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

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 Field @ 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

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

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

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

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