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Resonance correction: -Q x +2Q y =6

for the AP-group. Resonance correction: -Q x +2Q y =6. Etienne Forest Alexander Molodozhentsev KEK. January 12, 2005. Dynamic Aperture for RCS 3D_BM & QFF & CC. {kL} SEXT – SAD simulation 3 independent families Hotchi san’s data 1000 turns Observation: entrance BM 1. (2). (1).

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Resonance correction: -Q x +2Q y =6

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  1. for the AP-group Resonance correction:-Qx+2Qy=6 Etienne Forest Alexander Molodozhentsev KEK January 12, 2005

  2. Dynamic Aperture for RCS3D_BM & QFF & CC {kL}SEXT – SAD simulation 3 independent families Hotchi san’s data 1000 turns Observation: entrance BM1 (2) (1) Main limitation of DA (1) is caused by the sextupole field nonlinearity used for the chromaticity correction. Additional contribution to the normal octupole resonance (2). modified 16.12.04

  3. Resonance correction - simulation approach • To provide the differentiation in s-direction… • …representation of the TOSCA 3D field data of the RCS bending magnet • by the Gaussian wavelet (Daubechies, 1992)… 2. Normal form analysis… • Integrated resonance driving term [-1,2] … definition of the required • strength of the sextupole correctors to make zero the cosine and sine • parts of the resonance driving term.

  4. Single particle tracking:before the resonance [-1,2] correction PTC#3: Qx=6.56817 Qy=6.26662 (… min of beam survival) p/p=0 Observation: #38 (rc6H_02) NEGATIVE_BM X-X/ Y-Y/ Lost -0.10 0.10 X0=Y0=0.028m X/0=Y/0=0 Gaussian wave-let

  5. Single particle tracking:before & after the resonance [-1,2] correction Observation: #38 (rc6H_02) NEGATIVE_BM PTC#3: Qx=6.56817 Qy=6.26662 (… min of beam survival) p/p=0 X-X/ Y-Y/ Stable Lost White … BEFORE correction; Yellow … AFTER correction X0=Y0=0.028m X/0=Y/0=0

  6. Sextupole correctors • 6 sextupole correctors in the dispersion-free straight sections • 2 independent families (SC1 & SC2) • Leff = 0.15 m • Required integrated strength of the sextupole correctors: • ksL (SC1) = 0.112770195 m-2 • ksL (SC2) = 0.113920857 m-2 …definition … • Strength of the sextupole magnets for the chromaticity correction: • (ksL) SDA:= -0.319012465119 [m-2] • SFA:= 0.378052080173 [m-2] • SDB:= -0.304307265885 [m-2]]

  7. DA after correction PTC#3: Qx=6.56817 Qy=6.26662 (… min of beam survival (X=Y)MAX) p/p=0 X0 =Y0 = 0.028, 0.035, 0.040, 0.0415, 0.0420, 0.0425 (lost) X/0 = Y/0 = 0 1000 turns Y-Y/ X-X/ 0.002 -0.002 Observation: #38 (rc6H_02) NEGATIVE_BM -0.10 -0.10 0.10

  8. DA and resonance correction 3D_BM QFF Chrom_Sextupoles RC_Sextupoles (1) (1) Dynamic Acceptance_AFTER (BM_3D&QFF&CC&RSC): AX = (X0,max)2 x ~ 529.mm.mrad Ay = (Y0,max)2y ~ 423.mm.mrad (2) (2) Dynamic Acceptance_BEFORE (BM_3D&QFF&CC): AX = (X0,max)2 x ~ 216 .mm.mrad Ay = (Y0,max)2y ~ 187 .mm.mrad H-V coupling X, Y – initial particle coordinates, (X/=Y/=0)

  9. DA: On- & Off-momentum 3D_BM QFF Chrom_Sextupoles RC_Sextupoles Dynamic Acceptance_AFTER (dp/p=0.01) (BM_3D&QFF&CC&RSC): AX = (X0,max)2 x ~ 410.mm.mrad Ay = (Y0,max)2y ~ 301.mm.mrad

  10. Conclusion • The 3D-field data can be represented by the Gaussian wavelet to provide the resonance analysis. • After the [-1,2] resonance correction the DA has been improved about 2 times for the on- and off-momentum particles. • The correction scheme requires moderate strength of the sextupole correctors.

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