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LCLS Undulator Tolerance Budget Analysis

This document provides a detailed analysis of the tolerance budget for the LCLS Undulator, including simulations and fit results for various error sources.

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LCLS Undulator Tolerance Budget Analysis

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  1. Physics RequirementsHeinz-Dieter Nuhn, SLAC / LCLSOctober 20, 2005 • System Component Description • Tolerance Budget based on Genesis Simulations • Requirements and Procedures 1

  2. Far Hall Undulator Near Hall Linac Coherent Light Source 2

  3. 3

  4. Summary of Nominal Undulator Parameters Undulator Type planar hybrid Magnet Material NdFeB Wiggle Plane horizontal Gap 6.8 mm Period Length 30.0±0.05 mm Effective On-Axis Field 1.249 T Range of Effective Undulator Parameter K 3.500 - 3.493 (3.480) Tolerance for K ± 0.015% Accumulated Segment Phase Error Tolerance ± 10 degrees(at any point along segment) Segment Length 3.40 m Number of Segments 33 Undulator Magnetic Length 112.2 m Standard Break Lengths 47.0 - 47.0 - 89.8 cm Nominal Total Device Length 131.52 m Quadrupole Magnet Technology EMQ Nominal Quadrupole Magnet Length 7 cm Integrated Quadrupole Gradient 3.0 T 4

  5. Undulator Segment Prototype 5

  6. Short Break Section Components Beam Finder Wire RF Cavity BPM Undulator Segment Quadrupole Cherenkov Detector Undulator Segment 6 Courtesy of Dean Walters

  7. Long Break Section Components Beam Finder Wire Diagnostics Tank RF Cavity BPM Undulator Segment Quadrupole Cherenkov Detector Undulator Segment 7 Courtesy of Dean Walters

  8. Requirement Documents 8

  9. 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 9

  10. 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) 10

  11. 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 11

  12. Step I – Error1b: 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. Transformation from negative exponential to Gaussian: z < 1.41 Z. Huang Simulations 12

  13. Comparison of z vs. b/b0 Simplifies at waist location: + - or, resolved for b 1-s value 13

  14. Step I – Error 2: Transverse Beam Offset 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. 14

  15. Step I – Error 3: Module Detuning 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. 15

  16. Step I – Error 4: Horizontal Module Offset 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. 16

  17. Step I – Error 5: Vertical Module Offset 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. 17

  18. Step I – Error 6: Quad Field Variation 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. 18

  19. Step I – Error 7: Transverse Quad Offset Error 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. 19

  20. Step I – Error 8: Break Length Error 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. 20

  21. 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 tolerance fitted rms fi=xi/si unit weights n = 8 21

  22. 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 22

  23. Step II - Tolerance Budget (cont’) z < 1.1 Can be mitigated through steering. 23

  24. Model Detuning Sub-Budget 24

  25. 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 Beff adjusted to desired value 25

  26. Using Undulator Roll-Away and K Adjustment Function • Standard Undulator Segment Axis (SUSA) as defined during tuning process. • SUSA defines Girder Axis (GA) in neutral Segment position. • SUSA moves with Segment, GA does not. • Both axes refer to undulator fiducials. • GA is the basic reference line for the relative alignment of Beamline components. SUSA GA Neutral; K=3.5000; Dx=+0.0 mm PowerTp; K=3.4804; Dx=+8.5 mm SUSA GA SpontTp; K=3.4929; Dx=+3.0 mm RollAway; K=0.0000; Dx=+100 mm 26

  27. Segment K Adjustments for Overall Tapering • The following list contains the nominal K values for the 33 undulator segments for the 6.8 mm gap height: To compensate energy loss from spontaneous radiation This amount of tapering requires only a negligible adjustment for break lengths. After achieving goal performance, tapering beyond saturation point is desirable. (up to 0.6% total) 27

  28. Measurement of SASE Gain Using Rollout Undulator Segments can be removed by remote control from the end of the undulator. They will not effect radiation produced by earlier segments. 28

  29. Root Requirements for FEL Gain • Effective K Value ToleranceThe effective K value for each undulator along the electron path shall not deviate by more that ±0.024 % from its design value. • Undulator Tuning • Temperature Control • Undulator Segment Alignment • Pole Canting with Horizontal Position Control • Phase ToleranceThe average longitudinal electron bunch position shall not deviate by more that ±10 degrees of x-ray phase (±4 pm) from its design value over the distance of one gain length. • Trajectory Control (Tight Control and Stability of Quadrupole Centers) • Overlap ToleranceThe rms deviation between the transverse center of the electron beam and the center of the radiation field shall be less than 10% of the rms of the electron beam distribution. • Control and Stabilization of Launch Coordinates • Trajectory Control 29

  30. Implication from Phase Tolerance • Tight Phase Tolerance Requires • Extremely straight trajectory(~3 µm rms over 10 m) • Precise positioning of quadrupoles(±2 µm wrt. straight line) • Use of Beam Based Alignment (BBA) methods • Basic Conventional Alignment and Motion Strategy • Alignment of components as needed to start BBA • Monitoring of component motion during and between BBA procedures. The latter is to mitigate effects of ground motion and to lengthen time needed between BBA procedures. 30

  31. Main Alignment Monitoring Elements • Hydrostatic Leveling System Device (HLS) • Monitored Degrees of Freedom: y, pitch, and roll • Wire Position Monitoring Device (WPM) • Monitored Degrees of Freedom: x, yaw, and roll • Temperature Sensors • BPMs (Transverse Locations Tracked by HLS and WPM) 31

  32. Main Alignment Control Elements • Relative alignment between undulator segments and break section components will be achieved and maintained through common-girder mounting • Overall alignment are (remotely) controlled through Girder movement based on cam-shaft technology • During initial alignment • For quadrupole position control, i.e. beam steering during BBA • For compensation of ground motion effects etc. • Quadrupoles are used as beam steering elements • Main steering function comes from off-center dipole fields. Change is done through cam-based girder motion, which will align all girder components to the beam. • Dipole trim-windings are used for fine adjustments 32

  33. Girder Components Summary • Main girder components include • Beam Finder Wire • Undulator strongback arrangement mounted on horizontal slides • Vacuum chamber support • BPM • Quadrupole • WPM sensors • HLS sensors • (diagnostics components) • The undulator strongback arrangement (Segment) is mountable on and removable from the girder with the vacuum chamber in place and without compromising the alignment of the vacuum chamber • Segments will be taken off the girder for magnetic measurements • Segments need to be mechanically interchangeable • The complete Girder assembly will be aligned on the Coordinate Measurement Machine (CMM). 33

  34. Undulator Motion Summary • Remotely Controlled Motion: • Undulator: x • Provides control of undulator field on beam axis. • Horizontal slide stages move undulator strongback independent of Girder and vacuum chamber. • Girder: x, y, pitch, yaw, roll • Enables alignment of all beamline components to beam axis. • transverse motion of meeting girder ends can be coupled • roll motion capability is to be used to keep roll constant • Additional Manual Adjustments: • Rough CAM position adjustability relative to fixed support. • Quadrupole, BFW, Vacuum Chamber, and BPM position adjustability to Girder. 34

  35. Segment Alignment using Beam Finder Wire • Downstream quad and upstream monitor fiducialized to undulator ends • BBA facilitates alignment of downstream cradle end and straightens electron beam • Use Beam Finder Wire reading to determine and correct “loose” end offset • Monitoring System WPM and HLS provide real-time girder position information • Info can be used as feed-back for mover system to maintain initial alignment Before any BBA performed Quad Undulator Strongback After BBA: Quad, BPM and one end of undulator aligned Girder RF BPM Beam Finder Wire After centering of Upstream Monitor: Both ends of undulator aligned Beam 35

  36. Undulator – to – BFW AlignmentTolerance Budget Individual contributions are added in quadrature 36

  37. Undulator – to – Quad AlignmentTolerance Budget Individual contributions are added in quadrature 37

  38. Main Alignment Procedures Overview • Undulator Segment Tuning and Fiducialization (Establishes SUSA) • Quadrupole Fiducialization • Beam Finder Wire Fiducialization • Complete Component Installation and Alignment on Girder • Earth Field Compensation Measurement in Tunnel • Girder Installation and Pre-Alignment in Tunnel • Complete Installation and Checkouts of WPM and HLS • Undulator Segment Installation on Girder • Girder Alignment with Portable WPM / HLS • Continuous Component Position Monitoring through WPM and HLS • Beam-Based Alignment • Periodic Rebaselining to Correct for Ground Motion etc. 38

  39. Conventional Alignment Tolerance Overview 39

  40. Conclusions • The X-ray-FEL puts very tight tolerances on magnetic field quality, electron beam straightness, and Segment alignment. • Alignment tolerances from electron beam straightness requirements can not be achieved with conventional alignment but require Beam Based Alignment (BBA) Procedure. • Main task of conventional alignment and motion systems are • SUSA determination and fiducialization • Alignment of undulator segments (relative to adjacent quadrupole centers) • Conventional alignment as prerequisite for BBA • Provision of remotely controlled motion capability to support, alignment processes • Monitoring of component positions in the presence of ground motion etc. • Requirements and Specifications are available from the LCLS WEB site. • The main Physics Requirements Document (PRD) outlining the requirements for the undulator system is PRD1.4-001. 40

  41. End of Presentation 41

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