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Beam dynamics requirements on MQT

Field Quality Working Group. Beam dynamics requirements on MQT. A. Lombardi and Y. Papaphilippou. March 21st, 2006. MQT/MQS/MO. Tuning and Skew Quadrupole correctors. 2 families of 8 per ring and sector (MQTF,MQTD), from Q14 to Q21

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Beam dynamics requirements on MQT

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

  2. MQT/MQS/MO 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 FQWG, A.Lombardi, Y.Papaphilippou

  3. 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) 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 • The tolerance is taken as 2.5 standard deviations 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 FQWG, A.Lombardi, Y.Papaphilippou

  6. 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 FQWG, A.Lombardi, Y.Papaphilippou

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