1. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Physics Update Heinz-Dieter Nuhn, SLAC / LCLS October 12, 2004 FY2004 Parameter Change Summary Canted Poles Electromagnetic Quadrupoles Wakefield Simulations including AC Conductivity FY2004 Parameter Change Summary Canted Poles Electromagnetic Quadrupoles Wakefield Simulations including AC Conductivity

2. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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 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 Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Pole Canting 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 B eff adjusted to desired value Source: Liz Moog Suggested by J. Pflueger, DESY

4. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Roll-Away and K Adjustment Function Neutral; K=3.4965;  x=+0.0 mmFirst; K=3.5000;  x=-1.5 mm Last; K=3.4929;  x=+1.5 mmRollAway; K=0.0000;  x=+100 mm PowerTp; K=3.4804;  x=+7.0 mm

5. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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  B/B = 1.5x10 -4, or  B = 2 Gauss, which translates to  x = 0.3 mm ( or 1 micron in gap) Source Liz Moog

6. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Period-averaged horizontal trajectories at 14.1 GeV Trajectories are all well behaved and well within the 2  m tolerance for maximum walk-off from a straight line (X in mm) Source Liz Moog

8. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Canting the poles helps in many ways Facilitates final setting of B eff 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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  ) 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  m (rms) off beam axis adding to the undulator segment alignment budget

12. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Advantages of EMQ technology become apparent Provide fast verification and refinement of quadrupole’s alignment with respect to beam position. Precision 2-3  m 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Limitation of BBA based on PMQs Standard BBA leaves small local bumps

14. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Quad Offset Detection with 20% Gradient Variation 20% gradient change 14  m offset Offset prediction from fit using downstream BPMs

15. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Improved BBA with EMQs

16. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Magnet quantity33 Magnet core steel length7 cm Effective magnetic length 7.4cm Magnet bore radius0.4 cm Max. integrated gradient  3.6 T Nom. integrated gradient  3.0 T Max. pole-tip field  0.195 T Max. excitation current  52A Turns / coil6 Power dissipated in magnet27W Power dissipated in cables356W Water flow per magnet0.5gpm Magnet quantity33 Magnet core steel length7 cm Effective magnetic length 7.4cm Magnet bore radius0.4 cm Max. integrated gradient  3.6 T Nom. integrated gradient  3.0 T Max. pole-tip field  0.195 T Max. excitation current  52A Turns / coil6 Power dissipated in magnet27W Power dissipated in cables356W Water flow per magnet0.5gpm EMQ Magnet Parameters

17. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Magnet quantity33 Effective magnetic length7.4 cm Maximum dipole field  50G Maximum excitation current  2A Turns/coil8 Power dissipated in magnet0.06W Power dissipated in cables0.12W Equivalent EMQ displacement  123  m Magnet quantity33 Effective magnetic length7.4 cm Maximum dipole field  50G Maximum excitation current  2A Turns/coil8 Power dissipated in magnet0.06W Power dissipated in cables0.12W Equivalent EMQ displacement  123  m EMQ Dipole Trim Parameters

18. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu May 2003Today Undulator Type planar hybrid Magnet Material NdFeB Wiggle Planehorizontal Gap6.06.8mm Gap Canting Angle0.04.5 mrad Period Length 30.0 ± 0.05mm Effective On-Axis Field1.3251.249 T Effective Undulator Parameter K3.630 ± 0.015% 3.500 ± 0.015% Module Length 3.40m Number of Modules 33 Undulator Magnet Length112.2m Standard Break Lengths18.7 - 18.7 - 42.1 48.2 - 48.2 - 94.9 cm Total Device Length121.0 131.9 m Lattice Type FODO Magnet TechnologyPMQEMQ Quadrupole Core Length 5 7cm Integrated QF Gradient 5.355 3.000 T Integrated QD Gradient-5.295 -3.000 T Average  Function at 1.5 Å 18 30m Average  Function at 15. Å7.3 10 m May 2003Today Undulator Type planar hybrid Magnet Material NdFeB Wiggle Planehorizontal Gap6.06.8mm Gap Canting Angle0.04.5 mrad Period Length 30.0 ± 0.05mm Effective On-Axis Field1.3251.249 T Effective Undulator Parameter K3.630 ± 0.015% 3.500 ± 0.015% Module Length 3.40m Number of Modules 33 Undulator Magnet Length112.2m Standard Break Lengths18.7 - 18.7 - 42.1 48.2 - 48.2 - 94.9 cm Total Device Length121.0 131.9 m Lattice Type FODO Magnet TechnologyPMQEMQ Quadrupole Core Length 5 7cm Integrated QF Gradient 5.355 3.000 T Integrated QD Gradient-5.295 -3.000 T Average  Function at 1.5 Å 18 30m Average  Function at 15. Å7.3 10 m Summary of Undulator Parameter Changes

19. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu May 2003TodayChange Electron Beam Energy14.3513.64GeV-5.0 % Emittance0.0430.045nm rad+5.2 % Avg. Electron Beam Radius2735µm+27.5 % Avg. Electron Beam Divergence1.61.3µrad -17.5 % Peak Beam Power4946TW-5.0 % FEL Parameter (3D)0.00033 0.00032 -3.5 % Power Gain Length (3D)4.24.3 m+3.6 % Saturation Length (w/o Breaks)8286m+4.9 % Saturation Length (w/ Breaks)89101m+13.5 % Peak Saturation Power7.47.6GW+2.5 %* Coherent Photons per Pulse1.4×10 12 1.5×10 12 +2.5 %* Peak Brightness1.5×10 33 1.5×10 33** +2.5 %* Average Brightness4.6×10 22 4.7×10 22** +2.5 %* Peak Spont. Power per Pulse9173GW-19.7 % *Increase due to 3D effects (reduction in diffraction due to beam radius increase) ** [Ph./s/mm 2 /mr 2 /.1%] May 2003TodayChange Electron Beam Energy14.3513.64GeV-5.0 % Emittance0.0430.045nm rad+5.2 % Avg. Electron Beam Radius2735µm+27.5 % Avg. Electron Beam Divergence1.61.3µrad -17.5 % Peak Beam Power4946TW-5.0 % FEL Parameter (3D)0.00033 0.00032 -3.5 % Power Gain Length (3D)4.24.3 m+3.6 % Saturation Length (w/o Breaks)8286m+4.9 % Saturation Length (w/ Breaks)89101m+13.5 % Peak Saturation Power7.47.6GW+2.5 %* Coherent Photons per Pulse1.4×10 12 1.5×10 12 +2.5 %* Peak Brightness1.5×10 33 1.5×10 33** +2.5 %* Average Brightness4.6×10 22 4.7×10 22** +2.5 %* Peak Spont. Power per Pulse9173GW-19.7 % *Increase due to 3D effects (reduction in diffraction due to beam radius increase) ** [Ph./s/mm 2 /mr 2 /.1%] Performance Impact of Changes (1.5 Å)

20. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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. 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Past Wake Function (dc Cu) ParmelaParmela ElegantElegant space-charge compression, wakes, CSR, … Start-To-End Simulations Convolution with Single Electron Wake Function Charge Distribution Bunch Wake Function

22. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Corrected Wake Function (ac+dc Cu)

23. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Alternative Material : Aluminum (ac+dc Al)

24. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Wake Functions used in Simulations Wakefield effect equivalent to tapering Region of reasonable gain Optimum taper when energy gain over L sat is about 2  ac+dc Cu dc Al dc Cu ac+dc Al Gain for dc Cu and dc Al can be improved by actual undulator tapering

25. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu FEL Power Predicted by GENESIS ParmelaParmela ElegantElegantGenesisGenesis space-charge compression, wakes, CSR, … SASE FEL with wakes Start-To-End Simulations ac Cu no wake dc Cu ac Al Power at End: no wake: 12 GW dc Cu: 10 GW ac Cu: 8 GW ac Al: 5 GW

26. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu X-Ray Pulse Profile for Cu DC Model Deviation from earlier results due to accidental coarse phase space reconstruction

27. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu X-Ray Pulse Profile for Cu AC Model

28. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu X-Ray Pulse Profile for Al AC Model

29. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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. 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Alternate Vacuum Chamber Radius ? Present case:  n ID Gap Period Energy L sat P sat [  m] [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):  n ID Gap Period Energy L sat P sat [  m] [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. Present case:  n ID Gap Period Energy L sat P sat [  m] [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):  n ID Gap Period Energy L sat P sat [  m] [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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Wake Function Dependence on Radius (ac+dc Cu)

32. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Wake Function Dependence on Radius (ac+dc Al)

33. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 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 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. Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu End of Presentation