Tracking Calculations for the LHC Upgrade - Collision Optics -

Bernhard Holzer, CERN BE-ABPand many colleagues !!!

Q4

Q5

LHC Standard Collision Optics ... and the Upgrade

critical issues for the DA ??? error tables ... at the triplett ? ... at the new D1 ? ... at the matching section ?

and which multipoles?

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

LHC - Upgradeerror table for the new MQXC triplett quadrupole

" ITD1_error table_V1"

col_9

vertical detuning with amplitude

initial amplitude 0 10

-0.01

0

0.01

" the worst case"triplett errors onD1 errors onno correction

horizonal detuning with amplitude

initial amplitude 0 10

-0.01

0.01

0

col_9" the worst case"

triplett errors onD1 errors onno correction

below 6 sigma !!

col_1_2 " problem Nr. 1"triplett errors on, corrected via b3 / b6 D1 errors on D1 errors off

D1 errors on

D1 errors off

... the D1 is a problem of its own

col_2_5_6

col_2_5_8

" problem Nr. 2"triplett errors correctionD1 errors off

D1 errors offb3, b6 offD1 errors off

b3 on, b6 off

D1 errors offb3 on, b6 on

D1 errors offb3,a3,b4,a4,b6 on

D1 errors offb3, b6 off

D1 errors offb3, b6 on

... we need much more than b3, b6 !!!

" problem Nr. 3 ? ... a non-problem" triplett errors correction via a3,b3,a4,b4,b6 matching quads Q4 ... Q7 ? higher order multipoles ( > 11)

a3,b3,a4,b4, b6 onerrors Q4 ... Q7 off

D1 errors off

a3,b3,a4,b4, b6 onerrors Q4 ... Q7 on

a3,b3,a4,b4, b6 onmultipoles ≤ 11

... two non- problems: multipoles > 11 the matching quads Q4... Q7

beta beat comp & beam screen

beat beat comp. on

D1 errors off

beat beat comp. off

beam screen contribution .... negligiblebs off / bs on

*

! -----------------------------------------------------------------------

! ********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 ;

Error-Table: ~.V2

! 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

scaling multipole errors: Based on Q2 Magnet

effect of multipole on beam:

2

1

1*****

n

nref

nref R

bRlG

scaling via aperture radius r =17mm → r = 40mm scaling via optics

22

**)()(

n

old

new

n

new

oldnn R

Roldbnewb

→ new "target error table" ~ target 0

D1 errors off

" problem Nr. 4 ... triplett error table ~.v1Ezios new error table ~.v2 (gaps filled)scaled error table via ref radius and optics

scaled error tablevia ref radius and optics~.target_0

... the problem is the large multipole contributions of the new MQXC quarupole

error table ~.v2 / v1

Error-Tables: Hunting the Mutlipoles collision, "uncertainty"

b1U_MQXCD_col := 0.0000b2U_MQXCD_col := 0.0000b3U_MQXCD_col := 0.4600b4U_MQXCD_col := 0.6400b5U_MQXCD_col := 0.4600b6U_MQXCD_col := 1.7700b7U_MQXCD_col := 0.2100b8U_MQXCD_col := 0.1600b9U_MQXCD_col := 0.0800

b10U_MQXCD_col := 0.2000b11U_MQXCD_col := 0.0300b12U_MQXCD_col := 0.0200b13U_MQXCD_col := 0.0200b14U_MQXCD_col := 0.0400b15U_MQXCD_col := 0.0000

~.V2 ~target_0 /

a1U_MQXCD_col := 0.0000a2U_MQXCD_col := 0.0000a3U_MQXCD_col := 0.8900a4U_MQXCD_col := 0.6400a5U_MQXCD_col := 0.4600a6U_MQXCD_col := 1.2700a7U_MQXCD_col := 0.2100a8U_MQXCD_col := 0.1600a9U_MQXCD_col := 0.0800

a10U_MQXCD_col := 0.1400a11U_MQXCD_col := 0.0300a12U_MQXCD_col := 0.0200a13U_MQXCD_col := 0.0100a14U_MQXCD_col := 0.0300a15U_MQXCD_col := 0.0000

b1U_MQXCD_col := 0.0000b2U_MQXCD_col := 0.0000b3U_MQXCD_col := 0.2550b4U_MQXCD_col := 0.1440b5U_MQXCD_col := 0.1590b6U_MQXCD_col := 0.4400b7U_MQXCD_col := 0.0980b8U_MQXCD_col := 0.0284b9U_MQXCD_col := 0.0606

b10U_MQXCD_col := 0.2000b11U_MQXCD_col := 0.0300b12U_MQXCD_col := 0.0200b13U_MQXCD_col := 0.0200b14U_MQXCD_col := 0.0400b15U_MQXCD_col := 0.0000

bn

an

a1U_MQXCD_col := 0.0000a2U_MQXCD_col := 0.0000a3U_MQXCD_col := 0.3220a4U_MQXCD_col := 0.4110a5U_MQXCD_col := 0.1220a6U_MQXCD_col := 0.4840a7U_MQXCD_col := 0.0800a8U_MQXCD_col := 0.0670a9U_MQXCD_col := 0.0800

a10U_MQXCD_col := 0.1000a11U_MQXCD_col := 0.0300a12U_MQXCD_col := 0.0200a13U_MQXCD_col := 0.0100a14U_MQXCD_col := 0.0300a15U_MQXCD_col := 0.0000

correction scheme: a3,b3,a4,b4,b6

Error-Tables: random, collision

~.V2 ~target_0 /

bn

an

a1R_MQXCD_col := 0.0000a2R_MQXCD_col := 0.0000a3R_MQXCD_col := 0.3910a4R_MQXCD_col := 0.3590a5R_MQXCD_col := 0.1980a6R_MQXCD_col := 0.3300a7R_MQXCD_col := 0.1290a8R_MQXCD_col := 0.1330a9R_MQXCD_col := 0.0560

a10R_MQXCD_col := 0.0600a11R_MQXCD_col := 0.0300a12R_MQXCD_col := 0.0200a13R_MQXCD_col := 0.0100a14R_MQXCD_col := 0.0100a15R_MQXCD_col := 0.0000

b1R_MQXCD_col := 0.0000b2R_MQXCD_col := 0.0000b3R_MQXCD_col := 0.4850b4R_MQXCD_col := 0.1440b5R_MQXCD_col := 0.3030b6R_MQXCD_col := 0.6480b7R_MQXCD_col := 0.1180b8R_MQXCD_col := 0.0455b9R_MQXCD_col := 0.0800

b10R_MQXCD_col := 0.0600b11R_MQXCD_col := 0.0300b12R_MQXCD_col := 0.0200b13R_MQXCD_col := 0.0100b14R_MQXCD_col := 0.0100b15R_MQXCD_col := 0.0000

b1R_MQXCD_col := 0.0000b2R_MQXCD_col := 0.0000b3R_MQXCD_col := 0.8900b4R_MQXCD_col := 0.6400b5R_MQXCD_col := 0.4600b6R_MQXCD_col := 1.2800b7R_MQXCD_col := 0.2100b8R_MQXCD_col := 0.1600b9R_MQXCD_col := 0.0800

b10R_MQXCD_col := 0.0600b11R_MQXCD_col := 0.0300b12R_MQXCD_col := 0.0200b13R_MQXCD_col := 0.0100b14R_MQXCD_col := 0.0100b15R_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

col_19

vertical detuning with amplitude

initial amplitude 0 10

-0.01

0

0.01

horizonal detuning with amplitude

initial amplitude 0 10

-0.01

0.01

0

" beta beat compensation"finally a good news

D1 errors off

Resumé: we need better quadrupoleswe have to compensate a large number of multipoles in MQXCwe need to think about D1

col9: D1 errors on triplett errors on, error table v1 no correction

col19: D1 errors off triplett errors on, error table target 0 correction via b3,a3,b4,a4,b6

Further Plans:

* identify the most critical multipoles

* define tolerance limits for the new triplett quadrupole

* re - include the D1 errors ... and compensate ?

Conclusion ...