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RCS QM shuffling

RCS QM shuffling. 平成１８年６月９日 發知　英明. GL data of QMA (QFN,QDN,QDX). QFN. 0.181 to 3 GeV. GLmax. GLac. QDN. GLdc. D GL/<GL>. GLmin. QDX. MAG#. GL data of QMB (QFM). 0.181 to 3 GeV. GLmax. D GL/<GL>. GLac. GLdc. GLmin. MAG#. GL data of QMC (QFX). D GL/<GL>. MAG#.

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RCS QM shuffling

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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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