20.08.2002 SSWG / J. Wenninger 1

Induced Chromaticity ModelInduced Chromaticity Model

The present chromaticity correction for the ramp is based on the model for the induced chromaticity given by :

where the first two terms model remanent field effects and the third term accounts for the eddy currents.

P

Pc

P

baind

PlanePlane aa b [GeV/c]b [GeV/c] c [s]c [s]

HH 0.210.21 -4.63-4.63 0.300.30

VV -0.07-0.07 10.010.0 -0.28-0.28

20.08.2002 SSWG / J. Wenninger 2

Chromaticity trims in the rampChromaticity trims in the ramp

The model does not fully account for the observed chromaticity :

important trims are required in addition. less efficient cycle setups. trims are copied from one cycle to the next (and not always in the

best way..).

Goal of this analysis :

• Recover the trims under known conditions (i.e. with complete chromaticity measurements [multiQ]) :

• 2 nominal LHC cycles (537,540) to 540 GeV.• one special LHC cycle (542) to 80 GeV.

• Check the reproducibility.• Establish a better model.• …

20.08.2002 SSWG / J. Wenninger 3

LHC Ramp Chromaticity TrimsLHC Ramp Chromaticity Trims

• Reconstructed total trim to obtain ~ +0.05 to +0.1 in the ramp (2 cycles).• Trims are reconstructed from the PC currents (“bug” in the target function setting).• Reproducibility is good, ~ 0.05 or better.

Correction of the natural chromaticity

(~ 1.26) excluded !

20.08.2002 SSWG / J. Wenninger 4

Model versus TrimsModel versus Trims

Example of the difference between total trim [] and modeled trim [-].

Observed ~ twice as large as model.

Un-modeled “bump”peaking @ 400 GeV.

20.08.2002 SSWG / J. Wenninger 5

Model versus Trims (II)Model versus Trims (II)

Difference between total trim [] and modeled trim [-] – 80 GeV cycle.

Change due to dP/dt (eddy currents) ~ correct !

Measured is smooth over this transition.

20.08.2002 SSWG / J. Wenninger 6

Model ImprovementModel Improvement

•The default model cannot account for the “bump” between 100 and 400 GeV…

• Empirically add a term :

where p0 ~ 400 GeV/c.

0

00 ,)(

pp

pppp

e

dind

Very good fit, but with differentvalues for a and b. The eddy current term c ~ unchanged.

20.08.2002 SSWG / J. Wenninger 7

b3 Components in Dipolesb3 Components in Dipoles

With Angeles Faus-Golfe’s SPS model including field errors (b3, b4, b5), one can convert the chromaticity trims into b3 field components for the MBA and MBB dipoles.

The relation between chromaticity and b3 components is :

V

H

b

a

Q

Q

b

b

'

'

330.0150.0

122.0252.0

3

3

(b3 in 10-3 m-2), Q’ is the “usual” chromaticity….

b

a

V

H

b

b

Q

Q

3

3

89.332.2

89.110.5

'

'

20.08.2002 SSWG / J. Wenninger 8

b3 Components in Dipoles (II)b3 Components in Dipoles (II)

Results from measurements@ 26 GeV in 2001

Uncertainties on b3 ~ 0.4 10-3 m-2

20.08.2002 SSWG / J. Wenninger 9

SummarySummary

• For the LHC cycles in the SPS :• the chromaticity trims seem to be very reproducible, but we must

be careful when copying trims between cycles.

• the present model for the chromaticity is off by a factor ~ 2, it can be improved by an empirical correction.

• Next step :• During the next long MD, trim back the settings of the FT cycle to the time of the setup where was measured over most of the cycle. Recover the sextupole currents and reconstruct the trims.

• Refit the model with the FT settings, consistency with LHC cycle.

• For FT, the eddy currents effects are much more violent.