1. Beam dynamics requirements on MQT
Field Quality Working Group
Beam dynamics requirements on MQT
A. Lombardi and Y. Papaphilippou
March 21st, 2006

2. Tuning and Skew Quadrupole correctors
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
MQT/MQS/MO
MQT/MQS
17mm [T]
2.04
Current [A]
550
Mag. Length [m]
0.32
Ap. Diameter [mm] 56
Number
160/32
21/03/2006
FQWG, A.Lombardi, Y.Papaphilippou

3. FQWG, A.Lombardi, Y.Papaphilippou
Precision needed in transfer function (FQWG, 03/05/05 and S. Fartoukh and O. Bruning, LHC Report 501)
Evaluate the effect of MQT on the injection:
1 unit error on the TF of one MQT (equivalent to T/m) induces a ΔQ=
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)
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 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 T 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)
21/03/2006
FQWG, A.Lombardi, Y.Papaphilippou

4. 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
21/03/2006
FQWG, A.Lombardi, Y.Papaphilippou

5. Field quality (FQWG, 02/03/04 and 16/11/04)
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
equivalent to b10=-15 units in the MQT
21/03/2006
FQWG, A.Lombardi, Y.Papaphilippou

6. FQWG, A.Lombardi, Y.Papaphilippou
MQT error table (nov04)
random units systematic units random units systematic units from 0402
b from spec study b2
b3 17 b a a3 7.35
b4 8 b a a4 3
b b a a5 1.84
b b a a6 3.67
b b a a7 0.73
b b a a8 0.00
b b a a9 0.00
b b a a
b b a a
21/03/2006
FQWG, A.Lombardi, Y.Papaphilippou