2020同步年報

Facility Status 093 of optimization of the magnetic field for an EPU. The optimization of a magnetic field consists of two parts: the first part is block selection and position determination, called magnet sorting; the second part is adjustment of the local magnetic field, called field shimming. If the mag- net sorting has better results, less time is required for field shimming. To develop an effective sorting algorithm in the construction of an EPU is hence important. Before elimi- nating errors, we must understand their source. Magnetic errors are classified generally into two groups: random and systematic. Random errors result primarily from the vari- ation of the characterizations of individual permanent mag- nets, such as the magnetic remanence, orientation of the magnetization and magnetic inhomogeneity. Mechanical error, especially the deflection of the backing beam, pro- duces systematic errors. The magnet group has developed an efficient sorting algorithm that measures the strength of the magnetic field of each magnet and the mechanical accuracy of the entire machine. Based on these data, the distribution of magnetic field of the entire machine after installation of magnets can be expected to proceed as follows. The method of simulated annealing is then used to find the best arrangement. This method is similar to a grad- ual cooling of liquids to form a crystalline state, as opposed to an amorphous state after a sudden cooling. This sorting code is effective. For example, with a phase-II EPU66, the r.m.s. phase error is as large as 30 o when the magnets are randomly arranged, and is significantly decreased to 4.1 o when the optimal arrangement is determined with the sorting algorithm, as seen in Fig. 2(a) . The results of that optimization optimize not only the phase error but also the trajectory of the electron beam, as seen in Fig. 2(b) . Field shimming of the magnetic field is applied in the final stage of tweaking the local magnetic field so as to optimize the performance. Several methods have been developed by the magnet group. The main approach is to perform a mechanical movement of magnets to a sub-millimetre extent. To perform tens of micro-scale adjustments, a move- ment of magnet blocks using a screw-driven wedge and slide mechanism is convenient, which is called virtual shim- ming; this method has been implemented for the TPS EPU and is almost a standard. The r.m.s. phase errors eventually decreased to 3.1°, as seen in Fig. 2(a) . These results maintain a great spectral intensity, even for a high harmonic energy. Schemes to Diminish Beam Dynamic Issues After improvement of the spectral intensity, the next issue is to minimize the net effect on an electron beam. The inte- gral along the actual trajectory of an electron beam must be considered. This integral can be divided into two parts, static and dynamic field integral. The inhomogeneity of the magnet blocks contributes static multipole errors, which become measurable using a stretched wire system. In the case of an EPU, there is a discrepancy of the field integral between separate phase modes, resulting in a phase- dependent multipole error. The magnet group manipulated iron shims with phase-dependent properties to solve this issue. Besides understanding the behaviour of an iron shim on a vertical and horizontal magnetization magnet block, symmetry theory has been used to determine the location of iron shims. After the implementation of iron shims, the vertical and horizontal field integrals of all phase modes were aligned within ± 15 G cm. The residual phase- independent field integral is generally decreased using magnet chips ( i.e . magic finger), located at both ends of an EPU. The best arrangement of the chips was selected based on simulated annealing. Flattening of the field integral distribution was specifically optimized in the range ± 20 mm. After shimming, the static field integrals are flattened within ± 25 G cm. As the true trajectory of an electron beam in an ID is wig- gling rather than linear, the static field integral can be used only to illustrate the case of an ID with a wide region of Fig. 2 : (a) Distribution of phase error for three cases: random arrangement, the best sorting and shimming result. The number in brackets represents r.m.s. phase error. (b) Trajectory of an electron beam for random and sorting arrangements of magnets.