1. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Physics Requirements and Alignment Heinz-Dieter Nuhn, SLAC / LCLS April 7, 2005 Final Break Length Choice Mitigation of AC Conductivity Wakefield Effects Undulator Tolerance Budget Considerations Cradle Component Arrangement and Alignment Earth Magnetic Field Compensation Radiation Damage Calculations Final Break Length Choice Mitigation of AC Conductivity Wakefield Effects Undulator Tolerance Budget Considerations Cradle Component Arrangement and Alignment Earth Magnetic Field Compensation Radiation Damage Calculations

2. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths Old Strategy Characteristic Lengths Length of Undulator Strongback (Segment): L seg = 3.4 m Distance for 113 x 2  Phase Slippage: L 0 = 3.668 m Distance for 2  Phase Slippage in Field Free Space: L inc = u (1+K 2 /2) = 0.214 m Standard Break Lengths Used Use parameter n to characterize different phase length choices L n = L 0 - L seg +(n-1)L inc Use 2 Short Breaks Followed by 1 Long Break in n-Pattern 2 – 2 – 4 [0.482 m – 0.482 m – 0.910 m] Fine Tuning of Initial Break Length Suggested by N. Vinokurov based on Simulations by R. Dejus and N. Vinokurov using Linear Simulation Code, RON Small length increases for first 3 break lengths [0.045 m – 0.020 m – 0.005 m] Total Undulator Length (from beginning of strongback 1 – end of strongback 33): L und = 131.97 m Characteristic Lengths Length of Undulator Strongback (Segment): L seg = 3.4 m Distance for 113 x 2  Phase Slippage: L 0 = 3.668 m Distance for 2  Phase Slippage in Field Free Space: L inc = u (1+K 2 /2) = 0.214 m Standard Break Lengths Used Use parameter n to characterize different phase length choices L n = L 0 - L seg +(n-1)L inc Use 2 Short Breaks Followed by 1 Long Break in n-Pattern 2 – 2 – 4 [0.482 m – 0.482 m – 0.910 m] Fine Tuning of Initial Break Length Suggested by N. Vinokurov based on Simulations by R. Dejus and N. Vinokurov using Linear Simulation Code, RON Small length increases for first 3 break lengths [0.045 m – 0.020 m – 0.005 m] Total Undulator Length (from beginning of strongback 1 – end of strongback 33): L und = 131.97 m

3. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths GINGER Simulation Summary As undulator gets closer to construction phase lock-down of segment spacing is required. R. Dejus requests checking of RON results with nonlinear FEL simulation codes before break length distances are being frozen. Phase correction scheme was tested recently by Bill Fawley and Sven Reiche using non-linear FEL codes, GINGER and GENESIS, respectively. With canted poles, phase corrections can be implemented with K adjustments rather than break lengths adjustments. The simulations used changes in break length. As undulator gets closer to construction phase lock-down of segment spacing is required. R. Dejus requests checking of RON results with nonlinear FEL simulation codes before break length distances are being frozen. Phase correction scheme was tested recently by Bill Fawley and Sven Reiche using non-linear FEL codes, GINGER and GENESIS, respectively. With canted poles, phase corrections can be implemented with K adjustments rather than break lengths adjustments. The simulations used changes in break length.

4. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths GINGER Simulations Time Domain Results GINGER Simulations for three different applications of the Vinokurov/Dejus correction Reduced [-0.045 m, -0.020 m, -0.005 m] Nominal Increased [+0.045 m, +0.020 m, +0.005 m] Increased lengths produce slightly more power but no significant change in gain length. GINGER Simulations for three different applications of the Vinokurov/Dejus correction Reduced [-0.045 m, -0.020 m, -0.005 m] Nominal Increased [+0.045 m, +0.020 m, +0.005 m] Increased lengths produce slightly more power but no significant change in gain length. William Fawley

5. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths GENESIS Simulations Time Domain Results GENESIS results comparable to those from GINGER. Sven Reiche

6. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths GINGER Simulations Spectrum During linear regime uncorrected break pattern gives best results. Towards end of undulator no significant effect of corrections General outcome: No need for break in regular break pattern. New break pattern will consist of 22 short and 10 long break lengths only. During linear regime uncorrected break pattern gives best results. Towards end of undulator no significant effect of corrections General outcome: No need for break in regular break pattern. New break pattern will consist of 22 short and 10 long break lengths only. William Fawley

7. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Break Lengths (Old Strategy) New Strategy Characteristic Lengths Length of Undulator Strongback (Segment): L seg = 3.4 m Distance for 113 x 2  Phase Slippage: L 0 = (3.668 m) 3.656 m Distance for 2  Phase Slippage in Field Free Space: L inc = u (1+K 2 /2) = 0.214 m Standard Break Lengths Used Use parameter n to characterize different phase length choices L n = L 0 - L seg +(n-1)L inc Use 2 Short Breaks Followed by 1 Long Break in n-Pattern 2 – 2 – 4 ([0.482 m – 0.482 m – 0.910 m]) [0.470 m – 0.470 m – 0.898 m] Fine Tuning of Initial Break Length Suggested by N. Vinokurov based on Simulations by R. Dejus and N. Vinokurov using Linear Simulation Code, RON Small length increases for first 3 break lengths [0.045 m – 0.020 m – 0.005 m] Total Undulator Length (from beginning of strongback 1 – end of strongback 33): L und = (131.97 m) 131.52 m Characteristic Lengths Length of Undulator Strongback (Segment): L seg = 3.4 m Distance for 113 x 2  Phase Slippage: L 0 = (3.668 m) 3.656 m Distance for 2  Phase Slippage in Field Free Space: L inc = u (1+K 2 /2) = 0.214 m Standard Break Lengths Used Use parameter n to characterize different phase length choices L n = L 0 - L seg +(n-1)L inc Use 2 Short Breaks Followed by 1 Long Break in n-Pattern 2 – 2 – 4 ([0.482 m – 0.482 m – 0.910 m]) [0.470 m – 0.470 m – 0.898 m] Fine Tuning of Initial Break Length Suggested by N. Vinokurov based on Simulations by R. Dejus and N. Vinokurov using Linear Simulation Code, RON Small length increases for first 3 break lengths [0.045 m – 0.020 m – 0.005 m] Total Undulator Length (from beginning of strongback 1 – end of strongback 33): L und = (131.97 m) 131.52 m

8. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Mitigation of AC-Conductivity Wakefield Effects Change Vacuum Pipe Properties (See Bane talk) Change Surface Material from Copper to Aluminum Change Cross Section from Round to Oblong (10x5 mm) Move to Low-Charge Operating Point (see Emma talk) Use Tapering to Enhance Gain (see Huang talk) Change Vacuum Pipe Properties (See Bane talk) Change Surface Material from Copper to Aluminum Change Cross Section from Round to Oblong (10x5 mm) Move to Low-Charge Operating Point (see Emma talk) Use Tapering to Enhance Gain (see Huang talk)

9. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Revisiting the Undulator Tolerance Budget Separate budgets exist for undulator tolerances Undulator Field Tuning Segment Alignment BBA Floor Stability A Monte Carlo model is being developed which simultaneously includes all of the above errors Calculates the cumulative phase error with MC statistics Shows the relative importance of different tolerances Next step is to test putative tolerance budgets against FEL code, including beam tolerances. Answer the question: For a give overall tolerance budget, what is the probability that the FEL flux will be above 10 12 photons/pulse? Separate budgets exist for undulator tolerances Undulator Field Tuning Segment Alignment BBA Floor Stability A Monte Carlo model is being developed which simultaneously includes all of the above errors Calculates the cumulative phase error with MC statistics Shows the relative importance of different tolerances Next step is to test putative tolerance budgets against FEL code, including beam tolerances. Answer the question: For a give overall tolerance budget, what is the probability that the FEL flux will be above 10 12 photons/pulse? Jim Welch

10. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Undulator Segment Alignment Tolerance Based on K Tolerance  K depends on vertical distance from mid-plane.  Canted poles make K also dependent on horizontal position Tolerance Amplitudes Horizontal +/- 180 microns Vertical +/- 70 microns Based on K Tolerance  K depends on vertical distance from mid-plane.  Canted poles make K also dependent on horizontal position Tolerance Amplitudes Horizontal +/- 180 microns Vertical +/- 70 microns

11. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Problem Characterization Two-Fold Problem for Segment Alignment  Initial installation and alignment to a straight line  Alignment maintenance in the presence of ground motion Two Strategies under Consideration Cradle Coupling (Train-Link) Upstream-Downstream Beam Position Monitors Two-Fold Problem for Segment Alignment  Initial installation and alignment to a straight line  Alignment maintenance in the presence of ground motion Two Strategies under Consideration Cradle Coupling (Train-Link) Upstream-Downstream Beam Position Monitors

12. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Problem Description BBA will only correct alignment of quadrupoles. Undulator segment alignment is not affected. Additional alignment strategy needed. BBA will only correct alignment of quadrupoles. Undulator segment alignment is not affected. Additional alignment strategy needed. Quad Vertical Before BBA After BBA Before BBA After BBA Horizonal

13. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Solution 1: Cradle Coupling (CLIC) Coupling will be adjusted on appropriately designed setup in MMF. Quadrupole motion during BBA will through coupled cradle motion. Cradles will be aligned in the process. Coupling will be adjusted on appropriately designed setup in MMF. Quadrupole motion during BBA will through coupled cradle motion. Cradles will be aligned in the process. Quad Vertical Before BBA After BBA Before BBA After BBA Horizonal

14. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Solution 2: Downstream Monitor Monitor downstream of the undulator, fiducialized to the strongback, will be used to correct undulator alignment after BBA. Monitor could be RF Cavity BPM (either the one used for BBA or additional) or a pair of wire scanners. Use of BBA BPM for the strongback alignment restricts freedom in BPM positioning. Monitor downstream of the undulator, fiducialized to the strongback, will be used to correct undulator alignment after BBA. Monitor could be RF Cavity BPM (either the one used for BBA or additional) or a pair of wire scanners. Use of BBA BPM for the strongback alignment restricts freedom in BPM positioning. Quad Vertical Before BBA After BBA Before BBA After BBA Horizonal Monitor

15. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Winning Candidate Monitor (wire scanner) upstream of the undulator fiducialized the strongback to control undulator alignment after BBA. RF Cavity BPM for BBA mounted next to quadrupole. Monitor (wire scanner) upstream of the undulator fiducialized the strongback to control undulator alignment after BBA. RF Cavity BPM for BBA mounted next to quadrupole. Quad Vertical Before BBA After BBA Before BBA After BBA Horizonal Monitor BPM Beam

16. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Cradle Component Arrangement and Alignment Undulator – to – Quad Tolerance Budget Individual contributions are added in quadrature See R. Ruland Talk for discussion

17. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Earth Magnetic Field Compensation Strategy Earth Magnetic Field along Beam Trajectory in Undulator requires compensation. Estimated strength 0.43±0.06 Gauss : (0.18±0.03, -0.38±0.07,0.08±0.05) Gauss Based on Measurements by K. Hacker. (see LCLS-TN-05-4) Compensation Strategy: Position the Undulator on Magnetic Measurement Bench in same direction as in Undulator Tunnel. Add correction field if necessary. Compensate Earth Field Component in Undulator in Shimming Process Scheduling Issues Earth Magnetic Field along Beam Trajectory in Undulator requires compensation. Estimated strength 0.43±0.06 Gauss : (0.18±0.03, -0.38±0.07,0.08±0.05) Gauss Based on Measurements by K. Hacker. (see LCLS-TN-05-4) Compensation Strategy: Position the Undulator on Magnetic Measurement Bench in same direction as in Undulator Tunnel. Add correction field if necessary. Compensate Earth Field Component in Undulator in Shimming Process Scheduling Issues

18. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Earth Magnetic Field Compensation Schedule Issues Milestone Dictionary 07/03/2006 Delivery of Undulator 1st Articles to MMF (MS2_UN010) 07/28/2006 27% Production Undulators Received (MS3_UN015) 07/28/2006 MMF Qualified & Ready to Measure Prod Undulators (MS3_UN005) 08/28/2006 MMF Qualified & Ready to Measure Prod Undulators (MS2_UN005) 10/17/2006 50% Production Undulators Received (MS3_UN022) 01/03/2007 75% Production Undulators Received (MS3_UN027) 03/09/2007 Undulator Production Unit (33) Received (MS3_UN029) 05/03/2007 Undulator Facility Beneficial Occupancy (MS3BO_035) 07/02/2007 Undulator Facility Beneficial Occupancy (MS2BO_035) 07/18/2008 Start Undulator Commissioning (1st Light ) (MS3_UN025) 08/18/2008 Start Undulator Commissioning (1st Light ) (MS2_UN025) Undulator Hall Beneficial Occupancy occurs 2 months after 33 rd undulator is received. Undulator Hall Magnetic Field can not be measured before tuning of most of the undulator segments is complete Risk that field found in undulator hall is different from field used during shimming. Tolerance for error field is 0.1 G. Milestone Dictionary 07/03/2006 Delivery of Undulator 1st Articles to MMF (MS2_UN010) 07/28/2006 27% Production Undulators Received (MS3_UN015) 07/28/2006 MMF Qualified & Ready to Measure Prod Undulators (MS3_UN005) 08/28/2006 MMF Qualified & Ready to Measure Prod Undulators (MS2_UN005) 10/17/2006 50% Production Undulators Received (MS3_UN022) 01/03/2007 75% Production Undulators Received (MS3_UN027) 03/09/2007 Undulator Production Unit (33) Received (MS3_UN029) 05/03/2007 Undulator Facility Beneficial Occupancy (MS3BO_035) 07/02/2007 Undulator Facility Beneficial Occupancy (MS2BO_035) 07/18/2008 Start Undulator Commissioning (1st Light ) (MS3_UN025) 08/18/2008 Start Undulator Commissioning (1st Light ) (MS2_UN025) Undulator Hall Beneficial Occupancy occurs 2 months after 33 rd undulator is received. Undulator Hall Magnetic Field can not be measured before tuning of most of the undulator segments is complete Risk that field found in undulator hall is different from field used during shimming. Tolerance for error field is 0.1 G.

19. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 0.1-Gauss Earth’s field in x-direction – perfect system, quads on, no steering Paul Emma Earth Magnetic Field Effect on Trajectory 0.1-Gauss Earth’s field in x-direction – perfect system, after BBA

20. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 0.1-Gauss Earth’s field in x-direction – standard errors, after BBA no Earth’s field – standard errors, after BBA Paul Emma Earth Magnetic Field Effect on Trajectory

21. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu 0.2-Gauss Earth’s field in x-direction – standard errors, after BBA Earth Magnetic Field Effect on Trajectory 0.1-Gauss Earth’s field in x-direction – standard errors, after BBA Paul Emma

22. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Earth Magnetic Field Compensation Adjustable Shim Concept Risk arises from the lack of precise knowledge of the earth field in the tunnel at the time of undulator segment tuning. Considering mitigation strategy based on use of a small number of precisely adjustable shims along each undulator. One extra shim per segment will reduce phase error by factor 4. Shims could be installed before undulator tuning, but adjusted before undulator installation when field errors have been determined. Will not affect definition of magnetic center of undulator (Standard Undulator Axis, SUSA, [see PRD 1.4-001 4.7]) Risk arises from the lack of precise knowledge of the earth field in the tunnel at the time of undulator segment tuning. Considering mitigation strategy based on use of a small number of precisely adjustable shims along each undulator. One extra shim per segment will reduce phase error by factor 4. Shims could be installed before undulator tuning, but adjusted before undulator installation when field errors have been determined. Will not affect definition of magnetic center of undulator (Standard Undulator Axis, SUSA, [see PRD 1.4-001 4.7]) Quad BPM Undulator Shim PositionTrajectory w/ Shim Trajectory w/o Shim QuadBPM

23. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Radiation Damage Calculations from Inserted Screen Question: Can OTR Screen be used in the LCLS undulator without causing significant radiation damage to the magnets? Problem Setup and Initial FLUKA Simulations by A. Fasso (To be published as SLAC RADIATION PHYSICS NOTE) Question: Can OTR Screen be used in the LCLS undulator without causing significant radiation damage to the magnets? Problem Setup and Initial FLUKA Simulations by A. Fasso (To be published as SLAC RADIATION PHYSICS NOTE) Screen MaterialDiamond Screen Thickness100 microns Screen Location41 cm Upstream of 1 st Und Bunch Charge1 nC Bunch Repetition Rate120 Hz Electron Energy13.64 GeV Simulated Undulator Length83 m

24. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Radiation Damage Calculations from Inserted Screen Longitudinal Distribution of Dose Deposited in Magnets (3) Alberto Fassò

25. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Radiation Damage Measurements on NdFeB Change in Intrinsic Remnant Induction from Fast –Neutron Irradiation in 252 Cf Spectrum [Fig 16 from J. Alderman, P.K. Job, R.C. Martin, C.M. Simmons, G.D. Owen, J. Puhl, “Radiation-Induced Demagnetization of Nd-Fe-B Permanent Magnets,” APS Report LS-290 (2000)] On-set of field change at 10 14 n/cm 2. Fast-Neutron Fluence most likely source of damage.

26. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Radiation Damage Calculations from Inserted Screen Longitudinal and Vertical Distribution of Neutron Fluence (6a) Alberto Fassò [cm] Maximum at 10 13 n/cm 2 /day n/cm 2/ /day n/cm 2 /electron

27. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Radiation Damage Calculations from Inserted Screen Damage clearly observed for neutron fluences of the order of 10 14 n/cm 2 by J. Alderman, P.K. Job, R.C. Martin, C.M. Simmons, G.D. Owen, and J. Puhl, “Radiation-Induced Demagnetization of Nd-Fe-B Permanent Magnets,” APS Report LS-290 (2000) Integrated levels of neutron fluences of 10 14 n/cm 2 would be reached after 10 days for 120 Hz, 1 nC, when keeping a 100 micron thick screen continuously inserted. Integrated radiation doses can be strongly reduced under controlled operation at 10 Hz,.1 nC, with a 1-micron thick screen. This increases time to reach integrated fluence levels at continuous use to more than 300 years. The planned occasional use of OTR screens should not present any problem. Damage clearly observed for neutron fluences of the order of 10 14 n/cm 2 by J. Alderman, P.K. Job, R.C. Martin, C.M. Simmons, G.D. Owen, and J. Puhl, “Radiation-Induced Demagnetization of Nd-Fe-B Permanent Magnets,” APS Report LS-290 (2000) Integrated levels of neutron fluences of 10 14 n/cm 2 would be reached after 10 days for 120 Hz, 1 nC, when keeping a 100 micron thick screen continuously inserted. Integrated radiation doses can be strongly reduced under controlled operation at 10 Hz,.1 nC, with a 1-micron thick screen. This increases time to reach integrated fluence levels at continuous use to more than 300 years. The planned occasional use of OTR screens should not present any problem.

28. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu Conclusions Break lengths structure simplified and finalized AC conductivity risk can be mitigated. (Al, Oblong Cross-Section, Gain Tapering) Fine tuning of undulator tolerance budget is underway. Cradle component arrangement issues are being addressed. Mitigation for insufficient knowledge of earth field component inside undulator hall is under investigation. System for radiation damage calculations has been set up for FLUKA. Initial result look supportive for use of OTR screens. Break lengths structure simplified and finalized AC conductivity risk can be mitigated. (Al, Oblong Cross-Section, Gain Tapering) Fine tuning of undulator tolerance budget is underway. Cradle component arrangement issues are being addressed. Mitigation for insufficient knowledge of earth field component inside undulator hall is under investigation. System for radiation damage calculations has been set up for FLUKA. Initial result look supportive for use of OTR screens.

29. Undulator Physics Requirements April 7, 2005 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting Nuhn@slac.stanford.edu End of Presentation