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

2. 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

3. 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)
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

4. 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

5. 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

6. 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.

7. 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

8. 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.

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 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.

10. 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

11. 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.

12. 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

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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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.

21. 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.

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