1. Design and Measurement Results for the Permanent Magnet Undulators for the Linac Coherent Light Source Facility II D. Arbelaez BeMa2014, 01/02/2014

2. 2 Outline Basic HXR and SXR undulator parameters and design Undulator field requirements Tuning method analysis and design One meter prototype results Improved sorting procedure BeMa2014, 01/02/14

3. 3 LCLS-II Baseline Includes Delivery Of 21 Soft X-Ray And 32 Hard-X-Ray Undulator Segments LBNL Scope: 32 HXR 21 SXR LBNL SCOPE INCLUDES MEASUREMENT AND TUNING OF ½ OF ALL HXR UNDULATORS. LBNL SCOPE DOES NOT INCLUDE UNDULATOR CONTROL SYSTEM AND UNDULATOR INSTALLATION. LCLS-II Undulator Configuration BeMa2014, 01/02/14

4. Undulator Prototype Segment “HXU-32” Illustrates LBNL Fabrication And Assembly Scope Alignment Platform Strongback Encoder Flexure Drive System Structural Frame Single Magnet Module Controls 4 BeMa2014, 01/02/14

5. 5 A Modular Magnetic Structure Design has been Adopted for Efficient and Accurate Production Module Array with Strongback, ~3.4m Long 2 End Modules 3 Periodic Modules Strongback BeMa2014, 01/02/14

6. 6 Periodic Modules Incorporate the Basic Periodic Design and the Tuning Features HXR and SXR undulators use periodic modules with the appropriate pole and magnet mounts and tuning features Keeper (Aluminum) Pole Assemblies and Magnet Blocks VP Poles NdFeB Magnets VP Poles NdFeB Magnets Rotor Tuner Magnets Rotor Tuner Magnets Pole Assembly with SST flexure adjustment Magnet Blocks BeMa2014, 01/02/14

7. 7 Undulator Field Requirements HXR UndulatorSXR Undulator Period length (mm)2639 B eff @ 7.2mm gap> 1.01 T> 1.49 T |1/2 (1/K eff )  2 K eff /  x 2 | (1/mm 2 ) < 3.4 ×10 -4 < 6.8 x 10 -4 |  B x,y dz|< 40  Tm |  B y dz 2 |< 150  Tm 2 |  B x dz 2 |< 50  Tm 2 Phase Shake (rms) < 4  < 5  * Undulator System Physics Requirements Document (LCLSII-3.2-PR-0038) BeMa2014, 01/02/14

8. 8 Tuning Method and Error Analysis Analysis code was developed to analyze many of the possible fabrication errors and tuning methods Vertical pole position and permanent magnet rotors were chosen for tuning The two methods have different gap dependence for effective cancellation of errors over the entire gap range Simulation of Errors and Tuning Methods Vertical Pole Position PM rotor BeMa2014, 01/02/14

9. 9 Vertical Field Tuning Features Have Been Incorporated for Effective Tuning at All Gaps PM rotor Pairs: PM slugs, magnetized perpendicular to axis Rotate to change pole excitation Pair is counter-rotated to cancel axial fields Vertical pole position: Adjust the vertical position for By correction Maximum adjustment range is +50 / -100 μm Tighten To Lower Tighten To Raise Pivot BeMa2014, 01/02/14

10. 10 Horizontal Field Tuning Features Have Been Incorporated for Effective Tuning at All Gaps PM slugs: PM slugs, magnetized parallel to axis Slugs are used in sets of four Vertical pole position: Adjust the angle (about z) for Bx correction Maximum adjustment angle is 2 mrad BeMa2014, 01/02/14

11. 11 One Meter Module Prototype Results A one meter prototype was fabricated to test the basic undulator design and the tuning methods -Previous baseline design with a period length of 32 mm -Incorporates the permanent magnet rotors and pole adjustment flexures Basic design and tuning methods were validated with the prototype -Measured effective field and field roll-off values agree with the calculated results -End design meets the undulator requirements -Tuning method response was validated -Using the available tuning methods the prototype was tuned to meet the specifications BeMa2014, 01/02/14

12. 12 Magnetic Measurements of Tuning Features We experimentally verified the expected gap dependencies for both tuning methods as based on modeling results The different gap dependencies allow for effective gap-dependent tuning Normalized First Integral BeMa2014, 01/02/14

13. 13 First and Second Vertical Field Integral Requirements are Met at All Gaps After Tuning Gap [mm] Second Field Integral vs. z Required Limits,  50  Tm 2 Field Integral vs. gap Required Limits,  40  Tm * Hall Probe Measurements + PW integral correction * PW measurements Second Field Integral vs. gap Required Limits,  50  Tm 2 * PW measurements Validation of end Design Calculations BeMa2014, 01/02/14

14. 14 Improved Magnet Block Measurement Enables Superior Magnet Sorting Based On Magnet Non-Uniformity Data A sorting method was developed using a limited number of surface field measurements Measurement procedure is compatible with the large quantities of magnets Analysis was performed to derive the figure of merit for sorting Performed full surface maps on a random sample of magnets Developed a model to sub-divide blocks to capture non-uniformities Calculated the integral errors from the sub-block magnetization errors Used a reduced point procedure that adequately predict the simulated field integrals BeMa2014, 01/02/14

15. Permanent Magnet Non-Uniformity Analysis North FieldSouth Field Sensitivity Matrix is generated and bounded least squares is used to determine the sub-block magnetizations Minor components are exaggerated by a factor of 20 Undulator field error due to sub-block magnetization is determined BeMa2014, 01/02/14

16. 16 The Simulation Results Show a High Degree of Correlation between the Expected Integral and The 5-point N/S Function Full scans were performed for 25 blocks and the simulated integrals were determined A fit function was determined to better correlate the five surface field values with the simulated field integral errors produced by the PM block in the undulator 5 point measurements were used in the sort to minimize integral errors between magnets across the gap Correlation Between Simulated Integral and Five Point N/S Measurement Correlation Between Simulated Integral and Single Point N/S Measurement r = 0.69 r = 0.96 BeMa2014, 01/02/14

17. Phase Shake vs. gap 17 Comparison of Integral Results at Minimum Gap Second Integral Results for Sort # 2 Field Integral Results for Sort # 2 5-Point Measurement Provides Superior Sort Results (Results shown for all cases before tuning) SORTING BASED ON MAGNET MOMENT ONLY NO SORTING SORTING INCL. MAGNET INHOMOGENITY INFO Required Limits,  40  Tm Required Limits 3° Requirement BeMa2014, 01/02/14

18. 18 Conclusions The magnet module design and assembly procedures have been optimized for precise assembly and minimal tuning time Efficient pole position adjustment allows for initial leveling of the poles to within ±5 μm An improved sorting procedure can considerably reduce the amount of tuning that is necessary Pole position and permanent magnet rotor adjustments have been incorporated in the design for the vertical magnetic field tuning Tuning methodology has been validated with the short scale prototype Ease of pole and magnet rotor adjustments will allow fast tuning of the production devices Horizontal field tuning will be performed with pole canting adjustment and horizontal permanent magnet slugs BeMa2014, 01/02/14