Beam dynamics requirements on

MQT

March 21st, 2006

Field Quality Working Group

A. Lombardi and Y. Papaphilippou

FQWG, A.Lombardi, Y.Papaphilippou 221/03/2006

2 families of 8 per ring and sector (MQTF,MQTD), from Q14 to Q21 32 additional powered individually per ring in Q12 and Q13, (total of 160) In addition, 2 pairs of skew quadrupoles MQS (MQT tilted 45o) in Q23 and Q27

powered in series or independently depending on the sector (total of 32) MQT’s used for independent tune-adjustment for both beams. Strong enough to

produce 1 unit of tune-shift but limited to ±0.1. MQS’s used for compensating coupling due to systematic a2 of dipoles + other

random sources Beam dynamics issues: a) Transfer function, b) Alignment, c) Field quality

Tuning and Skew Quadrupole correctors

MQT/MQS/MO

MQT/MQS

Field @ 17mm [T] 2.04

Current [A] 550

Mag. Length [m] 0.32

Ap. Diameter [mm] 56

Number 160/32

FQWG, A.Lombardi, Y.Papaphilippou 321/03/2006

Evaluate the effect of MQT on the tune @ injection: 1 unit error on the TF of one MQT (equivalent to 0.012 T/m) induces a ΔQ=1.8 10-4

Tune stability range gives the accuracy needed during commissioning The width of stability range around the nominal working point is ΔQ=± 10-2 (% level for TF)

Precision needed in transfer function (FQWG, 03/05/05 and S. Fartoukh and O. Bruning, LHC Report 501)

Quadrupole Transfer Functions of MQT modules, T=1.9 K

1.20E-03

1.25E-03

1.30E-03

1.35E-03

1.40E-03

0 100 200 300 400 500 600

Current [A]

TF [T

m/A

]

MM001MM002

Hysteresis at low field

Resolution of measurement system gives beam based correction accuracy and establishes max. tolerance on hysteresis effect for reproducibility

The tune can be measured with accuracy of 0.75 x 10-3. Than the MQT can be calibrated to better than the % level.

The hysteresis effect is not seen by the measurement, if its width is less than 0.0001T at 17mm radius

Operational margin for the needed accuracy during operation

The operational margin for the tune is ±3 x 10-3 (TF accuracy of ‰ needed)

FQWG, A.Lombardi, Y.Papaphilippou 421/03/2006

Alignment issues for the MQT (FQWG 10/01/06, and LHC Report 501)

The random misalignments’ tolerance for the quadrupole correctors MQT/MQS may be computed for creating an orbit distortion < 0.1mm due to feed-down (dipole) when all families are powered for providing a tune-shift of 0.1

There rms value is estimated at 0.3mm with respect to the MQ (0.2mm w.r.t. to the GA)

The rms value for the roll angle is ~ 2.5mrad, for inducing a coupling coefficient c-=0.001 induced by MQTs powered to create a tune-shift of 0.1

Corrector Reference frame RMS standard deviation [mm]

MQT/MQS SSS GA 0.2 (0.2 expected)

The tolerance is taken as 2.5 standard deviations

FQWG, A.Lombardi, Y.Papaphilippou 521/03/2006

The effect of the field harmonics on the dynamic aperture should be such that the local integrated effect over half lattice cell should not exceed by more than 10% the MQ effect (backed by DA tracking).

Especially for b3 (a3 for MQS), the error should be small enough in order to provide negligible chromatic effect (orthogonality of knobs)

An error table was produced by rescaling with integrated kick of the MQ, i.e. the field at the reference radius and the effective length

Out of tolerance errors: Systematic a4 (3 vs. 1.8),

Systematic b10 (-15 vs. -2)

Random b3 (17 vs. 15)

Random b4 (8 vs. 3) DA tracking performed

assuming rescaled errors

in the MQs Only b10 worrying, the rest

not a big impact in DA Some consolidation work

still needed

Field quality (FQWG, 02/03/04 and 16/11/04)

DA vs b10 in MQ

1010.5

11

11.512

12.5

-15 -10 -5 0units

DA

[σ

]

min DA

aveDA

equivalent to b10=-15 units in the MQT

FQWG, A.Lombardi, Y.Papaphilippou 621/03/2006

MQT error table (nov04)

random units systematic units random units systematic units from 0402

b1 from spec.study

b2 b3 17 b3 3.67 a3 15.94 a3 7.35

b4 8 b4 1.84 a4 14.94 a4 3

b5 5.70 b5 1.84 a5 5.70 a5 1.84

b6 6.65 b6 -7.44 a6 4.61 a6 3.67

b7 1.57 b7 0.73 a7 1.57 a7 0.73

b8 2.66 b8 0.80 a8 2.66 a8 0.00

b9 4.52 b9 0.00 a9 4.52 a9 0.00

b10 3.85 b10 -15 a10 3.85 a10 0.00

b11 2.61 b11 0.00 a11 2.61 a11 0.00