beam optics requirements for quadrupoles and correctors

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M. Giovannozzi – Review of the Tests of M. Giovannozzi – Review of the Tests of Superconducting Magnets in SM18Superconducting Magnets in SM18

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Beam optics requirements for Beam optics requirements for quadrupoles and correctorsquadrupoles and correctors

• Alignment tolerancesAlignment tolerances

• Transfer function issuesTransfer function issues

• Other issuesOther issues

• CorrectorsCorrectors

• SummarySummary

Acknowledgements: Acknowledgements: O. Brüning, S. Fartoukh, J.-B. O. Brüning, S. Fartoukh, J.-B. Jeanneret, J.-P. Koutchouk, A.-M. LombardiJeanneret, J.-P. Koutchouk, A.-M. Lombardi

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Alignment tolerances: MQs - IAlignment tolerances: MQs - I

Transverse displacement:Transverse displacement:Impact on available apertureImpact on available apertureImpact on rms closed orbitImpact on rms closed orbitImpact on closed orbit corrector Impact on closed orbit corrector strength strength

Tolerances take into accountTolerances take into accountrandom b1 in main dipolesrandom b1 in main dipolesMQ misalignmentMQ misalignmentBeam Position Monitor (BPM) Beam Position Monitor (BPM) misalignmentmisalignment

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Alignment tolerances: MQs - Alignment tolerances: MQs - IIII

S. Fartoukh LHC Project Note S. Fartoukh LHC Project Note 260260

Rms Rms valuesvalues

Hor. Disp. Hor. Disp. (mm)(mm)

Ver. Disp. Ver. Disp. (mm)(mm)

Roll Roll angle angle

(mrad)(mrad)

MQMQ 0.370.37 0.370.37 0.50.5

BPMBPM 0.240.24 0.240.24

Alignment Mini-Alignment Mini-Workshop (Dec. Workshop (Dec. 2000), LHC Project 2000), LHC Project Note 297, LHC Project Note 297, LHC Project Report 397Report 397

Roll angle:Roll angle: Impact on couplingImpact on coupling Values of tolerancesValues of tolerances

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Alignment tolerances: DS and MS Alignment tolerances: DS and MS quads - Iquads - I

Similar arguments hold as for MQs, butSimilar arguments hold as for MQs, but

Aperture is tighter (higher values of beta-Aperture is tighter (higher values of beta-function)function)

The situation can be The situation can be improved by improved by reducing reducing *, but *, but there are still limits there are still limits in Q10/Q11in Q10/Q11

S. Fartoukh 23 LTC Meeting S. Fartoukh 23 LTC Meeting ““New optics solutions in IR1 New optics solutions in IR1 and IR5”and IR5” (31 March 2004) (31 March 2004)

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Alignment tolerances: DS and MS Alignment tolerances: DS and MS quads - IIquads - II

IR2 – Beam2 IR2 – Beam2

O. Brüning 23 LTC Meeting O. Brüning 23 LTC Meeting ““New optics solutions in IR2 New optics solutions in IR2 and IR8”and IR8” (31 March 2004) (31 March 2004)

IR8 – Beam1 IR8 – Beam1

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Alignment tolerances: DS and MS Alignment tolerances: DS and MS quads- IIIquads- III

Values of tolerances (assuming realignment after one year)Values of tolerances (assuming realignment after one year)

Rms Rms valuesvalues

Hor. Hor. Disp. Disp. (mm)(mm)

Ver. Ver. Disp. Disp. (mm)(mm)

Roll Roll angle angle

(mrad)(mrad)

MQM(L,CMQM(L,C))

0.430.43 0.430.43 0.30.3

MQYMQY 0.430.43 0.430.43 0.30.3A. Verdier, presentation at the MEB A. Verdier, presentation at the MEB meetingmeeting

Measurements of Measurements of geometric/magnetic axes are geometric/magnetic axes are requiredrequired

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Transfer function issues - ITransfer function issues - IGradient errors generate:Gradient errors generate:

Tune variationTune variationBeta-beatingBeta-beatingSpurious dispersionSpurious dispersion

Tune correction is performed by means of:Tune correction is performed by means of:Independent Independent small tune correctionsmall tune correction (trim (trim quadrupoles between Q14 and Q21).quadrupoles between Q14 and Q21).Independent Independent large tune correction. large tune correction. These can be These can be performed by usingperformed by using

MQTL quads: located in Dispersion Suppressors (DS). MQTL quads: located in Dispersion Suppressors (DS). However, they induce strong beta-beating if used for However, they induce strong beta-beating if used for generating generating Q>0.1Q>0.1Retuning insertionsRetuning insertions

All this requires, eitherAll this requires, eitherGood knowledge of the transfer functionGood knowledge of the transfer function, or, orBeam based approachBeam based approach

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Transfer function issues - IITransfer function issues - IIBeta-beating (random b2):Beta-beating (random b2):

Peak value is limited to Peak value is limited to 21%21% (injection) (injection)Off-momentum beta-beating is estimated to Off-momentum beta-beating is estimated to 7%7% (injection)(injection)Budget for peak beta-beating is: Budget for peak beta-beating is: 14%.14%.Such a budget is already taken by: MBs, MQs, feed-down Such a budget is already taken by: MBs, MQs, feed-down from nonlinear correctors.from nonlinear correctors.

It is found that It is found that // = Cost * (random b2) = Cost * (random b2)

WithWith InjectioInjectionn

MQsMQs MQM(C,L)MQM(C,L)ss

MQYsMQYs

CostCost 2525 1414 99

2020 1515These large values can be attained These large values can be attained assuming quads are stronger than assuming quads are stronger than nominal optics (flexibility is nominal optics (flexibility is mandatory)mandatory)

MQs: 392 magnetsMQs: 392 magnets

MQM(C,L)s: 86 MQM(C,L)s: 86 magnetsmagnets

MQY: 24 magnetsMQY: 24 magnets

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Transfer function issues - IIITransfer function issues - IIIAdding (quadratically) the contribution of Adding (quadratically) the contribution of DS and MS quadrupoles (assuming 10 DS and MS quadrupoles (assuming 10 units rms of b2) givesunits rms of b2) gives

// 14.9 % or 15.9% 14.9 % or 15.9%The allocated budget is The allocated budget is exceededexceeded (small (small amount)!amount)!Spurious normalised dispersion:Spurious normalised dispersion:

Dx/ Dx/ √√= Cost * (random b2)= Cost * (random b2)

MQsMQs MQM(C,L)MQM(C,L)ss

MQYMQYss

CosCostt

44 1.41.4 0.20.2

Tolerance at injection Tolerance at injection is set to is set to

Dx/ √Dx/ √< 1.3 10< 1.3 10-2-2 m m1/21/2

b2 random of 10 units b2 random of 10 units (rms) is well within (rms) is well within budgetbudget

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Other issues: squeeze - IOther issues: squeeze - IDuring the squeeze, gradients of DS and MS During the squeeze, gradients of DS and MS quadrupoles will change. This requires a very good quadrupoles will change. This requires a very good knowledge of time-dependent effects, hysteresis etc.knowledge of time-dependent effects, hysteresis etc.

S. Fartoukh 23 LTC Meeting “S. Fartoukh 23 LTC Meeting “New optics solutions in IR1 and New optics solutions in IR1 and IR5”IR5” (31 March 2004) (31 March 2004)

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Other issues: squeeze - IIOther issues: squeeze - IIO. Brüning 23 LTC O. Brüning 23 LTC Meeting “New optics Meeting “New optics solutions in IR2 and solutions in IR2 and IR8” (31 March 2004)IR8” (31 March 2004)

In general:In general:

Q4, Q5, Q6 decrease Q4, Q5, Q6 decrease during beta-squeeze during beta-squeeze (IR1, IR5, IR8)(IR1, IR5, IR8)

QTL11, QT12, QT13 QTL11, QT12, QT13 deserve special care deserve special care (IR1, IR5)(IR1, IR5)

Measurements of time-Measurements of time-dependent effects, dependent effects, hysteresis are requiredhysteresis are required

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Other issues: DA - IOther issues: DA - IImpact on DA of Impact on DA of field quality of DS field quality of DS and MS is by far and MS is by far non-negligible.non-negligible.

Presented at Presented at FQWG (09/12/03, FQWG (09/12/03, 21/09/04).21/09/04).

Initial assumption Initial assumption of MQ-like field of MQ-like field quality for DS and quality for DS and MS quads MS quads produced a produced a dramatic loss of dramatic loss of DA.DA.

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Other issues: DA - IIOther issues: DA - IIMeasured field Measured field errors for DS errors for DS and MS quads and MS quads improved DA.improved DA.

Impact of MQMs Impact of MQMs on DA is on DA is marginal (unless marginal (unless at 45º).at 45º).

Impact of MQYs Impact of MQYs is clearly visible, is clearly visible, but less but less pronounced than pronounced than before.before.Measurements of Measurements of field quality are field quality are requiredrequired

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Correctors - ICorrectors - ICan be powered to any value => Can be powered to any value => control control of hysteresisof hysteresis

Are adjusted during setting up and Are adjusted during setting up and commissioning => commissioning => knowledge of the knowledge of the transfer functiontransfer function

Compensate for errors => Compensate for errors => field quality field quality such that there is no effect on the DAsuch that there is no effect on the DA

Nested correctors => Nested correctors => knowledge of knowledge of cross-talkcross-talk

The measurement accuracy of the The measurement accuracy of the observable to be corrected sets the observable to be corrected sets the targets.targets.

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Correctors - IICorrectors - IIRequirements were discussed atRequirements were discussed at

FQWG meetingsFQWG meetingsS. Fartoukh (March 2004)S. Fartoukh (March 2004)M. Giovannozzi (November 2004)M. Giovannozzi (November 2004)A. Lombardi (March and November 2004)A. Lombardi (March and November 2004)

MAC meetingMAC meetingA. Lombardi (July 2004)A. Lombardi (July 2004)

Status of measurements in Block 4 were also Status of measurements in Block 4 were also reviewed at FQWG (V. Venturini Delsolaro, reviewed at FQWG (V. Venturini Delsolaro, November 2004):November 2004):

For some magnet classes the warm/cold For some magnet classes the warm/cold correlations are not considered good enough, correlations are not considered good enough, essentially because of poor statistics.essentially because of poor statistics.

Conclusions on the strategy of magnetic Conclusions on the strategy of magnetic measurements for corrector will be drawn in measurements for corrector will be drawn in few months by FQWG.few months by FQWG.

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Conclusions - IConclusions - IMQsMQs

Strategy discussed at Arc SSS Review (19 May Strategy discussed at Arc SSS Review (19 May 2004) should be pursued.2004) should be pursued.

DS and MS quadsDS and MS quads

Aperture is rather critical at injection (DS Aperture is rather critical at injection (DS quadrupoles): accurate quadrupoles): accurate axis (magnetic/geometric) axis (magnetic/geometric) measurements importantmeasurements important. .

Transfer functionTransfer function is crucial (beta-beating, IR is crucial (beta-beating, IR tuning). The required accuracy is about 10 units.tuning). The required accuracy is about 10 units.

DetailedDetailed magnetic measurements (time-magnetic measurements (time-dependent effects, hysteresis)dependent effects, hysteresis) should be foreseen should be foreseen for quadrupoles with critical behaviour during for quadrupoles with critical behaviour during squeeze.squeeze.

Field qualityField quality is also crucial and should be is also crucial and should be measured.measured.

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Conclusions - IIConclusions - IICorrectorsCorrectors

Targets values for the field quality Targets values for the field quality (in a (in a broad sense, including also alignment and broad sense, including also alignment and transfer function) transfer function) of correctors were of correctors were presented and discussed at many FQWG presented and discussed at many FQWG meetings. This activity should be completed.meetings. This activity should be completed.

The poor statistics of magnetic The poor statistics of magnetic measurements for some magnet classes measurements for some magnet classes makes the warm/cold correlations not good makes the warm/cold correlations not good enoughenough..

It is recommended to continue the spot It is recommended to continue the spot checks of the series correctors in Block 4 checks of the series correctors in Block 4 (baseline).(baseline).

beam optics requirements for quadrupoles and correctors

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