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Tracking Calculations for the LHC Upgrade - Collision Optics -

Tracking Calculations for the LHC Upgrade - Collision Optics -. Bernhard Holzer, CERN BE-ABP and many colleagues !!!. LHC Standard Collision Optics ... and the Upgrade. Q4. Q5.

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Tracking Calculations for the LHC Upgrade - Collision Optics -

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  1. Tracking Calculations for the LHC Upgrade - Collision Optics - Bernhard Holzer, CERN BE-ABP and many colleagues !!! LHC Standard Collision Optics ... and the Upgrade Q4 Q5 critical issues for the DA ??? error tables ... at the triplett ? ... at the new D1 ? ... at the matching section ? and which multipoles?

  2. Problem: multipole coefficients from Q1, Q2, Q3 & D1 ... and beyond ?? how many multipole correctors do we need ?

  3. LHC - Upgrade error table for the new MQXC triplett quadrupole " ITD1_error table_V1"

  4. col_9 horizonal detuning with amplitude vertical detuning with amplitude 0.01 0.01 0 0 -0.01 -0.01 10 0 initial amplitude 10 0 initial amplitude " the worst case" triplett errors on D1 errors on no correction

  5. col_9 " the worst case" triplett errors on D1 errors on no correction below 6 sigma !!

  6. col_1_2 " problem Nr. 1" triplett errors on, corrected via b3 / b6 D1 errors on D1 errors off D1 errors off D1 errors on ... the D1 is a problem of its own

  7. col_2_5_6 " problem Nr. 2" triplett errors correction D1 errors off D1 errors off b3 on, b6 on D1 errors off b3, b6 off D1 errors off b3 on, b6 off col_2_5_8 D1 errors off b3,a3,b4,a4,b6 on D1 errors off b3, b6 on D1 errors off b3, b6 off ... we need much more than b3, b6 !!!

  8. " problem Nr. 3 ? ... a non-problem" triplett errors correction via a3,b3,a4,b4,b6 matching quads Q4 ... Q7 ? higher order multipoles ( > 11) D1 errors off a3,b3,a4,b4, b6 on errors Q4 ... Q7 off a3,b3,a4,b4, b6 on errors Q4 ... Q7 on a3,b3,a4,b4, b6 on multipoles ≤ 11 ... two non- problems: multipoles > 11 the matching quads Q4... Q7

  9. beta beat comp & beam screen D1 errors off beat beat comp. on * beat beat comp. off beam screen contribution .... negligible bs off / bs on

  10. scaling multipole errors: Based on Q2 Magnet ! ----------------------------------------------------------------------- ! ********Magnet type : MQXC/MQXD (new Inner Triplet Quad)*************** ! ----------------------------------------------------------------------- bn in collision b1M_MQXCD_col := 0.0000 ; b1U_MQXCD_col := 0.0000 ; b1R_MQXCD_col := 0.0000 ; b2M_MQXCD_col := 0.0000 ; b2U_MQXCD_col := 0.0000 ; b2R_MQXCD_col := 0.0000 ; b3M_MQXCD_col := 0.0000 ; b3U_MQXCD_col := 0.4600 ; b3R_MQXCD_col := 0.8900 ; b4M_MQXCD_col := 0.0000 ; b4U_MQXCD_col := 0.6400 ; b4R_MQXCD_col := 0.6400 ; b5M_MQXCD_col := 0.0000 ; b5U_MQXCD_col := 0.4600 ; b5R_MQXCD_col := 0.4600 ; b6M_MQXCD_col := 0.0000 ; b6U_MQXCD_col := 1.7700 ; b6R_MQXCD_col := 1.2800 ; b7M_MQXCD_col := 0.0000 ; b7U_MQXCD_col := 0.2100 ; b7R_MQXCD_col := 0.2100 ; b8M_MQXCD_col := 0.0000 ; b8U_MQXCD_col := 0.1600 ; b8R_MQXCD_col := 0.1600 ; b9M_MQXCD_col := 0.0000 ; b9U_MQXCD_col := 0.0800 ; b9R_MQXCD_col := 0.0800 ; b10M_MQXCD_col := 0.0000 ; b10U_MQXCD_col := 0.2000 ; b10R_MQXCD_col := 0.0600 ; b11M_MQXCD_col := 0.0000 ; b11U_MQXCD_col := 0.0300 ; b11R_MQXCD_col := 0.0300 ; b12M_MQXCD_col := 0.0000 ; b12U_MQXCD_col := 0.0200 ; b12R_MQXCD_col := 0.0200 ; b13M_MQXCD_col := 0.0000 ; b13U_MQXCD_col := 0.0200 ; b13R_MQXCD_col := 0.0100 ; b14M_MQXCD_col := 0.0000 ; b14U_MQXCD_col := 0.0400 ; b14R_MQXCD_col := 0.0100 ; b15M_MQXCD_col := 0.0000 ; b15U_MQXCD_col := 0.0000 ; b15R_MQXCD_col := 0.0000 ; effect of multipole on beam: Error-Table: ~.V2 scaling via aperture radius r =17mm → r = 40mm scaling via optics ! an in collision a1M_MQXCD_col := 0.0000 ; a1U_MQXCD_col := 0.0000 ; a1R_MQXCD_col := 0.0000 ; a2M_MQXCD_col := 0.0000 ; a2U_MQXCD_col := 0.0000 ; a2R_MQXCD_col := 0.0000 ; a3M_MQXCD_col := 0.0000 ; a3U_MQXCD_col := 0.8900 ; a3R_MQXCD_col := 0.8900 ; a4M_MQXCD_col := 0.0000 ; a4U_MQXCD_col := 0.6400 ; a4R_MQXCD_col := 0.6400 ; a5M_MQXCD_col := 0.0000 ; a5U_MQXCD_col := 0.4600 ; a5R_MQXCD_col := 0.4600 ; a6M_MQXCD_col := 0.0000 ; a6U_MQXCD_col := 1.2700 ; a6R_MQXCD_col := 0.3300 ; a7M_MQXCD_col := 0.0000 ; a7U_MQXCD_col := 0.2100 ; a7R_MQXCD_col := 0.2100 ; a8M_MQXCD_col := 0.0000 ; a8U_MQXCD_col := 0.1600 ; a8R_MQXCD_col := 0.1600 ; a9M_MQXCD_col := 0.0000 ; a9U_MQXCD_col := 0.0800 ; a9R_MQXCD_col := 0.0800 ; a10M_MQXCD_col := 0.0000 ; a10U_MQXCD_col := 0.1400 ; a10R_MQXCD_col := 0.0600 ; a11M_MQXCD_col := 0.0000 ; a11U_MQXCD_col := 0.0300 ; a11R_MQXCD_col := 0.0300 ; a12M_MQXCD_col := 0.0000 ; a12U_MQXCD_col := 0.0200 ; a12R_MQXCD_col := 0.0200 ; a13M_MQXCD_col := 0.0000 ; a13U_MQXCD_col := 0.0100 ; a13R_MQXCD_col := 0.0100 ; a14M_MQXCD_col := 0.0000 ; a14U_MQXCD_col := 0.0300 ; a14R_MQXCD_col := 0.0100 ; a15M_MQXCD_col := 0.0000 ; a15U_MQXCD_col := 0.0000 ; a15R_MQXCD_col := 0.0000 ; systematic uncertainty random → new "target error table" ~ target 0

  11. " problem Nr. 4 ... triplett error table ~.v1 Ezios new error table ~.v2 (gaps filled) scaled error table via ref radius and optics D1 errors off scaled error table via ref radius and optics ~.target_0 error table ~.v2 / v1 ... the problem is the large multipole contributions of the new MQXC quarupole

  12. Error-Tables: Hunting the Mutlipoles collision, "uncertainty" ~.V2 ~target_0 / b1U_MQXCD_col := 0.0000 b2U_MQXCD_col := 0.0000 b3U_MQXCD_col := 0.2550 b4U_MQXCD_col := 0.1440 b5U_MQXCD_col := 0.1590 b6U_MQXCD_col := 0.4400 b7U_MQXCD_col := 0.0980 b8U_MQXCD_col := 0.0284 b9U_MQXCD_col := 0.0606 b10U_MQXCD_col := 0.2000 b11U_MQXCD_col := 0.0300 b12U_MQXCD_col := 0.0200 b13U_MQXCD_col := 0.0200 b14U_MQXCD_col := 0.0400 b15U_MQXCD_col := 0.0000 b1U_MQXCD_col := 0.0000 b2U_MQXCD_col := 0.0000 b3U_MQXCD_col := 0.4600 b4U_MQXCD_col := 0.6400 b5U_MQXCD_col := 0.4600 b6U_MQXCD_col := 1.7700 b7U_MQXCD_col := 0.2100 b8U_MQXCD_col := 0.1600 b9U_MQXCD_col := 0.0800 b10U_MQXCD_col := 0.2000 b11U_MQXCD_col := 0.0300 b12U_MQXCD_col := 0.0200 b13U_MQXCD_col := 0.0200 b14U_MQXCD_col := 0.0400 b15U_MQXCD_col := 0.0000 bn correction scheme: a3,b3,a4,b4,b6 a1U_MQXCD_col := 0.0000 a2U_MQXCD_col := 0.0000 a3U_MQXCD_col := 0.3220 a4U_MQXCD_col := 0.4110 a5U_MQXCD_col := 0.1220 a6U_MQXCD_col := 0.4840 a7U_MQXCD_col := 0.0800 a8U_MQXCD_col := 0.0670 a9U_MQXCD_col := 0.0800 a10U_MQXCD_col := 0.1000 a11U_MQXCD_col := 0.0300 a12U_MQXCD_col := 0.0200 a13U_MQXCD_col := 0.0100 a14U_MQXCD_col := 0.0300 a15U_MQXCD_col := 0.0000 a1U_MQXCD_col := 0.0000 a2U_MQXCD_col := 0.0000 a3U_MQXCD_col := 0.8900 a4U_MQXCD_col := 0.6400 a5U_MQXCD_col := 0.4600 a6U_MQXCD_col := 1.2700 a7U_MQXCD_col := 0.2100 a8U_MQXCD_col := 0.1600 a9U_MQXCD_col := 0.0800 a10U_MQXCD_col := 0.1400 a11U_MQXCD_col := 0.0300 a12U_MQXCD_col := 0.0200 a13U_MQXCD_col := 0.0100 a14U_MQXCD_col := 0.0300 a15U_MQXCD_col := 0.0000 an

  13. Error-Tables: random, collision ~.V2 ~target_0 / b1R_MQXCD_col := 0.0000 b2R_MQXCD_col := 0.0000 b3R_MQXCD_col := 0.8900 b4R_MQXCD_col := 0.6400 b5R_MQXCD_col := 0.4600 b6R_MQXCD_col := 1.2800 b7R_MQXCD_col := 0.2100 b8R_MQXCD_col := 0.1600 b9R_MQXCD_col := 0.0800 b10R_MQXCD_col := 0.0600 b11R_MQXCD_col := 0.0300 b12R_MQXCD_col := 0.0200 b13R_MQXCD_col := 0.0100 b14R_MQXCD_col := 0.0100 b15R_MQXCD_col := 0.0000 b1R_MQXCD_col := 0.0000 b2R_MQXCD_col := 0.0000 b3R_MQXCD_col := 0.4850 b4R_MQXCD_col := 0.1440 b5R_MQXCD_col := 0.3030 b6R_MQXCD_col := 0.6480 b7R_MQXCD_col := 0.1180 b8R_MQXCD_col := 0.0455 b9R_MQXCD_col := 0.0800 b10R_MQXCD_col := 0.0600 b11R_MQXCD_col := 0.0300 b12R_MQXCD_col := 0.0200 b13R_MQXCD_col := 0.0100 b14R_MQXCD_col := 0.0100 b15R_MQXCD_col := 0.0000 bn a1R_MQXCD_col := 0.0000 a2R_MQXCD_col := 0.0000 a3R_MQXCD_col := 0.3910 a4R_MQXCD_col := 0.3590 a5R_MQXCD_col := 0.1980 a6R_MQXCD_col := 0.3300 a7R_MQXCD_col := 0.1290 a8R_MQXCD_col := 0.1330 a9R_MQXCD_col := 0.0560 a10R_MQXCD_col := 0.0600 a11R_MQXCD_col := 0.0300 a12R_MQXCD_col := 0.0200 a13R_MQXCD_col := 0.0100 a14R_MQXCD_col := 0.0100 a15R_MQXCD_col := 0.0000 a1R_MQXCD_col := 0.0000 a2R_MQXCD_col := 0.0000 a3R_MQXCD_col := 0.8900 a4R_MQXCD_col := 0.6400 a5R_MQXCD_col := 0.4600 a6R_MQXCD_col := 0.3300 a7R_MQXCD_col := 0.2100 a8R_MQXCD_col := 0.1600 a9R_MQXCD_col := 0.0800 a10R_MQXCD_col := 0.0600 a11R_MQXCD_col := 0.0300 a12R_MQXCD_col := 0.0200 a13R_MQXCD_col := 0.0100 a14R_MQXCD_col := 0.0100 a15R_MQXCD_col := 0.0000 an

  14. col_19 " beta beat compensation" finally a good news D1 errors off horizonal detuning with amplitude 0.01 vertical detuning with amplitude 0.01 0 0 -0.01 10 -0.01 0 initial amplitude 0 10 initial amplitude

  15. Resumé: we need better quadrupoles we have to compensate a large number of multipoles in MQXC we need to think about D1 col19: D1 errors off triplett errors on, error table target 0 correction via b3,a3,b4,a4,b6 col9: D1 errors on triplett errors on, error table v1 no correction

  16. Further Plans: * identify the most critical multipoles * define tolerance limits for the new triplett quadrupole * re - include the D1 errors ... and compensate ? Conclusion ...

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