Technical Note Amman, October 29, 2006 (draft) Note: M ... - SESAME

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Figure 27. Horizontal tune shift across the x-axis for all undulator phases at min. gap. 0.0016 0.0014 Vertical Tune Shift 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 vertical horizontal circular 0 -30 -20 -10 0 10 20 30 x [ mm ] Figure 28. Vertical tune shift across the x-axis for all undulator phases at min. gap. Horizontal Tune Shift 0.2 0.15 0.1 vertical horizontal circular 0.05 0 -6 -4 -2 0 2 4 6 -0.05 -0.1 -0.15 z [ mm ] Figure 29. Horizontal tune shift across the z-axis for all undulator phases at min. gap. 18
0.025 Vertical Tune Shift 0.02 0.015 vertical horizontal circular 0.01 0.005 0 -6 -4 -2 0 2 4 6 -0.005 -0.01 z [ mm ] Figure 30. Vertical tune shift across the z-axis for all undulator phases at min. gap. 4.3. MACHINE FUNCTIONS AND DYNAMIC APERTURE Installing an EPU device in the SESAME lattice will create a beta beat (associated with the tune shifts) in both planes since there are magnetic fields in both directions. In the BETA code any insertion device can be described by interpolation tables which provide an angular kick in T 2 m 2 as a function of the coordinates of the particle passing that element, i.e. mapped insertion device [11]. Figures 31 to 33 show the effect of inserting an EPU device (mapped EPU) in a short straight section in the SESAME lattice, see Table 4, without using any active (trim coils for field integrals and copper strips for the angular kicks) or passive (shimming for both field or phase errors) correction scheme. The SESAME EPU maps are shown in Appendix A. The betatron beta beat is given by; β bare − β mod Beta − Beat[ %] = × 100% βbare Where bare is the beta value for the bare lattice and mod is the beta value with the EPU magnet engaged at different modes of operation. The vertical beta beat is not that significant, for the vertical mode of operation a maximum beta beat of 0.5 %, because of the low z value at the EPU location whereas the horizontal beta beat is rather significant, the worst case is with the vertical mode of operation where the peak horizontal field is B x = 0.9724 T, mainly due to the high x value of 13.3m. The beta beats in both planes for all modes of operation are shown in Figures 34 and 35. The quadrupole doublet flanking the EPU magnet can be used to compensate for the beat beats in both planes and restore the tunes to the bare lattice values [1]. Table 5 shows the change in the strength of the quadrupole doublet to match the beta beats in both planes. Table 5. Changes in strength of the quadrupole doublet to match the EPU’s effect. Mode of Bare Latice Matched lattice Percentage [%] Tunes operation QF QD QF QD QF QD Q x / Q z Horizontal 2.03217 -1.22628 2.02069 -1.20057 -0.56 -2.09 7.2300 / 6.1900 Circular 2.03217 -1.22628 2.04797 -1.23976 +0.78 +1.10 7.2300 / 6.1900 Vertical 2.03217 -1.22628 2.06450 -1.26312 +1.59 +3.00 7.2300 / 6.1900 19
Page 1 and 2: Technical Note ____________________
Page 3 and 4: The inclined mode of operation has
Page 5 and 6: Table 2. Flux densities, k-values a
Page 7 and 8: Flux Density [ T ] 0.7 0.6 0.5 0.4
Page 9 and 10: First vert. integral [ G.cm ] 100 8
Page 11 and 12: Trajectory [ micrometer ] 55 45 35
Page 13 and 14: 4. INTERACTION BETWEEN EPU AND ELEC
Page 15 and 16: 4.2. ANGULAR KICK AND TUNE SHIFT Th
Page 17: Depending on the position x,z of th
Page 21 and 22: OPTICAL FUNCTIONS 30 Beta Z Beta X
Page 23 and 24: Vertical Beta Beat 2 1.5 1 0.5 0 -0
Page 25 and 26: 10000 Vertical Force [Newton] 5000
Page 27 and 28: Brilliance [Photon/s/mm 2 /mrad 2 /
Page 29 and 30: REFERENCES [1] G. Vignola, M. Attal
Page 31 and 32: 0.004 0.003 Hor. Ang. Kick [T 2 m 2
Page 33 and 34: APPENDIX B FEASIBILITY OF HOUSING S
Page 35 and 36: Horizontal Beta Beat 3.5 3 2.5 2 1.

Technical Note Amman, October 29, 2006 (draft) Note: M ... - SESAME

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