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Multipole components in the RCS-BM

Multipole components in the RCS-BM. Hideaki Hotchi Nov. 24, 2004 @ Tokai. Central orbit. (cm). ideal orbit. d L=3.96872 - 3.970 = - 0.00128 m (- 0.00128 x 24= - 0.03072 m for whole circumference). 6.67mm. x. s. y. orbit estimated by tracking. (cm).

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Multipole components in the RCS-BM

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  1. Multipole componentsin the RCS-BM Hideaki Hotchi Nov. 24, 2004 @ Tokai

  2. Central orbit (cm) ideal orbit dL=3.96872-3.970 =-0.00128 m (-0.00128 x 24=-0.03072 m for whole circumference) 6.67mm x s y orbit estimated by tracking (cm)

  3. Field distribution (181 MeV)along the actual central orbit By (T) s (m)

  4. Estimation of muptipole field components in the BM Assuming Ax=Ay=0 and r→∞, y Central orbit q x Medium plane Assuming the mid-plane symmetry (no skew field) : an=0, Case1 : estimation with the By distribution on the medium plane Case2 : estimation with the By distribution along a circle (radius=R)

  5. Estimation of multipole field components (case1) ByL distribution for each region Ⅰ Ⅱ ByL (Tm) Ⅲ Ⅳ By distribution along the central orbit By (T) Ⅵ Ⅴ Ⅹ Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅶ Ⅷ s (m) The field area is divided into 10 pieces. Ⅸ Ⅹ x (m)

  6. Multipoles in the BM (case1) ByL (Tm) Ⅰ Ⅱ K0 K1 (m-1) Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅲ Ⅳ s (m) s (m) K2 (m-2) K3 (m-3) Ⅵ Ⅴ s (m) s (m) K4 (m-4) Ⅷ Ⅶ K5 (m-5) s (m) s (m) Ⅹ Ⅸ K6 (m-6) K7 (m-7) s (m) s (m) x (m) fitting curve

  7. Estimation of multipole field components (case2) s=0 By (T) y q (rad) s=1.38 m By (T) q x R=5.0 cm q (rad) By (T) s=1.75 m q (rad)

  8. Estimation of multipole field components (case2) - cont’d - ByL distribution for each region Ⅰ Ⅱ ByL (Tm) Ⅳ Ⅲ By distribution along the central orbit By (T) Ⅵ Ⅴ Ⅹ Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅶ Ⅷ s (m) The field area is divided into 10 pieces. Ⅹ Ⅸ q(rad)

  9. Multipoles in the BM (case2) where Ⅰ Ⅱ ByL (Tm) K0 K1 (m-1) Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅲ Ⅳ s (m) s (m) K2 (m-2) K3 (m-3) Ⅵ Ⅴ s (m) s (m) Ⅷ Ⅶ K4 (m-4) K5 (m-5) s (m) s (m) Ⅹ Ⅸ K6 (m-6) K7 (m-7) s (m) s (m) q(rad) Reconstructed curve (up to n=4)

  10. Comparison Blue - case1 Red - case2 K0 K1 (m-1) Ⅰ Ⅱ Ⅲ Ⅳ Ax, Ay≠0 in the end-field region !! Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ s (m) s (m) Assuming r→∞, K2 (m-2) K3 (m-3) s (m) s (m) K4 (m-4) K5 (m-5) s (m) s (m) The end field has a sextupole-like and octupole-like multipole field component. K6 (m-6) K7 (m-7) s (m) s (m)

  11. - cont’d- The parameters (bn, b0”,b1”) can be determined with the By distribution on the medium plane. s=0.0 m s=0.2 m By (T) s=0.4 m s=0.6 m The By distribution along a circle (r=5cm) can be reconstructed reasonably well using the parameters (bn, b0”,b1”) determined from the By distribution on the medium plane. s=0.8 m s=1.0 m s=1.2 m s=1.4 m s=1.6 m s=1.8 m q(rad)

  12. Tracking by SAD - modeling - - The bending field is considered as “step function”. - Multpole field components (K1～K4) are introduced as “thin lens” at the center of each region. By (T) Ⅹ Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ s (m)

  13. Tracking by SAD - condition - • The start point of tracking is set at the entrance of the 1st BM. • Initial condition of the beam particle : • x=y, x’=y’=0. • z=0., Dp/p=0., +0.5, +1.0% • Physical apertures are set for all the BEND, QUAD and SEXT. • Multipoles up to n=4 (decapole) are introduced for tracking. • The field strength of quadrupole magnets is refitted after introducing multipole components of the BM. • Q’s fringe : ON (f1=0.431) • Chromaticity correction : ON (full correction) and OFF • - Synchrotron oscillation : ON (assuming stationary bucket) • Number of turns : 1000

  14. Tracking by SAD - results (1) - • - Multipole field components estimated in the case2 • - Without chromatic correction • With synchrotron oscillation (assuming stationary bucket) Dp/p=0% Dp/p=0% blue line : Sasha’s calc. Qx-4Qy=-18 Qx-2Qy=-6 Qx-2Qy=-6 4Qx=27 Qx (Qy=6.27) Qy (Qx=6.60) Dp/p=0.5% Dp/p=0.5% Xmax=Ymax (cm) Xmax=Ymax (cm) Qy (Qx=6.60) Qx (Qy=6.27) Dp/p=1% Dp/p=1% Qy (Qx=6.60) Qx (Qy=6.27)

  15. Tracking by SAD - results (2) - • - Multipole field components estimated in the case2 • - Without chromatic correction • Without synchrotron oscillation Dp/p=0% Qx-2Qy=-6 Qx (Qy=6.27) Dp/p=0.5% Xmax=Ymax (cm) Qx (Qy=6.27) Dp/p=1% Qx (Qy=6.27)

  16. Tracking by SAD - results (3) - • - Multipole field components estimated in the case2 • - With chromatic correction (full correction) • With synchrotron oscillation (assuming stationary bucket) Dp/p=0% Dp/p=0% blue line : Sasha’s calc. Qx-2Qy=-6 Qx-2Qy=-6 Qx-4Qy=-18 4Qx=27 Qx (Qy=6.27) Qy (Qx=6.60) Dp/p=0.5% Dp/p=0.5% Xmax=Ymax (cm) Xmax=Ymax (cm) Qy (Qx=6.60) Qx (Qy=6.27) Dp/p=1% Dp/p=1% Qy (Qx=6.60) Qx (Qy=6.27)

  17. Tracking by SAD - results (4) - • - Multipole field components estimated in the case1 • - Without chromatic correction • With synchrotron oscillation (assuming stationary bucket) Dp/p=0% Dp/p=0% blue line : Sasha’s calc. Qx-4Qy=-18 Qx-2Qy=-6 Qx-2Qy=-6 4Qx=27 Qx (Qy=6.27) Qy (Qx=6.60) Dp/p=0.5% Dp/p=0.5% Xmax=Ymax (cm) Xmax=Ymax (cm) Qy (Qx=6.60) Qx (Qy=6.27) Dp/p=1% Dp/p=1% Qy (Qx=6.60) Qx (Qy=6.27)

  18. Tracking by SAD - results (5) - • - Multipole field components estimated in the case1 • - With chromatic correction • With synchrotron oscillation (assuming stationary bucket) Dp/p=0% Dp/p=0% blue line : Sasha’s calc. Qx-4Qy=-18 Qx-2Qy=-6 Qx-2Qy=-6 4Qx=27 Qx (Qy=6.27) Qy (Qx=6.60) Dp/p=0.5% Dp/p=0.5% Xmax=Ymax (cm) Xmax=Ymax (cm) Qy (Qx=6.60) Qx (Qy=6.27) Dp/p=1% Dp/p=1% Qy (Qx=6.60) Qx (Qy=6.27)

  19. Mapping • - Multipole field components estimated in the case1 • - With chromatic correction • With synchrotron oscillation (assuming stationary bucket) • Start point of tracking : 1st QDX • Initial condition of the beam particle: ex=ey, x=(ex/gx)1/2, x’=0, y=(ey/gx)1/2, y’=0, z=0, Dp/p=0~0.5% • Number of turns : 5000 4Qx=27 Qx-Qy=0 Dp/p=0% Qx-2Qy=-6 Qy Qx-4Qy=-18 Qx Dp/p=0.5% Qy p mm mrad Qx 6Qx=39 ? 5Qx=33

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