1. Tune: Decay at Injection and Snapback Michaela Schaumann In cooperation with: Mariusz Juchno, Matteo Solfaroli Camillocci, Jorg Wennigner

2. Introduction to the effect Tune correction Decay at Injection Snapback at the start of RAMP 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback2 Outline

3. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback3 Origin of the Effect During injection the superconducting magnets are at constant current.  The magnetic field multipoles drift when the magnets are on a constant current plateau.  Changes tune and chromaticity.  Chroma decay from b3 of dipoles. (M. Solfaroli Camillocci, LBOC #41)  Tune decay believed to originate from decaying magnetization in superconducting cables. In the first few seconds of the ramp, when the magnetic field is increased, the original hysteresis state is restored:  snap-back These dynamic field changes depend on powering history of the magnets, e.g. flat-top (FT) length, flat-bottom (FB) length …

4. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback4 Tune Correction The tune is to be kept at the reference value. Several systems correct the bare tune evolution to the reference: Field description for the LHC (FIDEL): feed-forward system to compensate for predictable field variations of the magnets. Tune feed-back (QFB): beam based correction. Manual tune trims, applied when necessary. If the FIDEL prediction were perfect, the tunes would be constant at the nominal value, and the QFB and manual trims would be minimized.

5. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback5 Tune Decay at Injection Previous work: N. Aquilina et al., Tune variations in the Large Hadron Collider (Mathematical description of the effects and observations in 2011/12) M. Juchno, Presentation at FIDEL meeting 02/06/2015 To improve model prediction, bare tune evolution is studied. Bare tunes obtained from Q-measurement, by removing ALL applied trims. Bare decay is sum of exponentials, with multiples of a single time constant: Initial tune Amplitude of decay Mixing of slow & fast components: Fixed at d = 0.27 Time constant: Fixed at τ = 1000s Based on previous studies 2 Fit parameters

6. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback6 Tune Decay at Injection Example of bare tune decay at injection with corresponding exponential fit. Fits were performed for beams at injection plateau followed by ramp with beam Horizontal Vertical 50Hz lines (They decay with tune because trims were removed from whole data set, but they are not affected by trims)

7. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback7 Dependency on Powering History Main parameters affecting decay amplitude are 1)Ramp rate of previous cycle 2)Flat-top (FT) current of previous cycle 3)Time spent at flat-top in previous cycle, tFT 4)Time spent at pre-injection plateau, tFB Dipoles and Quadrupoles have different powering history and thus tFT and tFB are different. The same for all cycles Varies from one cycle to the next tFT tFB

8. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback8 Powering RB and RQD/RQF Dipoles and Quadrupoles have different powering history and thus tFT and tFB are different. Pre-cycle: RQD arrive at FT before RB RQD have shorter FT RQD longer rampdown => different tFB Nominal cycle: Synchronized start of ramp and rampdown RQD and RB arrive together at FT Equal tFT but different tFB RB RQD.A56 RQD.A81

9. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback9 Dependence on FT: Amplitude RB To exclude dependence on FB, select only cycles with tFB<800s (for RB) RQD Decay amplitude tends to decrease with FT length. Large spread between points - partly due to poor data/fit -especially for pre-cycles, which should be the most reproducible RB – zoom 1 st hour

10. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback10 Dependence on FT: Amplitude RB Fit to data: To exclude dependence on FB, select only cycles with tFB<800s (for RB) RQD This is not a good fit Not clear if there is a dependence and if yes, of what shape.

11. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback11 Dependence on FT: Initial Tune RB Very small decay of initial tune with tFT. => Less than 0.005/8h. RB and RQD very similar Constant offset irrelevant for FIDEL correction RQD To exclude dependence on FB, select only cycles with tFB<800s (for RB)

12. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback12 Dependence on FB: Amplitude To exclude dependence on FT, select only cycles with tFT> 4000s RB RQD No clear pattern of amplitude on tFB RB and RQD very similar

13. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback13 Dependence on FB: Initial Tune To exclude dependence on FT, select only cycles with tFT> 4000s RB RQD No clear pattern of initial tune on tFB. RB and RQD very similar Constant offset irrelevant for FIDEL correction

14. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback14 Predicted FIDEL Correction Current FIDEL implementation: No powering history dependence. Corrects rather ok already, but sometimes manual trims are necessary. Proposed FIDEL implementation: Scaling of decay amplitude with observed exponential tFT dependence:  Short tFT: similar to currently used function.  Long tFT: increase of trim amplitude.  Quickly approaching function with max. trim amplitude (tFT>3600s).

15. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback15 Applied Correction Horizontal Vertical Same example fill as before after applying derived correction. Tune evolution flat in V but overcorrected in H. An initial offset w.r.t. the reference value is still to be corrected. Tune slopes spread around zero, but with σ≈±0.004/h There could be a dependence on another parameter.

16. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback16 Snap-back N. J. Sammut et al., Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider Magnets. II. Dynamic field changes and scaling laws. PRSTAB 10, 082802 (2007) Magnet current Multipole component of magnetic field Snap-back to hysteresis curve in first few seconds of the ramp follows an exponential law. A ΔI The amplitude A depends on length of injection plateau & powering history. The current increase at the start of the ramp is parabolic.

17. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback17 Tune at Start of Ramp If the feed-forward correction is not good enough, it can be difficult for the QFB to keep the tunes constant and large tune excursions can occur.

18. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback18 Fit to Bare Tune Evolution A = initial point of data, τ = fit parameter. Fit to bare tune: Average τ over all ramps. Horizontal τ = 88 s^2 Vertical τ = 127 s^2 τ is NOT the width of the distribution!

19. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback19 Tune at Start of Ramp If the feed-forward correction is good, the QFB can correct the remaining error and keep the tunes constant.

20. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback20 Trim Knobs The total amplitude of the applied tune trims is the sum of two knobs: -TUNE_TRIM -TUNE_TRIM_FIDEL QH_TRIM_FIDEL 0 0.035 QH_TRIM 100s into the ramp 0 0.04 Screen-shots from Trim Editor

21. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback21 Conclusion Feed-forward corrections of the tune decay during injection and the snap-back in the first seconds of the ramp were derived from data. Decay at Injection: Potential dependence on FT duration is observed. Derived function would improve current implementation. More analysis needed before final conclusions can be made. Snap-back: Smoothing of FIDEL trims is under test. First results show that burden on QFB is reduced compared to linear implementation.

22. Back-up 30/06/2015 LBOC, M. Schaumann - Tune: decay at injection and snapback 22

23. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback23 Dependence on FT: Amplitude RB To exclude dependence on FB, select only cycles with tFB<800s (for RB) RQD Remove pre-cycles Still large spread and low statistics Linear fit results in slow reduction of amplitude with tFT NO saturation with linear fit RB and RQD give identical fits, as expected, since tFT are all equal.

24. 30/06/2015LBOC, M. Schaumann - Tune: decay at injection and snapback24 Predicted FIDEL Correction - VERTICAL