的时移。因为同步辐射运动，时移更长的束流有更高的动量偏差，所以通过该方法进行注入需要储存环提供足够大的能量接受度和动力学孔径。用SSRF-U的候选磁聚焦结构来展示纵向束流注入非线性优化的可行方法。由一系列高频频率的最佳结果可知，低于界限频率时kicker脉冲不会继续增长。在束流模拟中，采用界限频率与合适六级铁强度，可使SSRF-U储存环束流注入达到最高效率。
• Figure  1.  Longitudinal beam injection shown in the synchrotron phase space

Figure  2.  The beam optics in one fold of the SSRF-U storage ring

Figure  3.  The available energy acceptance as a function of the amplitude of the tune variation with momentum

Figure  4.  The maximum distance of the fully injected beam to the stored beam as a function of the RF frequency

Figure  5.  Fractional tunes as functions of momentum deviation (top) and on- and off-momentum DAs (bottom)

Figure  6.  Injection efficiency as a function of the center position of the injected beam in the synchrotron phase space (shown as contour maps)

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•  [1] Wei Lai, Chen Yong, Wang Shaoyi, Fan Quanping, Zhang Qiangqiang, Zhang Zhong, Wang Zhanshan, Cao Leifeng.  Suppression of higher diffraction orders using quasiperiodic array of rectangular holes with large size tolerance . 强激光与粒子束, 2020, 32(7): 072002-1-072002-6. doi: 10.11884/HPLPB202032.200117 [2] Niu Haihua, Li Youtang, He Yuan, Zhang Bin, Wang Zhijun, Chen Weilong, Yuan Chenzhang, Jia Huan.  A novel adjustable aperture for beam current controlling at China-ADS low energy beam transport line . 强激光与粒子束, 2020, 32(5): 054004-1-054004-7. doi: 10.11884/HPLPB202032.190393 [3] Wu Xu, Tian Shunqiang, Zhang Qinglei, Zhang Wenzhi.  Operation stability improvement for synchrotron light sources by tune feedback system . 强激光与粒子束, 2020, 32(4): 045107-1-045107-8. doi: 10.11884/HPLPB202032.190270 [4] 张满洲, 王坤, 张庆磊, 田顺强, 姜伯承.  DEPU对上海光源储存环的影响与补偿 . 强激光与粒子束, 2017, 29(07): 075103-. doi: 10.11884/HPLPB201729.170014 [5] 朱家鹏, 徐宏亮, 冯光耀, 蓝杰钦.  用于太赫兹光源的准等时性储存环的设计 . 强激光与粒子束, 2012, 24(06): 1453-1457. doi: 10.3788/HPLPB20122406.1453 [6] 杨建成, 夏佳文, 武军霞, 夏国兴, 刘伟, 殷学军, 刘勇, 周雪梅, 冒立军.  Tune调制对HIRFL-CSRm动力学孔径影响的模拟研究 . 强激光与粒子束, 2005, 17(07): 0- . [7] 王琳, 李永军, 冯光耀, 张赫, 徐宏亮, 李为民, 刘祖平.  合肥光源储存环上八极磁铁的动力学效应分析 . 强激光与粒子束, 2005, 17(09): 0- . [8] 樊宽军, 冯光耀, 王相綦, 王琳, 尚雷, 裴元吉.  合肥光源储存环注入凸轨系统满能量注入可行性研究 . 强激光与粒子束, 2000, 12(05): 0- .

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##### 出版历程
• 收稿日期:  2019-06-03
• 修回日期:  2019-09-07
• 刊出日期:  2019-12-01

## Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources

• 中图分类号: TL501

### English Abstract

 引用本文: 沈思淇, 田顺强, 张庆磊, 等. 衍射极限环光源纵向束流注入非线性优化[J]. 强激光与粒子束, 2019, 31: 125101.
Shen Siqi, Tian Shunqiang, Zhang Qinglei, et al. Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources[J]. High Power Laser and Particle Beams, 2019, 31: 125101. doi: 10.11884/HPLPB201931.190196
 Citation: Shen Siqi, Tian Shunqiang, Zhang Qinglei, et al. Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources[J]. High Power Laser and Particle Beams, 2019, 31: 125101.
• Synchrotron radiation light sources, serving a large number of users for scientific experiments, have been developed with three generations over the past fifty years. Electron beam emittance was reduced from hundreds of nanometer-radians to sub nanometer-radians, which was pushed by users’ increasing requirements of photon brightness and coherence. With the progress of high-gradient magnet and high-precise alignment, a medium-sized light source employing the Multi-Bend Achromatic (MBA) lattice can obtain very low beam emittance down to the X-ray diffraction limit [1-3]. However, strong chromaticity-correcting sextupoles make the MBA lattice suffer from a smaller Dynamic Aperture (DA), with which it is difficult to transversely inject the electron beam off-axis into the storage ring[4-7]. Two new injection methods which are transversely on-axis were proposed to solve the problem of small DA. The first one is the Swap-out method[8-9], in which a dipole-typed kicker is applied to not only inject a bunch or a bunch train into the storage ring but also kick the stored bunches back to an accumulation ring for reuse or out of the storage ring. Longitudinal beam injection method[10-13], the second one, uses the dipole-typed kicker to bring new beam with its time or/and momentum off from the stored beam into the storage ring. By radiation damping, the injected beam then merges with the stored one in the synchrotron phase space.

A draft of the longitudinal beam injection method is shown in Fig. 1. The abscissa of this figure uses $c\tau$ that has a linear relation with the phase as

Figure 1.  Longitudinal beam injection shown in the synchrotron phase space

 $$c\tau = \frac{c}{{{f_{{\rm{RF}}}}}}\frac{{\varphi - {\rm{\text{π} }}}}{{2{\rm{\text{π} }}}}$$ (1)

where c is the speed of light, τ is the time offset, fRF is the frequency of the Radio Frequency (RF) system, and $\varphi$ is the RF phase. Shown as black points in Fig. 1, the injected beam with a time offset to the stored beam is kicked into the closed orbit after the kicker pulse rose. Full pulse of the kicker (the dash line), which includes flat rising and falling time, cannot be longer than a bucket interval in order not to disturb the stored beam. It has to be less than two nanoseconds with the RF system of 500 MHz. Technique to generate this very short pulse is a challenge in the longitudinal beam injection. A solution to this problem is to reduce the RF frequency. The time offset of the injected beam is expected to increase in this way, so that the pulse can be lengthened (to 10 ns with 100 MHz, for example). Because of the synchrotron motion, the beam with large time offset will have a high momentum deviation. In the lattice, a large energy acceptance is required for efficient beam injection. Enough off-momentum DA of the lattice, usually several times of the injected beam size, is necessary to capture all the particles. At the same time, tune with high momentum deviation should be controlled away from the linear resonances[14]. A careful nonlinear optimization for the lattice is necessary to get these good performances.

The Shanghai Synchrotron Radiation Facility (SSRF)[15-17] has an upgrade plan to reach the soft X-ray diffraction limit. The upgraded facility is named as SSRF-U. This paper takes a candidate lattice of the SSRF-U storage ring as example to present the nonlinear optimization strategy. The optimization results with different RF frequencies show whether and how it takes full advantage of the reduced RF frequency. Beam injection of the lattice was simulated with the critical RF frequency and the optimal harmonic sextupole gradients. All the particle tracking and simulation in this paper were implemented within the Accelerator Toolbox[18].

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