Undulator Good Field Region and Tuning Strategy Heinz-Dieter Nuhn, SLAC / LCLS October 12, 2006

1. Undulator Good Field Region and Tuning StrategyHeinz-Dieter Nuhn, SLAC / LCLSOctober 12, 2006 • Tapering Requirements at 13.64 and 4.31 GeV • Field Integrals • Tapering Scenarios 1

2. Introduction • LCLS operation requires changes in strength (K-values) of the undulator segments for • Tapering, dependent on electron energy (DK/K=0.3 - 0.7 %) • K-sweep in support of beam-based K measurements (DK/K=±0.2 %) • Typically, one tunes an undulator at some fixed axis and then opens and closes the gap. This results in beam steering, which is normally removed with dipole correctors. • We create the K variation by shifting the undulators horizontally. • We tried tuning accurately over a broad transverse area (corresponding to DK/K=0.6 %) to be able to • tune all undulators to the same K value, • have full remove K adjustability, and • avoid K dependent dipole correctors. • Higher order multipoles, however, make tuning complex and difficult. • A revised tuning strategy is discussed in this presentation. 2

3. Tapering Requirements for the LCLS Undulators The LCLS tapering is considered for : • Compensation of spontaneous radiation (linear tapering over 132 m) • Compensation of vacuum chamber wakefields (linear tapering over 132 m, for 1nC) • Gain enhancement (linear tapering before saturation) • Enhanced energy extraction (linear tapering after saturation) The desirable total tapering range for 1 nC operation at 13.64 GeV [4.313 GeV] is thus • to saturation point • to undulator end 3

4. K Tapering Amplitudes • The ratio between changes in K and g to maintain the resonance condition at a given wavelength is • which translates the numbers in the previous slide to |DK/K| = |DB/B| = 0.32 % [0.35 % ] (at saturation point) |DK/K| = |DB/B| = 0.66 % [0.83 % ] (at undulator end) • PRD 1.4-001 requirement for the field fine adjustment range is set to 0.6 % 4

5. Figure 1: K Tapering Requirements K for segment 1 K for segment 33 1.5 Å spont  0.3 % wake gain post sat 15 Å spont  0.3 % gain wake post sat 5

6. Beff vs. x of 1st Article after Tuning Courtesy of Isaac Vasserman, ANL 6

7. Required Motion Range for 0.6 % Beff Change Isaac Vasserman fitted a 2nd order polynomial to his By(x) measurements resulting in with The fit was based on measurements taken roughly over a range of -5 mm < x < 5 mm The operational field for the first Undulator to have Keff=3.5 is B1=1.2595 T. For beam-based K measurement a sweep range of ±0.1% is desirable, i.e., Bstart=1.2507 T. PRD 1.4-001 requires a full tapering range for Beff of 0.6%, i.e., Bend = 1.2432 T. These two field values occur at xstart=-8.8 mm and xend=+1.5 mm, corresponding to a tuning range of The electron beam needs to run anywhere within this range, which makes is necessary that the undulator field exhibits the same good field quality over the entire range. 7

8. Figure 1: K Tapering Requirements K for segment 1 K for segment 33 1.5 Å spont  5.2 mm  0.3 % wake gain post sat 15 Å spont  5.2 mm  0.3 % gain wake post sat 8

9. Horizontal Field Integrals of 1st Article after Tuning Tolerances Courtesy of Isaac Vasserman, ANL 9

10. Vertical Field Integrals of 1st Article after Tuning 2nd Integral Tolerance 1st Integral Tolerance Courtesy of Isaac Vasserman, ANL 10

11. Isaac Vasserman Report (Summary) • Figures show result of tuning article 1 over the range of 5mm, as requested. • The horizontal field integrals are within tolerance over the entire X-region. • This is not the case for the vertical field due to a surprisingly strong octupole term. • An improvement can only be achieved with octupole shims, which we had not planned for. • The combination of dipole, sextupole and octupole shims is possible, but using them will require a lot of extra iterations. To do better requires a lot of extra efforts. • The homogeneity for  2 mm is easy to improve by a factor of 3 at least by changing the quadrupole at the upstream end, but this will make the integrals’ dependence on x outside of the 2 mm region worse. • The results shown here are just local, related to this particular device. Others could be better or worse. • If it will be decided to do more R&D related to tuning octupole components (for both vertical and horizontal fields) I am ready to help, 11

12. Mitigation Strategy 1: K Tapering Scenario (3 Bins) K for segment 33 K for segment 1 K at gap center 1.5 Å  0.12 %  2.0 mm 0.05% MinimumSweep Range K1 = 3.4979 K2 = 3.4931 K3 = 3.4889 15 Å Limit of good field region (± 2.0 mm) 12

13. Mitigation Strategy 2: K Tapering Scenarios (Continuous)Avoid Reliance on Good Field Region at 1.5 Å K at gap center K for segment 1 K for segment 33  0.12 %  2.0 mm 0.2 %Sweep Range K = 3.5002 - z × 0.000114 / m Limit of good field region (±2.0 mm) Initially more conservative approach. Replacements can be done based on binning. 13

14. Mitigation Strategy 3: Trajectory Correction The field integrals (I1x, I1y, I2x, I2y) cause kicks (x’(xseg), y’(xseg)) and displacements (x(xseg), y(xseg)) to the trajectory in both directions dependent on the horizontal segment position. These can be corrected using the trajectory correctors adjacent, i.e., upstream (A) and downstream (B), of each undulator segment. The upstream correctors are used to remove the 2nd field integrals: E is the electron energy, L is the distance between the correctors, e is the electron charge, and c the speed of light. The downstream correctors are used to remove both, the 1st field integrals and the kicks from the upstream correctors: 14

15. Trajectory Correction with Quadrupole Motion In the undulator system, quadrupole displacement (motion) is used to correct the trajectory. The relation between quadrupole motion Dr and change in trajectory kick Dr’ is With IgQ = 3 T being the nominal integrated quadrupole gradient. This removes the energy dependence from the four equations: These four functions will need to be calculated for each undulator. An example for the 1st article integrals are shown on the next slide. 15

16. Quadrupole Motion for Field Integral Compensation 16

17. Conclusion • As a result of the tuning experience with the first articles of the undulator production series, it has become clear that tuning over the full horizontal range as required in PRD 1.4-001 has proven difficult and time consuming. The good field region requirement needs to be reduced to ±2.0 mm. For this reason, not all undulators will be tuned to exactly the same K value. The tuning strategy has been changed to • Initially: Continuous Tuning • Tune the on-axis Keff for each undulator depending on the location that they will go. This will remove all interchangeability but relies the least on the good field region. • Long term option: Binned Tuning [Implemented if supported by tuning experience] • Tune three different groups with 11 identical segments in each. Each group having a different on-axis Keff. This will preserve some of the original interchangeability. • Initially, continuous tuning appears more conservative. During operation, binned tuning provides a better response time. The two strategies are compatible with each other. Migration into a binned tuning arrangement as part of the replacement program would make use of extra experience with tuning to wider good field regions. • Both strategies will provide sufficient tapering capabilities to cover, at 1.5 Å, spontaneous losses, wakefield losses, and gain enhancement. For longer wavelengths the reduced the reduced good field region is sufficient to compensate for spontaneous and wakefield losses to the end of the last segment (even if all segments are used). • To reduce steering effects during K-sweeps (as needed for beam-based K measurements), trajectory corrections dependent on horizontal segment position will be used. • We are asking for the committee's opinion on this topic. 17

18. End of Presentation 18