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

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Horizontal Angular Kick [ G.m ] horizontal circular vertical 1 0.8 0.6 0.4 0.2 0 -6 -4 -2 -0.2 0 2 4 6 -0.4 -0.6 -0.8 -1 z [ mm ] Figure 25. The horizontal angular kicks along the z-axis for all undulator phases at min. gap Vertical Angular Kick [ G.m ] 40 30 20 horizontal circular vertical 10 0 -6 -4 -2 -10 0 2 4 6 -20 -30 -40 z [ mm ] Figure 26. The vertical angular kicks along the z-axis for all undulator phases at min. gap 16
Depending on the position x,z of the electrons, focusing takes place due to the angular kicks. The focal lengths are given by [7 ]; Which induces a tune shiftδ given by [10 ]; Where x, z Q x , z 2 ∞ 2 1 1 ⎛ e ⎞ ∂ = − ⎜ ⎟ Φ( x, z, y)dy 2 F x 2 ⎝ γmc ∫ ⎠ ∂x −∞ 2 ∞ 2 1 1 ⎛ e ⎞ ∂ = − ⎜ ⎟ Φ( x, z, y)dy 2 F z 2 ⎝ γmc ∫ ⎠ ∂z −∞ 1 β δ Qx, z = 4π F β is the beta function at the location of the EPU magnet. The machine parameters used to evaluate the tune shifts are given in Table 4 at the middle of a short straight section of the <strong>SESAME</strong> lattice [1]. Table 4. Main parameters of the <strong>SESAME</strong> lattice. Beam Energy 2.5 GeV Beam Current 400 mA Horizontal Emittance 25.7 nm.rad Natural Energy Spread 1.086 × 10 -3 Coupling 1 % Betatron function in the middle of short straight section x / x / x / ' x 13.30m / 0 / 0.53m / 0 z / z / z / ' z 0.77m / 0 / 0 / 0 Figures 27 to 30 show the horizontal and vertical betatron tune shifts on both x and z-axis’s. The horizontal tune shift on the z-axis is a bit large mainly due to the large x at the EPU location. A possible cure for that is by running an electric current in a copper strips between the right and left subassemblies to generate a normal quadrupole component to locally compensate for the angular kick at different modes of operation. 0.01 x, z x, z 0.005 Horizontal Tune Shift 0 -30 -20 -10 0 10 20 30 -0.005 -0.01 -0.015 vertical horizontal circular -0.02 x [ mm ] 17
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: 4.2. ANGULAR KICK AND TUNE SHIFT Th
Page 19 and 20: 0.025 Vertical Tune Shift 0.02 0.01
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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