Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Suppression of injection bump leakage caused by sextupole magnets within a bump orbit
Introduction
Recent performance improvements of synchrotron radiation (SR) sources increase stored beam density. Although the high density contributes to the generation of brilliant and coherent photon beams, it causes the problem of shortened beam lifetime from electron–electron scattering in a bunch even in high-energy SR sources such as the 8-GeV SPring-8 [1], [2]. Thus, further low emittance conflicts with required long beam lifetime. The so-called top-up operation [3], [4] is a way to manage both the low emittance and the short beam lifetime.
In top-up operation, continuous beam injection at short intervals, e.g., 30 s, keeps the current approximately constant with a small current deviation, e.g., 0.1%. This means that the beam lifetime averaged over the period longer than the injection interval is, in a sense, equal to infinity. However, when the beam injection excites an oscillation of the stored beam with amplitude larger than the beam size, the photon beam experiments are disturbed. The excited oscillation effectively enlarges the stored beam emittance and modulates the photon beam intensity. Suppression of the stored beam oscillation is therefore crucial for achieving the ideal top-up operation for experimental users and for making the most of third generation SR sources.
The main causes for the transverse oscillation of the stored beam are two-fold. One cause is bump magnet errors, which can involve variations in the field patterns of the bump magnets, differences of the magnet configuration, differences in the magnet boundary conditions, magnet misalignments and parameters of the equivalent circuit of the magnet including the coaxial cables, etc. These magnet errors can be solved in principle by engineering improvement. The other cause is nonlinearity within an injection bump orbit. In general, sextupole magnets can be found within the bump orbit of third generation SR sources because dynamic stability of the stored beam requires more sextupole magnets. These sextupole magnets make the closing bump condition depend on the bump amplitude. Thus the bump orbit never closes for all amplitudes even when all bump magnets are powered ideally. Furthermore, this nonlinear effect causes a large oscillation and is the dominant perturbation for SPring-8. A long straight section (LSS) might make a nonlinearity-free bump orbit possible [5]. However, this solution is not easily applicable to existing and also to newly planned SR sources due to following reasons: (I) The necessary length for the injection gets longer as the stored beam energy is higher, (II) adoption of LSSs increases the construction cost and causes large scale modification in existing SR sources, and (III) LSSs are also valuable for generation of high-quality radiation and development of new radiation sources.
To suppress the injection bump leakage by the sextupole magnets, we have investigated the condition for minimum emittance of the bump leakage in the lowest order of a nonlinear perturbation. In the case where amplitude of the bump orbit is small, on the order of 0.01 m, the lowest nonlinear order mainly contributes to the leakage. We found that the minimum condition in the lowest order of the perturbation does not depend on the bump amplitude. This suggests that the optimization of the sextupole strengths can drastically reduce the oscillation excitation. The minimum condition is obtained by both optimizing the linear optics and satisfying a specific relation among integrated strengths of the sextupole magnets within the bump orbit.
We explain our suppression scheme in Section 2 and discuss its effect on the bump leakage in Section 3. We then describe how to enlarge the dynamic stability while suppressing the bump leakage in Section 4 and compare the calculation results with experimental ones for the case of SPring-8 in Section 5.
Section snippets
Proposed suppression scheme
The suppression scheme we present here is that of the bump leakage caused by the lowest order of the nonlinear perturbation. As we see later, the lowest- and second-order perturbations work as dipole and quadrupole field errors, respectively and have the different dependences on the bump amplitude. By utilizing the different dependences, our scheme can suppress both contributions simultaneously. First we describe the bump leakage by the sextupole magnets when the orbit comprises of four bump
Calculation of suppression effect on injection bump leakage
We estimate the effect of the proposed scheme on reducing the injection bump leakage, i.e., reduction of the stored beam oscillation by using the identical half-sine field patterns. In the calculation, the mirror symmetric arrangement of four bump magnets as shown in Fig. 1 was used. Within the bump orbit there are two sextupole families, S1 (=S4) and S2 (=S3) with integrated strengths and , respectively. To simplify the problem, the bump pulse width is made shorter than the revolution
Recovery of dynamic stability
In general a dynamic aperture (DA) of a ring accelerator must be large enough for stable beam injection. It is, however, difficult to realize sufficiently large DA for a low-emittance SR source. This is mainly due to strong sextupole magnets used for correcting large linear chromaticity. These strong magnets markedly excite harmful systematic resonance lines such as , , , where and are the horizontal and vertical betatron tunes, respectively, and is a multiple of the
Experimental results for suppression of injection bump leakage
We investigated the effect of the proposed suppression scheme experimentally in the SPring-8 storage ring. Four pulse bump magnets arranged almost the same way as shown in Fig. 1 generate the injection bump orbit. The strengths of the four bump magnets are adjusted so that the bump orbit closes at the peak amplitude. The bump pulse-width is 8.2 μs, which is larger than the revolution period of 4.79 μs. This means that the bump magnets kick a major part of the stored beam twice. Two families of
Summary
We propose a scheme to suppress the injection bump leakage caused by sextupole magnets within the bump orbit. The proposed scheme is based on suppression of the lowest order of the sextupole perturbation. Since this perturbation works as a dipole field error, the excited oscillation is suppressed for all bump amplitudes by optimizing both the linear optics and the strengths of sextupole magnets within the injection bump. This scheme can reduce the amplitude of the excited oscillation down to a
Acknowledgement
The authors wish to thank Dr. N. Kumagai and Dr. H. Ohkuma for their support and continuous encouragement. They would also like to express their sincere thanks to Dr. Louis Emery of the Advanced Photon Source who carefully read the manuscript and revised the English especially.
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