Magnetic Field optimization of EPU at TPS Ting-Yi Chung Magnet group, NSRRC, Taiwan IMMW19, October 27, 2015

Outline EPU at TPS Error source analysis and minimization Performance of EPU48 Beam-based study of dynamic multipole error of EPU56 at TLS Conclusion 2

EPU at TPS Two kinds of period and three APPLE-II type elliptically polarized undulators (EPU) total are designed, constructed, and installed in Phase-I at TPS. APPLE-II S.Sasaki et al, Nucl. Instr. Meth., A347,87 (1994) EPU46 EPU48 x2 Photon energy* (eV) 270-2000 230-2000 Deflection parameter 3.48/2.32 3.72/2.47 Period Length (mm) 46 48 Number of effective periods 82 67 Total physical length (m) 3.89 3.43 Range of magnet gap (mm) 13.5≦G≦110 13≦G≦120 Maximum field strength (T) By=0.81 Bx=0.54 By=0.83 Bx=0.55 Remanence NdFeB (T) ≧1.22 ≧1.24 * Operating at 3GeV

Requirements of APPLEII at a storage ring Error source analysis Requirements of APPLEII at a storage ring Desired properties of radiation. No net effect on an electron beam. Error sources : non-identical magnets in terms of geometry, magnetization direction or magnetic strength. Manufacturing error of mechanical assemble and machining. Phase error : degradation of the brilliance. Multipole error : impact on the electron beam. Systematic error (mechanical error). Random error (magnet block error). Static multipole error (mechanical and magnet block error). Dynamic multipole error (Intrinsic property, especially for the vertical linear mode). Prevention in design phase and treatment via the sorting and shimming process. 4

Minimization of mechanical error Design phase : to limit the effect of deflections and rotations of the magnet arrays so that the contribution to the r.m.s. phase error is less than 0.5o, corresponding to a gap variation of ±3um. Construction phase : In the case of EPU48, after mechanical and machining tuning, gap variation has been flattened from ± 75 to ± 20 um. This is able to improve the r.m.s. phase error from 9.8 to 3.4 degree. 5

Minimization of random error - Sorting Three steps in NSRRC: Individual blocks sorting : Each block measured by Helmholtz coil. Importing into RADIA code The resulting phase error < 2.3o for all modes. Sub-module 7 A sub-module with 7 or 9 blocks was measured to confirm quality. Obvious discrepancy in the horizontal distribution of the first field integral. => Measuring a practical magnetic field is necessary for an effective sorting.

Minimization of random error - Sorting , Three steps in NSRRC: Individual blocks sorting : Each magnet measured by Helmholtz coil. Importing into RADIA. Sub-modules holding 7 or 9 blocks sorting : Hall probe scan and stretched wire measurements. Optimization based on simulated annealing. 2-axis Hall probe (SENIS) Stretched wire (8 turns Litz wire) Submodule 7 and 9

Minimization of random error - Sorting , Three steps in NSRRC: Individual blocks sorting : Each magnet measured by Helmholtz coil. Importing into RADIA. Sub-modules holding 7 or 9 blocks sorting : Hall probe scan and stretched wire measurements. Optimization based on simulated annealing. The cost function consists of terms for multipole error and phase error, which means it takes into account the major influences on the electron beam and the spectrum. Weight factor E : cost energy, MP : multipole error term, ESy/x : error-storage (ES) with respect to vertical or horizontal direction, FSy/x field storage (FS), In represents the first field integral of the nth pole, and coefficients a … e are weight factors of each term.

Minimization of random error - Sorting , Three steps in NSRRC: Individual blocks sorting : Each magnet measured by Helmholtz coil. Importing into RADIA. Sub-modules holding 7 or 9 blocks sorting : Hall probe scan and stretched wire measurements. Optimization based on simulated annealing. The distribution of dI/I is not only the superposition of each sub-module data, but considering the interaction nearby an interface attributed to the non-unit effect. The contribution of the non-unit effect is periodic and up to 100Gcm.

Minimization of random error - Sorting After the second step sorting, the phase error contributed from magnets is suppressed to that from mechanical error, in the case of EPU48. 10

Minimization of random error - Shimming Three steps in NSRRC: Individual blocks sorting : Each magnet measured by Helmholtz coil. Importing the component of magnetization of each magnet into RADIA code to minimize the phase error in various polarization modes. Sub-modules holding 7 or 9 blocks sorting : Hall probe scan and stretched wire measurements. Magnetic field shimming : Phase error shimming : To improve straightness of trajectories, phase error, and static multipole error in all operation modes using a screw-driven wedge to move magnet blocks. Static multipole error shimming : To reduce the residual field integral using magnet chips and Fe-shim.

Trajectory Road map (straightness of trajectories) : After the submodule sorting, the straightness has been improved within ±11um. After shimming, it has even been improved within ±4um in all operation modes. 12

Phase error Road map (Phase error) : Phase errors for linear/circular mode are better than 2.5/4 degree. 13

Static multipole error Minimizing phase-dependent multipole error using iron shims. The difference of the vertical field integral of various modes with the HL mode Normal Quadrupole error 14

Static multipole error The residual phase independent field integral is decreased using magic fingers. Within ±15 mm, the horizontal and vertical field integrals are flattened within ±30 Gcm. After magic finger shimming

Dynamic multipole error APPLE-II has a gap between magnet rows and an inherent narrow Bx good field region, resulting in a so-called dynamic multipole errors. A shim pad design on magnets can improve roll off of vertical field By, but not of horizontal field Bx. The property of the narrow Bx good field region results in beam dynamics issues, especially at the vertical linear mode. electron 16

Minimizing dynamic multipole error Only VL mode needs at minimum gap, no inclined mode. TLS always at 1.5GeV. Passive compensation using L-shaped iron shims. electron EPU56 in TLS with 1.5GeV

Maintaining working tune Maintaining working tune as gap changes using L-shaped iron shims. Large horizontal defocusing Improving by a factor of 5 EPU56 in TLS with 1.5GeV No change of HL Slight Improving for others. Common vertical focusing

Improving injection efficiency A stable injection efficiency for all operating modes at the minimum gap 20 mm after shimming. A routine top-up operation is possible. EPU56 in TLS with 1.5GeV

Spectrum A demand from users that the third harmonic energy in a vertical linear mode must be smaller than the K-edge of absorption of nitrogen (~410 eV) for the resonant inelastic x-ray scattering (RIXS) experiment.

Conclusion The error sources of APPLEII have been analyzed and compensated via the sorting and shimming processes in NSRRC. Both effective sorting and shimming algorithms are implemented to satisfy the multi-objective optimization of APPLEII. Phase-dependent and phase-independent multipole error are eliminated via iron shims and the magic finger structure. The dynamic multipole error of APPLEII is studied and compensated to fulfill the user’s requirement at TLS and also to prepare for the commissioning at TPS.

Thank for your attention. At the current status, the commissioning of three EPU at TPS is coming. Bless us. Thank for your attention.