Analysis of Tune Variation and Decay in Large Hadron Collider

This analysis focuses on the tune variation and decay of the bare machine tune in the Large Hadron Collider. It covers the evolution of the bare tune, analysis of the tune decay after injection, fitting of decay constants, and data extraction from 2015. The study includes insights into beam commissioning, tuning variations, and decay characteristics observed in the collider.

• Analysis
• Tune Variation
• Decay
• Large Hadron Collider
• Beam Commissioning

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1. Bare tune decay and snap-back Mariusz Juchno Mariusz Juchno 1 20.09.2024

2. Introduction Analysis of the tune variation during beam commissioning 2015 Previous work: N. Aquilina et al. Tune Variation in the Large Hadron Collider Estimation of the bare machine tune base on measured tune and MQTF/D currents Nest step: Analysis of the tune decay after injection Multiple time constants First two terms of the decay law Mariusz Juchno 2 20.09.2024

3. Bare tune evolution Fill 2452 (2012) Fill 3621 (2015) Mariusz Juchno 3 20.09.2024

4. Introduction Analysis of the tune variation during beam commissioning 2015 Previous work: N. Aquilina et al. Tune Variation in the Large Hadron Collider Estimation of the bare machine tune base on measured tune and MQTF/D currents Nest step: Analysis of the tune decay after injection Multiple time constants First two terms of the decay law Mariusz Juchno 4 20.09.2024

5. Results from 2011 & 2012 5

6. Analysis of 2015 data Initial tune v and asymptotic decay amplitude c are fitted Decay constant ? fixed at 1000s Slow and fast decay mixing weight d fixed at 0.27 Value of 0.27 is based on 2012 data Fixing it does not seem to decrease the quality of the fit Fitting it doesn t give consistent results 6

7. Extracted data Time range from 2015-04-10 to 2015-06-02 Fills initially accepted: 117 Fills used for analysis: 54 (A) 25 fills with data < 10000s (B) 17 fills with data < 25000s (C) 12 fills with data < 35000s Data <1200s and >35000s is excluded Mariusz Juchno 7 20.09.2024

8. Pre-cycling and injection Mariusz Juchno 8 20.09.2024

9. Initial tune v vs TFT Mariusz Juchno 9 20.09.2024

10. QH Decay amplitude c vs TFT ? ??? = ?0+ ??(1 ? ???/?) B1 QH: c0 = -0.027 dc = -0.034 tau = 4277 B1 QV: c0 = -0.025 dc = -0.026 tau = 4277 B2 QH: c0 = -0.029 dc = -0.036 tau = 4277 B2 QV: c0 = -0.024 dc = -0.023 tau = 4277 Mariusz Juchno 10 20.09.2024

11. QV Decay amplitude c vs TFT ? ??? = ?0+ ??(1 ? ???/?) B1 QH: c0 = -0.027 dc = -0.034 tau = 4277 B1 QV: c0 = -0.025 dc = -0.026 tau = 4277 B2 QH: c0 = -0.029 dc = -0.036 tau = 4277 B2 QV: c0 = -0.024 dc = -0.023 tau = 4277 Mariusz Juchno 11 20.09.2024

12. Initial tune v vs TPREP Mariusz Juchno 12 20.09.2024

13. Decay amplitude c vs TPREP Mariusz Juchno 13 20.09.2024

14. Decay amplitude c vs TPREP for TFT< 650 s Mariusz Juchno 14 20.09.2024

15. Analysis summary TFT< 650s (17 fills) TFT> 15000s (9 fills) QH QV QH QV B1 v 59.349 64.229 59.347 64.227 v 0.002 0.004 0.002 0.002 c -0.029 -0.027 -0.062 -0.051 c 0.010 0.007 0.005 0.003 d 0.27 0.27 0.27 0.27 tau 1000 1000 1000 1000 B2 v 59. 331 64.204 59. 329 64.198 v 0.002 0.006 0.002 0.003 c -0.032 -0.026 -0.065 -0.047 c 0.009 0.007 0.005 0.004 d 0.27 0.27 0.27 0.27 tau 1000 1000 1000 1000 Mariusz Juchno 15 20.09.2024

16. Conclusions Double term decay formula (d and tau are fixed) Increase of decay amplitude more than 50% Dependence of decay amplitude on TFT Mariusz Juchno 16 20.09.2024