Nonlinear Field Quality Checks

Frank ZimmermannLHCCWG 12.07.2006

Based on presentation in Chamonix 2003 including references therein (O. Bruning, S. Fartoukh, M. Hayes, B. Jeanneret, J.-P. Koutchouk, R. Ostojic, Q. Qin, F. Schmidt, S. Weisz, and others)

LHC optics in a nutshell

8 arcs with 27 FODO cells each (23 regular cells, 2x2 cells for dispersion suppressor) phase advance/cell ~ 90 degrees

8 straight sections, 4 of which low- insertions

3 types of corrector circuits

• spool pieces at dipole ends for b3, b4 and b5; powered differently per arc and per beam; total number of circuits 48

• lattice correctors for a2, b2, a3, b3, and b4; total number of circuits 168

• correction coils for triplet field errors a3, b3, a4, b4, & b6; total number 40

total # of independent correction circuits: 256!

#arc correction circuits & #elements/circuit

type # circuits elements/circuitspool piece b3 16 154spool piece b4 16 77spool piece b5 16 77lattice corr b2 32 8lattice corr a2 24 4 or 2lattice corr b3d 32 11 or 12lattice corr b3f 32 10 or 9lattice corr a3 16 4lattice corr b4 32 8 or 13

nonlinear optics tolerancesobservable target tolerancedynamic aperture 12 0.5-1 tune spread 0.0 7x10-3

linear chrom. Q’x,y >0 0<Q’<2

2nd o. chrom. Q’’x,y 0 -103<Q’’<103

3rd o. chrom. Q’’’x,y 0 -5x105<Q’’<3x106

geom. det. dQx,y/d 0 +/-7x103 m-1

chr.-g. det. d2Qx,y/dd 0 +/-7x106 m-1

numbers include considerations on dynamic aperture, tune footprint, and off-momentum measurements [O. Bruning, S. Fartoukh, LHC PR 501]

general nonlinear measurement scheme

ds

Rxb

BBnQ n

ref

nco

n 1

20

41

[study by Jean-Pierre Koutchouk for RHIC low- insertions]

measure change on phase advance or tune resulting from an off-center orbit in a nonlinear field; orbit can be shifted either by closed-orbit bumps or using dispersion

02/ dsbnn 02 dsbD n

nx

0dsbn

orbit bump yields: dispersion bump yields:

MAD design:

differences are of the order of 10%!

10% variation in b3 or b5 corrector strengths can change dynamic aperture by >1 [Q. Qin, S. Weisz, LHC PN 42, 1996]

normal sextupole b3Local correction (arc by arc) to within 50% needed [M.

Hayes, LHC PR 522]

Proposed procedure:• pre-set spool pieces to values determined from magnet

measurements• adjust Q’ to ~2 units with 2 (pairs of) families of lattice

sextupoles• check local correction with local dispersion bumps or

groups of 7 bumps across individual arcs, octant by octant• complementarily or additionally, measure off-momentum

(chromatic) phase advance

local b3 correction: bumps across one arcscheme by M. Hayes [LHC PR 522] & O. Bruning [LHC PR 473]

orbit with 7 bump across one arc;peak value of 3 mm

tune difference vs. quality of correction

Q~0.01 for 20% mispowering of b3 spool pieces;→ we can adjust b3 to within 10% (much better than 50% target)

local b3 correction: chromatic phase advance

simulated for 1 kick for p/p=10-3 and p/p=0;3 cases: (1) no spool piece mispowered, (2) sextupole circuit KCS45 missing (BPMs 194 to 257), (3) decapole circuit KCD45 missingwe can detect missing b3 circuits, but not missing b5!

[Chamonix03]

example: chromatic phase-advance measurement in the SPS at 26 GeV

measured in the SPS from averaging over four 5-10 mm (2-4 ) kicks for p/p=5x10-3 and p/p=0 [R Tomas];large discrepancies remain – at the level of the expected missing b3 signature for LHC

skew sextupole a3J.-P. Koutchouk [LHC PN 113]: generation of 2nd o. chromaticity

2~'', 2

1 cQ III

yx QQ yxsxyx iKDdsc

exp21

,2~

322200 ,63500 ,~,

3,~,

armsarcUUarc cac

5.3~200'' ~ cQ

22~2 cQQ III

where ,

tolerance onthis effect

and ,

Proposed procedure: likely no correction needed; check with off-momentum closest tune approach

3102for 007.0 tolerance to meet:

normal octupole b4global correction to within 30% needed [M. Hayes, LHC PR

522]

Proposed procedure:• leave lattice octupoles switched off • separate tunes (to reduce contribution from a3) & minimize

Q’’• verify detuning with amplitude

If Qy’’ and dQx/dy are zeroed, dQx/dx, dQy/dy and Qx’’ are corrected to about 10%

uncor.: Q~10-3 at 3, cor.: Q<10-4 at 3

normal decapole b5Local correction (arc by arc) to within 50% needed [M.

Hayes, LHC PR 522]

Proposed procedure:• first minimize Q’’’ (global)• measure off-momentum detuning with amplitude; without

any correction expect Q~10-3 at 3 and =10-3 (8x smaller for single arc)

• complementarily, measure chromatic phase advance (effect could be difficult to detect)

• measure resonant driving terms (option) • varying kicks to obtain “frequency map’’ (option)

nonlinear chromaticity

simulated nonlinear chromaticities in the LHC; optics with all correctors active, and with missing b3 or b5 spool piece circuitthough fitted 3rd order coefficient changes, also here identification of missing b5 circuit looks challenging!

SPS as testbed for off-momentum studies?

observable

SPS (meas. 06/20/2002

LHC (simul. example)

LHC tolerance

|Q’’| 600 1500 <1000Q’’’ -1.8x106 -3x105 >5x105

SPS at 26 GeV as nonlinear as the LHC(3.5 times LHC tolerance in Q’’’)

conclusions• huge number of LHC corrector circuits; only spool

pieces considered • if effect of corrector important, we can adjust it with

beam-based methods• several alternative diagnostics schemes available for

each type of error• methods function well in simulations including BPM

noise (except b5)• reality may be different (SPS example)• verify as many procedures as possible in the SPS (or

PS,…)