1. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 1 Information for discussion about how to enlarge the bore of the QC3 style quads. 27 th /28 th February 2007 Cherrill Spencer, SLAC Member of ATF2 Magnet Team

2. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 2 At February 2006 ATF2 project meeting my design suggestion for Final Doublet Quads was accepted QF1 and QD0 requirements: Definition of K1 : Gradient = K1 x Brho / Effective length At 1.3 GeV, Brho = 4.3363 Tesla-meter Latest requirements are: QF1 K1 = 0.737 and QD0 K1= -1.351 These can be met using the “QC3” style FFTB quad [1.38Q17.72] of which 2 are available Original aperture: 35.06mm diameter ; Eff L= 0.4675m; Aperture needs to be larger to match S band BPM Effective length varies with aperture value

3. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 3 Views of both ends of QC-3 as sits in SLAC warehouse waiting for modification LCW fittings prevent BPM being installed this end Old beampipe will be removed. G10 coil supports stay.

4. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 4 Shape of pole tip and coil in the 1.38Q17.72 quad. Will machine pole tip to make larger aperture “Dog-eared” shape of coil ends starts at 56mm, but have also G10 coil support, uses ~25.4mm of the 56mm space. This is not enough for the S band BPM, so adapter needs to be designed. The 35 mm aperture is not compatible with S band BPM or shape of beam in QF1 and QD0.

5. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 5 Two old FFTB quads: 1.38Q17.72. are ready to have their poletips machined back to become QD0 & QF1 After several discussions decided to make bore aperture 50mm: –quad bore diameter= 40 + 2x 3.5 + 2x 2 = 50 mm 3.5mm=Cu beampipe thickness; 1mm= free space –have modelled in POISSON, see next slide for multipoles Solid steel core Water cooled coils, 24 turns of 0.255” sq hollow Cu conductor; 2 water circuits per coil. Predicted currents and voltages: –QD0: 127.9 amps, 8.85 volts, ∆T= 1.77 degrees C –QF1: 69.8 amps, 4.88 volts, ∆T= 0.53 degrees C STATUS: Need to find a machine shop with suitable machine that can machine back the poles and maintain some mechanical tolerances - which need to be established with regard to multipole tolerances.

6. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 6 Compare predictions of multipole content with tolerances from James Jones & S. Kuroda Magnet Name Tolerance 6 pole/quad At r=1cm Tolerance 12 pole/quad POISSON Prediction 12pole/quad Tolerance 20pole/quad POISSON Prediction 20pole/quad QF1 9.5x10 -5 2.46x10 -4 1.08x10 -4 1.19x10 -3 2.57x10 -6 QD0 5.26x10 -5 3.08x10 -3 1.08x10 -4 5.98x10 -1 2.57x10 -6 ABOVE TABLE IS FOR A 50mm diameter bore. Tightest 12pole/quad tolerance is for QF1. POISSON often under- predicts multipole value, we have 2.3 times margin. But if 12pole is too large we have at least 2 ways to reduce it: by chamfering poletip ends or by adding steel buttons on poletip end; Determine the button size and position by experiment :more on Spencer’s experience with this below.

7. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 7 Random Multipole Errors Introduced by Pole Excitation and Pole Placement Errors Random multipole errors are introduced if the poles are improperly excited or assembly errors which displace poles are introduced. If one can identify these errors, one can predict the multipole content of the magnet. The means for calculating these errors are summarized in two papers published by Klaus Halbach. The first paper describes the derivation of the relationships, the second computes and tabulates the coefficients used to calculate the multipole errors from the perturbations derived in the first paper. –Some of my “error” slides courtesy of Jack T. Tanabe

8. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 8 3 ways a poletip could be wrongly made In a regular quadrupole the first pole would be at 45º to the x axis

9. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 9 4 types of fabrication errors for each poletip. Each poletip can have independent errors Halbach developed a coefficient table to assist in calculating the effect of the various types of errors on the other errors. Excitation errors related to current in coils, or length of steel r 0 is the radius of the bore “1 mil” = 0.001” = 0.0254 mm

10. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 10 The Four Piece Magnet Yoke- even if poles are made correctly the 4 poles could be assembled with errors The ideal assembly satisfies the rotational symmetry requirements so that the only error multipoles are allowed multipoles, n=6, 10, 14... However, each segment can be assembled with errors with three kinematic motions, x, y and  (rotation). Thus, combining the possible errors of the three segments with respect to the datum segment, the core assembly can be assembled with errors with 3x3x3=27 degrees of freedom.

11. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 11 PREDICTIONS USING HALBACH’s 1969 “perturbations” paper SextupoleOctupoleDecapole (10-pole) 12-pole ATF2 Tolerances QF1 QD0 9.56E-05 -5.26E-05 1.01E-04 -1.58E-04 2.46E-04 -1.10E-03 2.46E-04 -3.08E-03 Single Poletip 1 mil Radial misplacement 8.15E-05 -8.15E-05 skew -1.33E-21 1.08E-05 skew 4.89E-06 4.89E-06 skew 1.14E-06 2.09E-22 skew Single Poletip 2 mil Radial 1.63E-04 -1.63E-04 skew -2.65E-21 2.16E-05 skew 9.78E-06 9.78E-06 skew 2.28E-06 4.19E-22 skew Single Poletip 1 mil Azimuthal -8.15E-05 -8.15E-05 skew -3.41E-05 -4.18E-21 skew -4.89E-06 -4.89E-06 skew -1.35E-22 7.35E-07 skew Single Poletip 2 mil Azimuthal -1.63E-4 -1.63E-4 skew -6.82E-05 -8.35E-21 skew -9.78E-06 9.78E-06 skew -2.70E-22 1.47E-06 skew All 4 Poletips ->Sextupole. Worst Case 1 mil Rad, Azi -6.52E-04 -2.40E-19 skew -1.06E-20 0.0 skew -3.91E-05 -3.26E-20 skew 1.08E-21 4.05E-21 skew All 4 Poletips ->Sextupole. Worst Case 2 mil Rad, Azi -1.30E-03 -4.80E-19 skew -2.12E-20 0.0 skew -7.82E-05 -6.52E-20 skew 2.16E-21 8.09E-21 skew All 4 Tips Oct. Worst Case 1 mil Azimuthal -7.99E-20 1.28E-19 skew -1.36E-4 -6.68E-20 skew 1.92E-21 -2.88E-21 skew -2.07E-21 0.0 skew All 4 Tips 12-pole Worst Case 2mm Radial -5.12E-18 -1.13E-17 skew 4.24E-19 0.0 skew 1.84E-19 3.68E-19 skew 3.65E-04 2.68E-19 skew

12. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 12 Conclusion from perturbation calculations Sextupole component is very sensitive to poletip being at wrong radius or the poletip being offset “azimuthally” Appears that errors of size 0.001” (=25 microns) are significant for producing unwanted sextupoles.

13. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 13 Not finished drawing showing how much of poletip needs to be removed. 2 Split planes here determine origin for machining. Spencer reckons they were made to 0.02mm flatness & 0.02mm perpendic. Red curve shows present hyperbolic poletip. Black lines are new. Green shape is G-10 coil clamp

14. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 14 Another reason to believe 0.0254mm tolerances are necessary Measurements of present QC3 quad’s bore diameters and adjacent pole distances : are correct to within 0.001” To achieve this the present poles must have been ground to better than 0.001”

15. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 15 Buttons added to an SLC quadrupole to reduce its 12 pole content

16. ATF2 Magnets ATF2 Magnets 27/28 Feb 2007Cherrill Spencer, SLAC. Info for QC3 machining discussion 16 Effect of 8 buttons on one end of RTL quadrupole Bore radius = 3.03” = 77 mm At r= 17.9mm –12pole/quad without buttons = 0.148% = 1.48x 10(-3) –12pole/quad with buttons = 0.017% = 1.7x10(-4) –BUT sometimes the octupole went UP with the buttons. –Effect of buttons on sextupole needs to be studied more- by Spencer- has data.