1. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 1 Undulator Physics Update Heinz-Dieter Nuhn, SLAC / LCLS October 27, 2005 Response to Recommendations Tolerance Budget based on Genesis Simulations Electron Beam Parameter ‘Tolerances’ Wakefield Budget Response to Recommendations Tolerance Budget based on Genesis Simulations Electron Beam Parameter ‘Tolerances’ Wakefield Budget

2. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 2 Response to FAC Recommendations Response: With regards to the undulator, Radiation Physics simulations have shown that OTR foils are not likely to cause a problem if designed and used properly. A foil of 10 microns thickness or less used for a few shots at a time will not cause a problem. The use of the foil will be interlocked to the MPS system. Also, bunches will not be allowed to enter the undulator area while the OTR foil is performing an insert or remove motion (indeterminate position). Presently, the plan for the undulator OTR foils is being reduced down to an R&D project. We are removing the funds for actually building and installing OTR foils in the undulator area from the base line. We will still have the ability to measure the x and y beam sizes at every undulator break by using the secondary function of the Beam Finder Wire (BFW). Response: With regards to the undulator, Radiation Physics simulations have shown that OTR foils are not likely to cause a problem if designed and used properly. A foil of 10 microns thickness or less used for a few shots at a time will not cause a problem. The use of the foil will be interlocked to the MPS system. Also, bunches will not be allowed to enter the undulator area while the OTR foil is performing an insert or remove motion (indeterminate position). Presently, the plan for the undulator OTR foils is being reduced down to an R&D project. We are removing the funds for actually building and installing OTR foils in the undulator area from the base line. We will still have the ability to measure the x and y beam sizes at every undulator break by using the secondary function of the Beam Finder Wire (BFW). FAC April 2005 Recommendation: The radiation produced by scattering from OTR foils in the undulator is a concern. The Committee recommends that a plan be developed to minimize risk of damage to undulators from OTR screen use. FAC April 2005 Recommendation: The radiation produced by scattering from OTR foils in the undulator is a concern. The Committee recommends that a plan be developed to minimize risk of damage to undulators from OTR screen use.

3. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 3 Response to FAC Recommendations Response: The need for the upstream beam monitor, i.e. the Beam Finder Wire (BFW), comes from the tight tolerances for positioning the electron beam on the undulator axis as defined during the tuning procedure. While this alignment can be achieved using a portable wire position monitor system, using such a system requires extended tunnel access during the commissioning process after a straight electron beam trajectory has been established with the beam-based alignment procedure. The BFW will provide a beam-based measurement, and allow this alignment task to be accomplished from the control room without the need for tunnel access. The portable wire position monitor system will serve as a backup. Response: The need for the upstream beam monitor, i.e. the Beam Finder Wire (BFW), comes from the tight tolerances for positioning the electron beam on the undulator axis as defined during the tuning procedure. While this alignment can be achieved using a portable wire position monitor system, using such a system requires extended tunnel access during the commissioning process after a straight electron beam trajectory has been established with the beam-based alignment procedure. The BFW will provide a beam-based measurement, and allow this alignment task to be accomplished from the control room without the need for tunnel access. The portable wire position monitor system will serve as a backup. FAC April 2005 Recommendation: The procedure to align the undulator appears to be feasible and offers additional redundancy; however, the justification for an upstream beam monitor was not made clear. FAC April 2005 Recommendation: The procedure to align the undulator appears to be feasible and offers additional redundancy; however, the justification for an upstream beam monitor was not made clear.

4. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 4 Response to FAC Recommendations Response: We have studied more carefully the tolerances for alignment variations over both short and long term time-scales, and have devised an escalating series of beam-based correction levels, each with an associated time-scale and tolerable FEL power loss, as was suggested by the FAC in April 2005. The ‘bulls-eye’ diagram proposed by the FAC has been tagged “Kem’s Zones” and has been described in some detail in Paul Emma’s presentation. Briefly, the correction levels extend from shot-to-shot trajectory feedback systems, to hourly ‘micado’ steering algorithms, to daily weighted steering or ‘BBA-light’, to weekly BBA, and finally to semi-annual conventional alignment. The outcome of these studies has also served to define the tolerable trajectory drift errors over short term (BBA execution duration: 1 hr) and longer term (diurnal variations: 1 day). These tolerances are incorporated into the undulator Physics Requirements Document (PRD) 1.4-001 and serve as a guideline for the design of supports, temperature regulation, and BPM systems. Response: We have studied more carefully the tolerances for alignment variations over both short and long term time-scales, and have devised an escalating series of beam-based correction levels, each with an associated time-scale and tolerable FEL power loss, as was suggested by the FAC in April 2005. The ‘bulls-eye’ diagram proposed by the FAC has been tagged “Kem’s Zones” and has been described in some detail in Paul Emma’s presentation. Briefly, the correction levels extend from shot-to-shot trajectory feedback systems, to hourly ‘micado’ steering algorithms, to daily weighted steering or ‘BBA-light’, to weekly BBA, and finally to semi-annual conventional alignment. The outcome of these studies has also served to define the tolerable trajectory drift errors over short term (BBA execution duration: 1 hr) and longer term (diurnal variations: 1 day). These tolerances are incorporated into the undulator Physics Requirements Document (PRD) 1.4-001 and serve as a guideline for the design of supports, temperature regulation, and BPM systems. FAC April 2005 Recommendation: Concern remains about the ground settlement and stability of the undulator hall floor. The Committee recommends that LCLS project physicists quantify the allowable ground motion given the range of instrumentation available, and provide specifications on ground motion based on realistic day-to-day alignment and periodic beam-based alignment. The physics analysis should include study of the extent to which the systems can accommodate movements beyond the survey tolerances. FAC April 2005 Recommendation: Concern remains about the ground settlement and stability of the undulator hall floor. The Committee recommends that LCLS project physicists quantify the allowable ground motion given the range of instrumentation available, and provide specifications on ground motion based on realistic day-to-day alignment and periodic beam-based alignment. The physics analysis should include study of the extent to which the systems can accommodate movements beyond the survey tolerances.

5. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 5 Response to FAC Recommendations Response: The temperature stability tolerances for the undulator tunnel have been re-examined both with respect to their influences on the undulator magnetic field as well as to the positional stability of the quadrupoles and BPMs. GENESIS simulations of the effects of errors of the average K values for each undulator segment, both random and systematic, show that temperature errors from a uniform distribution with a width of ±1 degree F (±0.56 degrees C) are consistent with a total overall error budget for a 25% reduction in FEL power (but not taking credit for simple undulator x-position adjustments to compensate temperature variations). In parallel, a thermal expansion study was carried out at the APS with the result that for temperature changes of ±0.5 degree C the critical components will stay with in the position tolerances (±5 microns over 24 hours). Based on these analyses, which will be presented during the next FAC meeting, the temperature tolerances for the undulator tunnel have been relaxed. The requirement specification says now: “The absolute temperature along the Undulator will stay within a range of 20±0.6 °C at all times.” Response: The temperature stability tolerances for the undulator tunnel have been re-examined both with respect to their influences on the undulator magnetic field as well as to the positional stability of the quadrupoles and BPMs. GENESIS simulations of the effects of errors of the average K values for each undulator segment, both random and systematic, show that temperature errors from a uniform distribution with a width of ±1 degree F (±0.56 degrees C) are consistent with a total overall error budget for a 25% reduction in FEL power (but not taking credit for simple undulator x-position adjustments to compensate temperature variations). In parallel, a thermal expansion study was carried out at the APS with the result that for temperature changes of ±0.5 degree C the critical components will stay with in the position tolerances (±5 microns over 24 hours). Based on these analyses, which will be presented during the next FAC meeting, the temperature tolerances for the undulator tunnel have been relaxed. The requirement specification says now: “The absolute temperature along the Undulator will stay within a range of 20±0.6 °C at all times.” FAC April 2005 Recommendation: The very tight temperature tolerances in the undulator tunnel (+/- 0.2 C) have severe implications on controls. There are plans to put electronics in the ceiling air return duct where it will be difficult to maintain and concerns that the stepping motors will give off more heat than allowed. The air conditioning system necessary to maintain that temperature stability is also very expensive. The accelerator physicists should have a hard look to see if there is a way to increase this tolerance. FAC April 2005 Recommendation: The very tight temperature tolerances in the undulator tunnel (+/- 0.2 C) have severe implications on controls. There are plans to put electronics in the ceiling air return duct where it will be difficult to maintain and concerns that the stepping motors will give off more heat than allowed. The air conditioning system necessary to maintain that temperature stability is also very expensive. The accelerator physicists should have a hard look to see if there is a way to increase this tolerance.

6. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 6 LCLS Undulator Tolerance Budget Analysis Based On Time Dependent SASE Simulations in 2 Phases Simulation Code: Genesis 1.3 Simulate Individual Error Sources Combine Results into Error Budget Based On Time Dependent SASE Simulations in 2 Phases Simulation Code: Genesis 1.3 Simulate Individual Error Sources Combine Results into Error Budget

7. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 7 Parameters for Tolerance Study The following 8 errors are considered: Beta-Function Mismatch, Launch Position Error, Module Detuning, Module Offset in x, Module Offset in y, Quadrupole Gradient Error, Transverse Quadrupole Offset, Break Length Error. The ‘observed’ parameter is the average of the FEL power at 90 m (around saturation) and 130 m (undulator exit) The following 8 errors are considered: Beta-Function Mismatch, Launch Position Error, Module Detuning, Module Offset in x, Module Offset in y, Quadrupole Gradient Error, Transverse Quadrupole Offset, Break Length Error. The ‘observed’ parameter is the average of the FEL power at 90 m (around saturation) and 130 m (undulator exit)

8. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 8 Step I - Individual Study Time-dependent runs with increasing error source (uniform distribution) and different error seeds. Gauss fit to obtain rms-dependence. Detailed Analysis Description

9. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 9 Step I – Error 1b: Optics Mismatch Simulation and fit results of Optics Mismatch analysis. The larger amplitude data occur at the 114-m- point, the smaller amplitude data at the 80-m-point. Optics Mismatch (Gauss Fit) LocationFit rmsUnit 080 m0.58 114 m0.71 Average0.64 Transformation from negative exponential to Gaussian:  < 1.41 Y. Ding Simulations

10. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 10 Comparison of  vs.  /  0 1-  value Simplifies at waist location: + - or, resolved for 

11. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 11 Step I – Error 2: Transverse Beam Offset Transverse Beam Offset (Gauss Fit) / LocationFit rmsUnit 090 m25.1µm 130 m21.1µm Average23.1µm Simulation and fit results of Transverse Beam Offset (Launch Error) analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m- point. S. Reiche Simulations

12. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 12 Step I – Error 3: Module Detuning Module Detuning (Gauss Fit) LocationFit rmsUnit 090 m0.042% 130 m0.060% Average0.051% Simulation and fit results of Module Detuning analysis. The larger amplitude data occur at the 130-m- point, the smaller amplitude data at the 90-m-point. Z. Huang Simulations

13. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 13 Step I – Error 4: Horizontal Module Offset Horizontal Model Offset (Gauss Fit) LocationFit rmsUnit 090 m0782µm 130 m1121µm Average0952µm Simulation and fit results of Horizontal Module Offset analysis. The larger amplitude data occur at the 130-m- point, the smaller amplitude data at the 90-m-point. S. Reiche Simulations

14. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 14 Step I – Error 5: Vertical Module Offset Vertical Model Offset (Gauss Fit) LocationFit rmsUnit 090 m268µm 130 m268µm Average268µm Simulation and fit results of Vertical Module Offset analysis. The larger amplitude data occur at the 130-m- point, the smaller amplitude data at the 90-m-point. S. Reiche Simulations

15. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 15 Step I – Error 6: Quad Field Variation Quad Field Variation (Gauss Fit) LocationFit rmsUnit 090 m8.7% 130 m8.8% Average8.7% Simulation and fit results of Quad Field Variation analysis. The larger amplitude data occur at the 130-m- point, the smaller amplitude data at the 90-m-point. S. Reiche Simulations

16. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 16 Step I – Error 7: Transverse Quad Offset Error Transverse Quad Offset Error (Gauss Fit) LocationFit rmsUnit 090 m4.1µm 130 m4.7µm Average4.4µm Simulation and fit results of Transverse Quad Offset Error analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point. S. Reiche Simulations

17. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 17 Step I – Error 8: Break Length Error Break Length Error (Gauss Fit) LocationFit rmsUnit 090 m13.9mm 130 m20.3mm Average17.1mm Simulation and fit results of Break Length Error analysis. The larger amplitude data occur at the 130-m- point, the smaller amplitude data at the 90-m-point. S. Reiche Simulations

18. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 18 Step II - Tolerance Budget Assuming that each error is independent on each other (validity of this assumption is limited) Each should yield the same degradation Tolerance is defined for a given power degradation 1 - P/P 0 f 20 %0.236 25 %0.268 n = 8 tolerance fitted rms fi=xi/ifi=xi/i fi=xi/ifi=xi/i unit weights

19. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 19 Step III - Correlated Error Sources For the simplest approach, the tolerance budget assumes uncorrelated errors of 8 different sources. Some tolerances (e.g. the break length error) are very relaxed and can be reduced to relax other tolerances, i.e. use individual tolerances. Next step is to combine all error sources in the simulation. Include BBA and other correction scheme in the runs For the simplest approach, the tolerance budget assumes uncorrelated errors of 8 different sources. Some tolerances (e.g. the break length error) are very relaxed and can be reduced to relax other tolerances, i.e. use individual tolerances. Next step is to combine all error sources in the simulation. Include BBA and other correction scheme in the runs

20. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 20 Step II - Tolerance Budget (cont’) Error Source  i  i  f fifi  i  f i Units f=0.268 (25% red.)(24.2% red.) Hor/Ver Optics Mismatch (  -1) 0.5 0.640.190.4530.32 Hor/Ver Transverse Beam Offset235.70.1773.7µm Module Detuning  K/K 0.0510.0160.4020.024% Module Offset in x9523010.125140µm Module Offset in y268720.29880µm Quadrupole Gradient Error8.72.30.0280.25% Transverse Quadrupole Offset4.41.30.2151.0µm Break Length Error17.15.40.0481.0mm Can be mitigated through steering.  < 1.1

21. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 21 Model Detuning Sub-Budget Parameter p i Typical Value rms dev.  p i Note K MMF 3.50.0003±0.015 % uniform KK -0.0019 °C -1 0.0001 °C -1 Thermal Coefficient TT 0 °C0.32 °C±0.56 °C uniform without compensation KK 0.0023 mm -1 0.00004 mm -1 Canting Coefficient xx 1.5 mm0.05 mmHorizontal Positioning

22. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 22 e- beam Tolerances Parameter Fits Parameter  Param (rms ) Unit nn 0.72µm ½ I pk 0.91kA ½  p/p 0.025% Saturation after Undulator End 1.72 µm 2.57 kA 0.025 %

23. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 23 e - -Beam Quality ‘Tolerance Budget’ Beam Parameter  i  fifi  i  f i Units Parameter Limit (50.2% red.) nn 0.720.7570.55µm ½ <1.5 µm I pk 0.910.7800.70kA ½ >2.9 kA  p/p 0.0250.4800.012%<0.012 % Will keep saturation before undulator end Beam Parameter  i  fifi  i  f i Units Parameter Limit (35.7% red.) nn 0.720.5430.39µm ½ <1.35 µm I pk 0.910.5990.50kA ½ >3.1 kA  p/p 0.0250.4800.012%<0.012 % Uses only half the saturation length budget

24. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 24 Wakefield Budget Undulator Wakefield Sources: Resistive Wall Wakefields (ac conductivity) => Main Contributor Mitigation: Aluminum Surface, Rectangular Cross Section Surface Roughness Wakefields Mitigation: Limit roughness aspect ration to larger than 300. Total contribution small compared to resistive wall wakefields Geometric Wakefields Sources: Rectangular to Round Transition BFW Replacement Chamber Mis-Alignment RF Cavity BPMs Bellows Shielding Slots Flanges Pump Slots Total contribution small compared to resistive wall wakefields Undulator Wakefield Sources: Resistive Wall Wakefields (ac conductivity) => Main Contributor Mitigation: Aluminum Surface, Rectangular Cross Section Surface Roughness Wakefields Mitigation: Limit roughness aspect ration to larger than 300. Total contribution small compared to resistive wall wakefields Geometric Wakefields Sources: Rectangular to Round Transition BFW Replacement Chamber Mis-Alignment RF Cavity BPMs Bellows Shielding Slots Flanges Pump Slots Total contribution small compared to resistive wall wakefields

25. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 25 Short Break Section Chamber Profile Chamber Diameter 8 mm Undulator Chamber 5x10 mm Chamber Diameter 10 mm Undulator Chamber 5x10 mm Flange Gaps.5 mm RF Cavity Length 10 mm Bellows Shielding Slots Gaps 20 mm / 10% BFW Replacement Chamber Pump Slot There are now 5 flanges per short break section

26. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 26 Long Break Section Chamber Profile Courtesy of Dean Walters Chamber Diameter 8 mm Undulator Chamber 5x10 mm Chamber Diameter 10 mm Undulator Chamber 5x10 mm Flange Gaps.5 mm RF Cavity Length 10 mm Bellows Shielding Slots Gaps 20 mm / 10% BFW Replacement Chamber Pump Slot

27. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 27 Geometric Wakefield Budget Summary totalcore ComponentCharacterizationCount <><>  <><>  [%] Transitions5mm x 10mm 8 mm dia33-0.0430.027-0.0220.002 BFW Replacement0.5 mm @ 8 mm dia33-0.0360.022-0.0190.002 Total Transition -0.0800.049-0.0410.004 Shielded Bellows20 mm gap @ 10 mm dia48-0.0040.002-0.0040.000 RF Cavity BPM10 mm length @ 8 mm dia.33-0.0090.003-0.0080.001 Flanges0.5 mm gap @ 8 mm dia170-0.0100.003-0.0080.001 Pump Slots10 mm dia33-0.0040.002-0.0030.000 Total Diffraction -0.0270.010-0.0220.003 Beam Energy = 13.64 GeV Undulator Length = 132 m Charge = 1 nC Core Charge = 0.45 nC

28. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 28 Transition Model Wake Field Summary Total Bunch: = -82.2 keV/m (-0.080 %) W t,rms = 50.7 keV/m ( 0.049 %) Bunch Core: = -42.5 keV/m (-0.041 %) W c,rms = 4.4 keV/m ( 0.004 %) Total Bunch: = -82.2 keV/m (-0.080 %) W t,rms = 50.7 keV/m ( 0.049 %) Bunch Core: = -42.5 keV/m (-0.041 %) W c,rms = 4.4 keV/m ( 0.004 %)  -> 52.0 keV/m

29. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 29 Diffraction Model Wake Field Summary Total Bunch: = -26.6 keV/m (-0.026 %) W t,rms = 9.9 keV/m ( 0.009 %) Bunch Core: = -23.2 keV/m (-0.041 %) W c,rms = 2.7 keV/m ( 0.004 %) Total Bunch: = -26.6 keV/m (-0.026 %) W t,rms = 9.9 keV/m ( 0.009 %) Bunch Core: = -23.2 keV/m (-0.041 %) W c,rms = 2.7 keV/m ( 0.004 %)

30. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 30 Surface Roughness Wake Field Summary Total Bunch: = -13.0 keV/m (-0.013 %) W t,rms = 26.9 keV/m ( 0.026 %) Bunch Core: = 2.9 keV/m ( 0.003 %) W c,rms = 4.6 keV/m ( 0.004 %) Total Bunch: = -13.0 keV/m (-0.013 %) W t,rms = 26.9 keV/m ( 0.026 %) Bunch Core: = 2.9 keV/m ( 0.003 %) W c,rms = 4.6 keV/m ( 0.004 %) Aspect Ratio 300

31. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 31 Resistive Wall Wake Field Summary Total Bunch: = -82.6 keV/m (-0.080 %) W t,rms = 88.1 keV/m ( 0.085 %) Bunch Core: = -36.1 keV/m (-0.035 %) W c,rms = 79.8 keV/m ( 0.077 %) Total Bunch: = -82.6 keV/m (-0.080 %) W t,rms = 88.1 keV/m ( 0.085 %) Bunch Core: = -36.1 keV/m (-0.035 %) W c,rms = 79.8 keV/m ( 0.077 %) AC Conductivity Al, parallel plates AC Conductivity Al, parallel plates

32. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 32 Total Wake Field Summary Total Bunch: =-204.3 keV/m (-0.198 %) W t,rms = 127.2 keV/m ( 0.123 %) Bunch Core: = -98.8 keV/m (-0.096 %) W c,rms = 78.3 keV/m ( 0.076 %) Total Bunch: =-204.3 keV/m (-0.198 %) W t,rms = 127.2 keV/m ( 0.123 %) Bunch Core: = -98.8 keV/m (-0.096 %) W c,rms = 78.3 keV/m ( 0.076 %)  -> 52.0 keV/m

33. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 33 Total Wake Budget Summary totalcore Wakefield ComponentParameters <><>  <><>  [%] Transition Model-0.0800.049-0.0410.004 Diffraction Model-0.0260.009-0.0220.004 Surface Roughness-0.0130.026 0.0030.004 Resistive Wall-0.0800.085-0.0350.077 Total -0.1980.123-0.0960.076 Beam Energy = 13.64 GeV Undulator Length = 132 m Charge = 1 nC Core Charge = 0.45 nC

34. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 34 S. Reiche Simulations GENESIS Simulated

35. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 35 S. Reiche Simulations Al Al + 200 kV/m no wake

36. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 36 S. Reiche Simulations Al Al + 200 kV/m no wake

37. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 37 S. Reiche Simulations

38. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 38 S. Reiche Simulations

39. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 39 S. Reiche Simulations

40. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 40 Summary An undulator tolerance budget analysis based on GENESIS simulations was presented. Several critical tolerances have been relaxed: Temperature Stability is now  0.56 o C (was  0.1 o C) Vertical Segment Alignment is now 80 µm (was 70 µm) rms Short Term (1hr ) Quadrupole Stability  2 µm (was  1 µm in 10 hrs) Long Term (24hrs ) Quadrupole Stability  5 µm An undulator wakefield budget analysis is used to keep track of the various wakefield sources during the component design phase. An undulator tolerance budget analysis based on GENESIS simulations was presented. Several critical tolerances have been relaxed: Temperature Stability is now  0.56 o C (was  0.1 o C) Vertical Segment Alignment is now 80 µm (was 70 µm) rms Short Term (1hr ) Quadrupole Stability  2 µm (was  1 µm in 10 hrs) Long Term (24hrs ) Quadrupole Stability  5 µm An undulator wakefield budget analysis is used to keep track of the various wakefield sources during the component design phase.

41. Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC Nuhn@slac.stanford.edu 41 End of Presentation