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Optimal Data Selection for QM Shuffling to Minimize Beta Modulation

Exploring the impact of different datasets on beta modulation before and after shuffling for precise beam control in particle physics experiments.

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Optimal Data Selection for QM Shuffling to Minimize Beta Modulation

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  1. RCS QM shuffling 平成１８年６月９日 發知　英明

  2. GL data of QMA (QFN,QDN,QDX) QFN 0.181 to 3 GeV GLmax GLac QDN GLdc DGL/<GL> GLmin QDX MAG#

  3. GL data of QMB (QFM) 0.181 to 3 GeV GLmax DGL/<GL> GLac GLdc GLmin MAG# GL data of QMC (QFX) DGL/<GL> MAG#

  4. GL data of QMD (QFL,QDL) QFL 0.181 to 3 GeV GLmax GLac GLdc DGL/<GL> QDL GLmin MAG#

  5. Which data should we use for the QM shuffling? DGLmin, DGLmax, DGLdc & DGLac ? We will perform the shuffling so as to minimize the beta modulation at “injection”.

  6. Grouping of QMA(33) into QFN(12), QDN(12), QDX(9) QFN QFN QDX QDX QDX DGLmin/<GLmin> QDN DGLmin/<GLmin> QDN QDN QFN DGLmin/<GLmin> QFN DGLmin/<GLmin>

  7. Grouping of QMD(12) into QFL(6), QDL(6) QFL QDL DGLmin/<GLmin> QDL QFL DGLmin/<GLmin>

  8. DGL of QMA (QFN,QDN,QDX) QFN ～1E-3 0.181 to 3 GeV GLmax QDN ～1E-3 GLac GLdc DGL/<GL> GLmin QDX ～1E-3 MAG#

  9. DGL of QMB (QFM) 0.181 to 3 GeV ～5E-4 GLmax DGL/<GL> GLac GLdc MAG# GLmin DGL of QMC (QFX) ～1E-3 DGL/<GL> MAG#

  10. DGL of QMD (QFL, QDL) QFL ～1E-3 0.181 to 3 GeV GLmax DGL/<GL> GLac QDL GLdc ～1E-3 GLmin MAG#

  11. Beta modulation caused by DGLminBEFORE shuffling |DGLmin/<GL>| < 1.0E-3 Beta modulation at (6.68,6.27) assuming the allocation in the order of Pro.# Horizontal bx,y (m) Vertical s (m) |Db/b|< 0.8% Dbx,y/bx,y Dnx /nx～-2.0E-5 Dny /ny～ 4.3E-7 s (m)

  12. Shuffling for QM [ k(s)=-k(s’) ] if Dy=np, [ k(s)= k(s’) ] if Dy=np/2 Phase advance at (6.68,6.27) yy yx 292° (3p/2) 182° (p) 197° (p) 83° (p/2) 7° (0p) 180° (p) 463° (5p/2)

  13. Beta modulation caused by DGLminAFTER shuffling Beta modulation at (6.68,6.27) BEFORE shuffling AFTER shuffling Dbx/bx AFTER “BAD” shuffling s (m) BEFORE shuffling AFTER shuffling Dby/by AFTER “BAD” shuffling |Db/b| 1%→0.8%→ 0.4% s (m)

  14. Tune dependence of Db/bat INJ (DGLmin) 2nx=13 Horizontal (BEFORE shuffling) Vertical (BEFORE shuffling) Horizontal (AFTER shuffling) Possible operating points Max[Dbx,y/bx,y] Vertical (AFTER shuffling) ny nx (ny=6.27 fixed) 2ny=13 Possible operating points Max[Dbx,y/bx,y] nx ny (nx=6.68 fixed)

  15. Comparison of Db/b at INJ(DGLmin) & EXT(DGLmax) “AFTER shuffling (using DGLmin)” Horizontal, INJ 2nx=13 Vertical, INJ Horizontal, EXT Vertical, EXT Possible operating points Max[Dbx,y/bx,y] |Db/b|～0.5% at INJ ～1% at EXT for the possible operating area. nx (ny=6.27 fixed) ny 2ny=13 Possible operating points Max[Dbx,y/bx,y] ny (nx=6.68 fixed) nx

  16. Single-particle trackingwith DGLmin & DGLmax (SAD) AFTER shuffling (using DGLmin) • - Multipole field in the BM and QM : OFF • Chromatic correction : OFF • Quadrupole field error : DGLmin ey ex= ey We looked for the maximum ex=ey for which the beam survives within the physical apertures up to 5000 turns. ex ny Surveyed lines nx

  17. Single-particle trackingwith DGLmin & DGLmax AFTER shuffling (using DGLmin) ＊ ＊ With DGLmin With no error With DGLmax With no error Max. ex= ey Max. ex= ey 4X-=27 X-2Y-=-6 2X-2Y=0 2X-=13 Horizontal unstable Horizontal unstable nx (ny=6.27 fixed) nx (ny=6.27 fixed) Max. ex= ey Max. ex= ey X-2Y-=-6 2Y-=13 Vertical unstable Vertical unstable ny (nx=6.68 fixed) ny (nx=6.68 fixed) STOPBAND: ~ 0.0007 for 2X=13 ~ 0.0004 for 2Y=13 ~ 0.0020 for 2X=13 ~ 0.0013 for 2Y=13

  18. Multi-particle tracking simulation(SIMPSONS) - Errors included in the simulations - (1) Multipole field components of BM & QM BM : MEASURED data & TOSCA QM : TOSCA (2) Field errors of BM & QM BM : MEASURED data, Shuffling QM : No data → Random error [ Gauss(2s) with s=5E-4 ] |DGL/GL| <1.0E-3 (3) Alignment errors of BM & QM Random error [ Gauss(2s) with s=0.1 mm for dx & dy, s=0.2 mrad for dq ]

  19. Field & Alignment errors of QM |DGL/GL| <1.0E-3 D(GL)/(GL) Dx (m) Dy (m) Dq (rad) QM No.

  20. Result from multi-particle tracking (6.72, 6.35) 0.6 MW @ Extr. Chromatic cor. : ACC Beam survival (0) W/O Mult (1) W/ Mult (COD=0) (3) W/ Mult, ERRORS, COD cor. (COD<0.8mm ) (2) W/ Mult, ERRORS (COD~5mm) turns The QM field error of |DGL/GL|<1.0E-3 may not lead to large beam loss.

  21. Beta modulation for the case (3) Horizontal Dbx/bx Vertical s (m) Dby/by |Db/b|< 1.5% s (m)

  22. Shuffling for RCS QM （配置案） QFN.12 (END) RF EXT INJ QDX.1 (START)

  23. QMA 1-33 QMB 1-3 Location DGLmin Prod. # DGLmax Location DGLmin Prod. # DGLmax QMC 1-12 QMD 1-12

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