Linear optics calibration and nonlinear optimization during the commissioning of the SSRF storage ring

Phase I commissioning of the SSRF storage ring on 3.0 GeV beam energy was started at the end of December 2007. A lot of encouraging results have been obtained so far. In this paper, calibrations of the linear optics during the commissioning are discussed, and some measured results about the nonlinearity given. Calibration procedure emphasizes correcting quadrupole magnetic coefficients with the Linear Optics from Closed Orbit (LOCO) technique. After fitting the closed orbit response matrix, the linear optics of the four test modes is substantially corrected, and the measured physical parameters agree well with the designed ones.     

基于LOCO的上海光源储存环线性光学参数校正

为了测量和校正线性光学参数,在上海光源储存环调束过程当中使用了基于响应矩阵的线性光学参数分析(LOCO)的方法。介绍了应用LOCO进行计算和校正的过程,包括：数值模拟得到束流位置探测器的测量精度对拟合结果的影响,调整四极铁电源电流强度来校正工作点和beta函数周期性的恢复。测量结果表明,在四极铁强度调整幅度在1.5%以内的情况下,储存环的束流光学参数成功地恢复到和设计值相当接近的状态,beta函数和色散函数畸变小于1%。通过束流光学参数的校正,使得在今后的工作当中可以轻松地控制储存环的工作模式。     

Design and first commissioning of a new mode with lower emittance in the SSRF storage ring

A new mode is designed with an emittance of 2.47 nm-rad at 3.0 GeV beam energy, lower than the nominal mode of the Shanghai Synchrotron Radiation Facility (SSRF) storage ring. Details of the linear optics design and the nonlinear optimization are presented in this paper. During Phase I commissioning of the storage ring we tested the new optics mode and some expected results were obtained. After restoring the linear optics by means of the linear optics with closed orbit technique, the main parameters of the real machine agree well with the designed values and the injection efficiency and beam lifetime are acceptable.     

Design and first commissioning of a new mode with lower emittance in the SSRF storage ring

A new mode is designed with an emittance of 2.47 nm-rad at 3.0 GeV beam energy, lower than the nominal mode of the Shanghai Synchrotron Radiation Facility （SSRF） storage ring. Details of the linear optics design and the nonlinear optimization are presented in this paper. During Phase I commissioning of the storage ring we tested the new optics mode and some expected results were obtained. After restoring the linear optics by means of the linear optics with closed orbit technique, the main parameters of the real machine agree well with the designed values and the injection efficiency and beam lifetime are acceptable.     

Excitation curve calibration for the SSRF magnet system

The needed electrical current for the magnet working under different energy loads can be easily calculated once the right relation between the magnet and the electrical current has been found. Therefore the excitation curve calibration for the magnet system is important to the SSRF. The measuring method on the magnet and the result of the excitation curve calibration are presented. The application of the excitation curve calibration for the bending magnet is given, and it is proved that the COD (Closed Orbit Distortion) and the working point of the storage ring are greatly affected by the current of the bending magnet.     

Excitation curve calibration for the SSRF magnet system

The needed electrical current for the magnet working under different energy loads can be easily calculated once the right relation between the magnet and the electrical current has been found. Therefore the excitation curve calibration for the magnet system is important to the SSRF. The measuring method on the magnet and the result of the excitation curve calibration are presented. The application of the excitation curve calibration for the bending magnet is given, and it is proved that the COD （Closed Orbit Distortion） and the working point of the storage ring are greatly affected by the current of the bending magnet.     

A design strategy of achievable linear optics for a complex storage ring lattice

A design strategy is discussed in this paper,and it provides much convenience for effectively exploring achievable linear optics and globally investigating the flexibility of a complex lattice with superperiodicity.A matching method of fractional steps,which means separately finding the standard cell setting and the matching cell setting,is adopted to simplify the complexity of the linear beam optics design in the complex lattice.The multi-objective genetic algorithm is used to find most of all the stable linear optics,and reach a target solution after multi-generational propagation,both in the standard cell and the matching cell.A fitting algorithm with gradient information is used to restore the periodicity and symmetry of the lattice,and finely adjust the linear optics for further optimization.This design strategy is applied in the Shanghai Synchrotron Radiation Facility(SSRF)storage ring,and the results are presented.     

Measurement of optics for the SSRF storage ring in commissioning

The Shanghai Synchrotron Radiation Facility (SSRF) is a low emittance third-generation synchrotron radiation light source. Some optics parameters of the storage ring were measured when commissioning. This report presents the common methods for measuring some optics parameters of the storage ring, including the betatron tune, beta function, chromaticity, natural chromaticity and dispersion. The results and analysis of measurement for the optics parameters are given here, which are indispensable for the orbit correction of the accelerator and the nonlinear optimization.     

Measurement of optics for the SSRF storage ring in commissioning

The Shanghai Synchrotron Radiation Facility (SSRF) is a low emittance third-generation synchrotron radiation light source. Some optics parameters of the storage ring were measured when commissioning. This report presents the common methods for measuring some optics parameters of the storage ring, including the betatron tune, beta function, chromaticity, natural chromaticity and dispersion. The results and analysis of measurement for the optics parameters are given here, which are indispensable for the orbit correction of the accelerator and the nonlinear optimization.     

New chromaticity compensation approach and dynamic aperture increase in the SSRF storage ring

Strong chromatic sextupoles used to compensate natural chromaticities in the third generation light source storage ring usually reduce dynamic aperture drastically.Many optimization methods can be used to find solutions that provide large dynamic apertures.This paper discusses a new optimization approach of sextupole strengths with step-by-step procedure,which is applied in the SSRF storage ring,and a better solution is obtained.Investigating driving terms generated by the sextupoles in every step can analyze their convergences and guide the weight setting among different terms in object function of the single resonance approach based on the perturbation theory.     

New chromaticity compensation approach and dynamic aperture increase in the SSRF storage ring

Strong chromatic sextupoles used to compensate natural chromaticities in the third generation light source storage ring usually reduce dynamic aperture drastically. Many optimization methods can be used to find solutions that provide large dynamic apertures. This paper discusses a new optimization approach of sextupole strengths with step-by-step procedure, which is applied in the SSRF storage ring, and a better solution is obtained. Investigating driving terms generated by the sextupoles in every step can analyze their convergences and guide the weight setting among different terms in object function of the single resonance approach based on the perturbation theory.     

A design strategy of achievable linear optics for a complex storage ring lattice

A design strategy is discussed in this paper,and it provides much convenience for effectively exploring achievable linear optics and globally investigating the flexibility of a complex lattice with super-periodicity.A matching method of fractional steps,which means separately finding the standard cell setting and the matching cell setting,is adopted to simplify the complexity of the linear beam optics design in the complex lattice.The multi-objective genetic algorithm is used to find most of all the stable linear optics,and reach a target solution after multi-generational propagation,both in the standard cell and the matching cell.A fitting algorithm with gradient information is used to restore the periodicity and symmetry of the lattice,and finely adjust the linear optics for further optimization.This design strategy is applied in the Shanghai Synchrotron Radiation Facility（SSRF） storage ring,and the results are presented.     

Observation of beam instability in the SSRF storage ring

During the SSRF(Shanghai Synchrotron Radiation Facility) storage ring phase-I commissioning, some instabilities have been observed, and the broadband impedance has also been measured. The primary instabilities at present stage are vertical beam blow up and resistive wall instability.     

Nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

In this paper, we present a rule to improve the nonlinear solution with frequency map analysis (FMA), and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF), and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented.     

Observation of beam instability in the SSRF storage ring

During the SSRF(Shanghai Synchrotron Radiation Facility) storage ring phase-I commissioning, some instabilities have been observed, and the broadband impedance has also been measured. The primary instabilities at present stage are vertical beam blow up and resistive wall instability.     

Nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

In this paper, we present a rule to improve the nonlinear solution with frequency map analysis （FMA）, and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF）, and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented.     

Beam based alignment of the SSRF storage ring

There are 140 beam position monitors (BPMs) in the Shanghai Synchrotron Radiation Facility (SSRF) storage ring used for measuring the closed orbit. As the BPM pickup electrodes are assembled directly on the vacuum chamber, it is important to calibrate the electrical center offset of the BPM to an adjacent quadrupole magnetic center. A beam based alignment (BBA) method which varies individual quadrupole magnet strength and observes its effects on the orbit is used to measure the BPM offsets in both the horizontal and vertical planes. It is a completely automated technique with various data processing methods. There are several parameters such as the strength change of the correctors and the quadrupoles which should be chosen carefully in real measurement. After several rounds of BBA measurement and closed orbit correction, these offsets are set to an accuracy better than 10 μm. In this paper we present the method of beam based calibration of BPMs, the experimental results of the SSRF storage ring, and the error analysis.     

Beam based alignment of the SSRF storage ring

There are 140 beam position monitors （BPMs） in the Shanghai Synchrotron Radiation Facility （SSRF） storage ring used for measuring the closed orbit. As the BPM pickup electrodes are assembled directly on the vacuum chamber, it is important to calibrate the electrical center offset of the BPM to an adjacent quadrupole magnetic center. A beam based alignment （BBA） method which varies individual quadrupole magnet strength and observes its effects on the orbit is used to measure the BPM offsets in both the horizontal and vertical planes. It is a completely automated technique with various data processing methods. There are several parameters such as the strength change of the correctors and the quadrupoles which should be chosen carefully in real measurement. After several rounds of BBA measurement and closed orbit correction, these offsets are set to an accuracy better than 10 μm. In this paper we present the method of beam based calibration of BPMs, the experimental results of the SSRF storage ring, and the error analysis.     

Orbit response matrix analysis and lattice periodicity restoration of the SSRF storage ring

In this paper, we present numerically and experimentally the linear beam-optics distortion in the SSRF storage ring and the correction of optics by using a number of quadrupole magnets installed in the storage ring. The measured orbit-response matrices were fitted to the model-response matrices to obtain the β and the dispersion functions in the storage ring. By readjusting the currents of quadrupole-magnet power supplies, we were able to successfully restore the optics parameters to values very close to the design ones, with rms deviations around 1%. This periodicity restoration is verified with the β function measurement,     

Analysis of sextupole effects on 13 function beating in the SSRF storage ring

In a storage ring, asymmetry of the 13 function with momentum deviation is the main reason for asymmetry of the dynamic aperture. This paper applies simulation method based on AT code in Matlab to investigate sensitivity of the β function beating and the tune shift to quadrupole field error with the presence of bending field error in the Shanghai Synchrotron Radiation Facility (SSRF) storage ring. Sextupole effect on the variation trend is analyzed. Dynamics of the lattice for working points close to and away from the second order structural resonance stop-band are compared. These results show that the β function beating with momentum deviation doesn't lie in the influence of the second order structural resonance stop-bands completely, but it is relevant to lattice structure.