Undulator Magnet Design / Measurement

1. Undulator Magnet Design / Measurement 11 August 2004 Liz Moog

2. Recent Undulator Developments • Wings are removed from poles • Poles are canted to allow Keff adjustment • Phasing between undulators is better understood

3. Tapped holes to hold poles Previously, Ti ‘wings’ extended from sides of poles for clamping. Now, instead, holes will be tapped in backs of poles and there will be no wings.

4. Pole clamping was tested for failure Screws were overtorqued to failure. In 5 tests, failure occurred at 50-55 in-lbs, either by the screw breaking adjacent to the pole, or by the socket head of the screw rounding out. There were no pole thread failures. All split lockwashers were permanently flattened.

5. Canting comes from wedged spacers • 3 mrad cant • Gap can be adjusted by lateral displacement of wedges • 1 mm shift in spacer means 3 microns in gap, or 6 Gauss • Beff adjusted to desired value

6. 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 DB/B = 1.5x10-4, or DB = 2 Gauss, which translates to Dx = 0.3 mm ( or 1 micron in gap)

7. Canting the poles helps in many ways • Facilitates final setting of Beff • 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

8. 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

9. Period-averaged horizontal trajectories at 14.1 GeV (X in mm) Trajectories are all well behaved and well within the 2 mm tolerance for maximum walk-off from a straight line

10. Magnetic needles for alignment Only one needle is required for alignment in the X direction One more needle has to be added at Y=0 for alignment in the Y direction

11. Hall probe center calibration in x one needle used Accuracy of calibration < 50 µm (limited by encoder resolution)

12. Hall probe center calibration in y one needle used (from side) Magnetic center of undulator defines y=0. Height of needle is where By = 0. The difference between them can be determined from the measurement, to an accuracy of < 5 µm.

13. Canting: other considerations The main disadvantage of the canted pole gap is that the undulator support must now be separate from the vacuum chamber support. Quadrupole support must be separate too. However, if the undulator support is separate, there may be the possibility of removing the undulator.

14. Fringe field at x=65 and 100 mm New shims don’t stick out as far on the sides Fringe field is similar to earth’s field at X=100 mm. (But steering corrections are needed to compensate for the earth’s field.)

15. Phasing between undulator segments • Static adjustment of end phasing to suit the physical break length is done with phase shims on magnets • A change in Beff alters the phasing relationship between segments • In original design, phasing adjustments were to be done by altering gap at undulator segment ends (‘floppy ends’) • Piezo adjusters were expensive • Long-term stability unknown

16. Break length change vs number of phase shims Shims are placed in pairs ( i.e., on top&bottom jaws) on magnet #7, then #6, etc., to #2

17. Complex amplitude & phase slippage definitions Complex amplitude of radiation Intensity of radiation is given by |A|2 Phase slippage Polar plots of A vs. z are quite useful….

18. A=|A| eiQ : Polar plot of |A| and Q vs z • Just for last 2 undulators • Near-ideal performance • |A| is radius at end of undulator

19. What if electron energy has changed by 0.4%? • Last two undulators only • Amplitude is very small • Performance is very sensitive to energy change

20. 0.4% energy change, but Keff corrected • Last two undulators only • Undulators shifted to correct Keff • Performance is 97.5% • Kink between undulators shows phasing between undulators needs adjusting

21. Better correction for Keff fixes kink • Last two undulators only • 0.4% energy change • Keff shifted slightly from ideal to correct for phasing between undulators • Performance is 99.2% • For 3 mrad cant, this is 8 mm shift in x. Perhaps undulator segment could be pretuned with –4 mm shift at nominal energy so shift is +4 mm at saturation.

22. What if an undulator segment is removed? • Last two undulators only (with an undulator-long drift space between them) • Nominal Keff = 3.63 • Keff shifted slightly from nominal to optimize phasing (0.8 mm in x) • Performance is 99.3% At this energy, removing a segment works.

23. Removing an undulator not OK at all energies • Last two undulators only (with an undulator-long drift space between them) • Nominal Keff = 3.44 • Keff shifted slightly from nominal to optimize phasing (3.2 mm in x) • Performance is 81.6% At this energy, removing one segment doesn’t work. But removing a pair would be OK.

24. Summary of advantages of canted poles • Initial fine tuning of Keff • Compensation for temperature • Run-time tweaking of field strength to maximize gain • Amplitude very sensitive to electron energy loss in saturation. Can compensate by adjusting Keff • Run-time adjustment necessary because of uncertainty of beam energy loss • Adjustment of phasing without ‘floppy ends’