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Advanced Measurement and Modeling of MQ Magnets for LHC Operation at CERN

This report presents detailed cold and warm measurements of MQ (Main Quadrupole) magnets at CERN, focusing on their operational parameters and geometric transfer functions. The analysis includes testing strategies for static and dynamic current cycles, including up-down cycles with variation from 400A to 11850A. Key findings include correlations between warm and cold measurements, identification of saturation behaviors in specific magnets, and the development of a reliable model with negligible error rates for understanding harmonics and decay characteristics during LHC operations.

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Advanced Measurement and Modeling of MQ Magnets for LHC Operation at CERN

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  1. MQs FiDeL Model Laurent Deniau Magnets, Superconductors and Cryostats Group Technology Department, CERN 28th April 2009

  2. MQ Cold Measurements • Device: 5m long shaft, 6 sectors, 5 tangential coils • Loadline: (STATIC MODEL) • Up-down cycle (400A to 11850A) • 17 currents with dI/dt=0 • 2 points per plateau • Geometric @5000A • 25 MQs, 50 apertures (6.4% of 784) • Machine cycle: (DECAY) • Simulate LHC operation (760A to 11850A) • Injection @760A, 1 point every ~30s • Injection 20 minutes (all MQs) • Injection 200 minutes (MQ383) • LHC injection @450GeV, RQD = ~686A, RQF = ~717A • 21 MQs, 41 apertures (5.2% of 784)

  3. TF and Harmonics Geometric

  4. Transfer Function Geometric 1/2 • 1 unit = 10-7 [T.m/A] • Warm stdev = 10.9 units (out layer MQ061) • Warm measurements random error = ~10 units • Geometric stdev = 14.4 units • Cold measurements random error = ~17 units (dominates) • No apparent correlation for Warm-Cold and Aperture 1 & 2 • Cross-correlation W/C = ~1.7 units MQ061

  5. Transfer Function Geometric 2/2 • W/C Offset 28 units, stdev 11.8 units. • Out layer MQ061 removed • 11 apertures removed for the model (22%) • Anormal saturation (MQs 061,120, Ap1 114,173, Ap2 151,268,263,264,384)

  6. Harmonics Geometric • Allowed harmonics • b6: systematic of 3.42 units (stdev 1.2 units) • b10: systematic of -0.19 units (stdev 0.06 units) • Good correlation Warm-Cold and Aperture 1 & 2 • Unallowed harmonics • a4: systematic of 0.41 units • Other systematics are close to zero (<0.1 units) • b3, a3 and a4: random of 1.5 to 1.8 units

  7. TF and Harmonics @Cold

  8. Unallowed Harmonics @Cold • Spread of b3 of 0.5 units for currents <GEO • Contribution from persistent currents

  9. Transfer Function Static Model • The model works well at high current (>GEO) • Strange residual magnetization at low current (1kA to 2.5kA) • Model errors are negligible (<1.3 unit) • Model error at 450GeV (RQD=686A, RQF=717A) is ~1.5 unit

  10. b6 Static Model • The model works very well • Saturation fits well with one component (symmetric curvature) • Model errors are negligible (<0.015 units)

  11. b10 Static Model • The model works well • Up-down asymmetry of persistent currents • Model errors are negligible (<0.035 units)

  12. TF and Harmonics Decay

  13. b6 Decay • The model works well • Time constant of 29 seconds • 90% contrib. comes from the slow component (~270 seconds) • Average decay is 0.56 units after 20 minutes (sigma ~0.45 units)

  14. TF & Other Harmonics Decay • No systematic decay observed • b2 decay is 0.8 units with a spread of 2.8 units • b3, a3 and a4 decay show a spread of 0.3 to 0.4 units

  15. Conclusion • All data are FiDeL 2009 (updated layout) • The geometric is provided for TF and all harmonics • per magnet: 392 magnets, 784 apertures • per circuit: 16 circuits, 32 apertures(stdev) • LHC wide: generic magnet (stdev) • REFPARM: ~17000 records (non-zero ~7000 records) • The static components are provided for (magnet generic) • Model for TF, b6, b10 (model errors are negligible) • Systematic and random for all other harmonics • Random is also given for <GEO and >GEO for MAD • The decay is provided for (magnet generic) • Model for b6 • Systematic and random for TF and all other harmonics

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