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Nonlinear Field Quality Checks. Frank Zimmermann LHCCWG 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).

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nonlinear field quality checks

Nonlinear Field Quality Checks

Frank Zimmermann

LHCCWG 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)

slide2

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-b insertions

3 types of corrector circuits
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!

nonlinear optics tolerances
nonlinear optics tolerances

numbers include considerations on dynamic aperture,

tune footprint, and off-momentum measurements

[O. Bruning, S. Fartoukh, LHC PR 501]

general nonlinear measurement scheme
general nonlinear measurement scheme

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

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

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 >1s [Q. Qin, S. Weisz, LHC PN 42, 1996]

normal sextupole b3
normal sextupole b3

Local 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 7p bumps across individual arcs, octant by octant
  • complementarily or additionally, measure off-momentum (chromatic) phase advance
slide8

local b3 correction: bumps across one arc

scheme by M. Hayes [LHC PR 522] & O. Bruning [LHC PR 473]

orbit with 7p bump across one arc;

peak value of 3 mm

tune difference vs.

quality of correction

DQ~0.01 for 20% mispowering of b3 spool pieces;

→ we can adjust b3 to within 10% (much better than 50% target)

slide9

local b3 correction: chromatic phase advance

[Chamonix03]

simulated Df for 1s kick for dp/p=10-3 and dp/p=0;

3 cases: (1) no spool piece mispowered,

(2) sextupole circuit KCS45 missing (BPMs 194 to 257),

(3) decapole circuit KCD45 missing

we can detect missing b3 circuits, but not missing b5!

slide10

example: chromatic phase-advance measurement

in the SPS at 26 GeV

measured Df in the SPS from averaging over four 5-10 mm

(2-4 s) kicks for Dp/p=5x10-3 and Dp/p=0 [R Tomas];

large discrepancies remain –

at the level of the expected missing b3 signature for LHC

slide11

skew sextupole a3

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

where ,

and ,

tolerance on

this effect

Proposed procedure: likely no correction needed;

check with off-momentum closest tune approach

tolerance to meet:

slide12

normal octupole b4

global 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/dey are zeroed, dQx/dex, dQy/dey and Qx’’ are corrected to about 10%

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

slide13

normal decapole b5

Local 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 DQ~10-3 at 3s and d=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)
slide14

nonlinear chromaticity

simulated nonlinear chromaticities in the LHC;

optics with all correctors active, and with missing

b3 or b5 spool piece circuit

though fitted 3rd order coefficient changes, also here

identification of missing b5 circuit looks challenging!

sps as testbed for off momentum studies
SPS as testbed for off-momentum studies?

SPS at 26 GeV as nonlinear as the LHC

(3.5 times LHC tolerance in Q’’’)

conclusions
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,…)