Undulator Physics Update Heinz-Dieter Nuhn, SLAC / LCLS October 12, 2004

1. Undulator Physics UpdateHeinz-Dieter Nuhn, SLAC / LCLSOctober 12, 2004 • FY2004 Parameter Change Summary • Canted Poles • Electromagnetic Quadrupoles • Wakefield Simulations including AC Conductivity

2. FEL Design Changes Since the May 2003 Lehman Review • Canted Undulator Poles • Remote Undulator Roll-Away and K Adjustment Function • Increase in Undulator Gap • Reduction in Maximum Beam Energy • Reduction in Quadrupole Gradient • Increase in Beta Function • Increase in Break Section Lengths •  Electromagnetic Quadruples Recent Change

3. Undulator Pole Canting Suggested by J. Pflueger, DESY • Canting comes from wedged spacers • 4.5 mrad cant angle • Gap can be adjusted by lateral displacement of wedges • 1 mm shift means 4.5 microns in gap, or 8.2 Gauss • Beff adjusted to desired value Source: Liz Moog

4. Undulator Roll-Away and K Adjustment Function Neutral; K=3.4965; Dx=+0.0 mm First; K=3.5000; Dx=-1.5 mm PowerTp; K=3.4804; Dx=+7.0 mm Last; K=3.4929; Dx=+1.5 mm RollAway; K=0.0000; Dx=+100 mm

5. Effective B field vs. x Measured slope of 6.6 Gauss/mm agrees with calculations(~ 5.7 Gauss/mm for 3 mrad cant) Field variation allowance between segments is DB/B = 1.5x10-4, or DB = 2 Gauss, which translates to Dx = 0.3 mm ( or 1 micron in gap) Source Liz Moog

6. RMS phase error at different x positions No significant dependence on X An RMS phase error of ~ 6.5 degree is an upper limit for near-perfect (~100%) performance Source Liz Moog

7. Period-averaged horizontal trajectories at 14.1 GeV (X in mm) Trajectories are all well behaved and well within the 2 mm tolerance for maximum walk-off from a straight line Source Liz Moog

8. Canting the poles helps in many ways • Facilitates final setting of Beff • Remote control of position allows run-time adjustment • Allows compensating for temperature effect on field strength: ±1.0°C temperature error would require ±1.2 mm lateral shift of undulator Source Liz Moog

9. Change in Undulator Quadrupole Technology • LCLS undulator contains 33 quadrupole magnets located in break sections. • Permanent magnet technology (PMQ) in the past • Now changed to electromagnet technology (EMQ) • Initial cost estimate $740k lower that costs budgeted for permanent magnet solution

10. Some of the reasons for using PMQ in the past • Sufficient for focusing of entire operational range • Sufficient for BBA • Small. Fit into small break sections • No heat dissipation. No cooling water requirements. • No magnet power supplies required. No wiring. • No problems from cooling water vibrations.

11. Quadrupole Functionality and PMQ Limitations • Three-fold purpose • (1) Focusing • Method: Focusing strength is reduced with beam energy. • PMQ sufficient because optimum gradient weakly dependent on energy. • (2) Beam steering • Method: Trajectory correction by transverse quad displacement • BBA will work but will leave small local bumps (significant Df) • Beam offsets can not be measured BBA can not be verified • (3) Undulator segment alignment • Method: Mechanical Quad-Undulator coupling is used to keep beam centered in Undulator. • BBA will leave PMQs ~20 mm (rms) off beam axis adding to the undulator segment alignment budget

12. Advantages of EMQ technology become apparent • Provide fast verification and refinement of quadrupole’s alignment with respect to beam position. Precision 2-3 mm with 20% gradient change. This will improve undulator segment alignment. • Extra space for EMQs now available due to increase in break section lengths. • EMQ can easily accommodate weak x and y dipole trim coils, removing need for additional vernier-movers on quadrupole. • Gradient tolerances for the undulator quadrupoles are very loose (4%). No need to standardize EMQ fields. • The costs of EMQs, including steering trims, power supplies, cooling water, and controls lower than costs budgeted for PMQs. • Power dissipation in magnets and cables does not present significant load for the HVAC and LCW system. This thermal load should not present a thermal stability or uniformity problem in the undulator hall. • Measurements of NLC prototype EMQs have demonstrated magnetic center stability against gradient changes, water flow, and thermal effects, well below that needed for the LCLS undulator quads. • EMQs provide beta-function adjustment. Present design will limit minimum beta-function at 14 GeV to 25 m with nominal value of 30 m.

13. Limitation of BBA based on PMQs Standard BBA leaves small local bumps Source: P. Emma

14. Quad Offset Detection with 20% Gradient Variation 14 mm offset 20% gradient change Offset prediction from fit using downstream BPMs Source: P. Emma

15. Improved BBA with EMQs Source: P. Emma

16. EMQ Magnet Parameters Magnet quantity 33 Magnet core steel length 7 cm Effective magnetic length 7.4 cm Magnet bore radius 0.4 cm Max. integrated gradient 3.6 T Nom. integrated gradient 3.0 T Max. pole-tip field 0.195 T Max. excitation current 52 A Turns / coil 6 Power dissipated in magnet 27 W Power dissipated in cables 356 W Water flow per magnet 0.5 gpm

17. EMQ Dipole Trim Parameters Magnet quantity 33 Effective magnetic length 7.4 cm Maximum dipole field 50 G Maximum excitation current 2 A Turns/coil 8 Power dissipated in magnet 0.06 W Power dissipated in cables 0.12 W Equivalent EMQ displacement  123 mm

18. Summary of Undulator Parameter Changes May 2003Today Undulator Type planar hybrid Magnet Material NdFeB Wiggle Plane horizontal Gap 6.0 6.8 mm Gap Canting Angle 0.0 4.5 mrad Period Length 30.0± 0.05 mm Effective On-Axis Field 1.325 1.249 T Effective Undulator Parameter K 3.630 ± 0.015% 3.500 ± 0.015% Module Length 3.40 m Number of Modules 33 Undulator Magnet Length 112.2 m Standard Break Lengths 18.7 - 18.7 - 42.148.2 - 48.2 - 94.9 cm Total Device Length 121.0131.9 m Lattice Type FODO Magnet Technology PMQ EMQ Quadrupole Core Length 5 7 cm Integrated QF Gradient 5.355 3.000 T Integrated QD Gradient -5.295-3.000 T Average b Function at 1.5 Å 18 30 m Average b Function at 15. Å 7.3 10 m

19. Performance Impact of Changes (1.5 Å) May 2003Today Change Electron Beam Energy 14.35 13.64 GeV -5.0 % Emittance 0.043 0.045 nm rad +5.2 % Avg. Electron Beam Radius 27 35 µm +27.5 % Avg. Electron Beam Divergence 1.6 1.3 µrad -17.5 % Peak Beam Power 49 46 TW -5.0 % FEL Parameter (3D) 0.00033 0.00032 -3.5 % Power Gain Length (3D) 4.2 4.3 m +3.6 % Saturation Length (w/o Breaks) 82 86 m +4.9 % Saturation Length (w/ Breaks) 89 101 m +13.5 % Peak Saturation Power 7.4 7.6 GW +2.5 %* Coherent Photons per Pulse 1.4×1012 1.5×1012 +2.5 %* Peak Brightness 1.5×1033 1.5×1033 ** +2.5 %* Average Brightness 4.6×1022 4.7×1022 ** +2.5 %* Peak Spont. Power per Pulse 91 73 GW -19.7 % *Increase due to 3D effects (reduction in diffraction due to beam radius increase) ** [Ph./s/mm2/mr2/.1%]

20. Resistive Wall Wakefield with AC Conductivity • Revised resistive wall wakefield theory by K. Bane and G. Stupakov. • Significant impact on bunch wake function • Study of impact on performance is underway using FEL simulations • Initial results are available.

21. Elegant Parmela space-charge compression, wakes, CSR, … Past Wake Function (dc Cu) Charge Distribution Start-To-End Simulations Convolution with Single Electron Wake Function Bunch Wake Function

22. Corrected Wake Function (ac+dc Cu)

23. Alternative Material : Aluminum (ac+dc Al)

24. S. Reiche: GENESIS 1.3 Wake Functions used in Simulations Wakefield effect equivalent to tapering Optimum taper when energy gain over Lsat is about 2 r ac+dc Cu Region of reasonable gain dc Al dc Cu ac+dc Al Gain for dc Cu and dc Al can be improved by actual undulator tapering

25. Elegant Genesis Parmela space-charge compression, wakes, CSR, … SASE FEL with wakes FEL Power Predicted by GENESIS Power at End: no wake: 12 GWdc Cu: 10 GWac Cu: 8 GWac Al: 5 GW S. Reiche: GENESIS 1.3 no wake ac Cu dc Cu ac Al Start-To-End Simulations

26. X-Ray Pulse Profile for Cu DC Model Deviation from earlier results due to accidental coarse phase space reconstruction S. Reiche: GENESIS 1.3

27. X-Ray Pulse Profile for Cu AC Model S. Reiche: GENESIS 1.3

28. X-Ray Pulse Profile for Al AC Model S. Reiche: GENESIS 1.3

29. Alternate Vacuum Chamber Cross Sections • Parallel plates reduce wakefield effect by 30-40%(as shown by K. Bane) • Elliptical or rectangular chamber with ratio 2:1 or larger is reasonable approximation. • This will be investigated with simulations.

30. Alternate Vacuum Chamber Radius ? • Present case: en    ID Gap  Period  Energy   Lsat     Psat[mm]   [cm] [cm]   [cm]    [GeV]    [m]    [GW] 1.20   0.5 0.68   3.00     13.64    101     7.6 1.65   0.5 0.68   3.00    13.64    130     4.9 • Maximum gap and period adjusted to keep the same power and keep the saturation length for 1.65 microns under 170 m: • Maximum gap case (Estimates): en    ID Gap  Period  Energy   Lsat    Psat[mm]   [cm] [cm]   [cm]     [GeV]    [m]     [GW] 1.20   1.0 1.20   3.85     14.05    127     7.6 1.65   1.0 1.20   3.85     14.05    167     4.6 • Extra 40 m of installed undulator needed, which will increase the impact from wakefields. [Under investigation] Requires redesign of the strongback assembly.

31. Wake Function Dependence on Radius (ac+dc Cu)

32. Wake Function Dependence on Radius (ac+dc Al)

33. Conclusions • Several Undulator Parameters have been Changed. • New K Adjustment and Roll-Away Option will aid undulator and FEL commissioning. • Move to EMQ technology to improve trajectory straightness • The newly recognized ac conductivity aspect of resistive wall impedance impacts the LCLS FEL performance. • Initial simulations with GENESIS 1.3 illustrate the expected effects: • Power Reduction • X-Ray Pulse Shortening • X-Ray Pulse Dependence on Electron Bunch Distribution Increased • Alternate Material Choices and Chamber Cross Sections are Investigated

34. End of Presentation