Field model deliverables for sector test and commissioning: when and what?

1. Field model deliverables for sector test and commissioning: when and what? • The implementation of an accurate magnetic model will be vital for efficient LHC commissioning with beam and subsequent machine performance. • The proposed implementation of a magnetic model is described. • Present state of the implementation • Proposed planning for the deliverables for sector test and initial commissioning. Field Model

2. MAIN DIPOLES • Transfer Function • Average over 154 dipoles per arc • DC components • Geometric • DC magnetization • Saturation • Residual • AC components • Decay • Snapback • Coupling Currents Steady state, reproducible from cycle to cycle, depending only on current Depend on current, ramp rate and powering history Field Model

3. MAIN DIPOLESCold Measurement Join databases: measurements, installation and LSA Measurements for all magnets to be installed in 7-8 Field Model

4. FiDeL Using data from series cold measurements FiDel models components of total field in aperture of magnet Mathematical formulation describing field and field errors Set of parameterized equations - fit to the measured behaviour of the set of magnets in a circuit Field Model

5. FiDeL- Field Field Model

6. Geometric MDC Saturation Data from cold test of magnets to be installed in sector 7-8 (65 magnets 130 apertures) Residual Field Model

7. Generate Transfer Functions - Implementation // DC Magnetisation double getBMDC(double x, double gamma, double mu, double p, double q, double m) { double mdc = mu * Iinj * Math.pow((x / Iinj), p) * Math.pow(((Ic - x) / (Ic - Iinj)), q) * Math.pow(((Math.pow(Tco,1.7) - Math.pow(T,1.7) ) / ( Math.pow(Tco,1.7) - Math.pow(Tmeas,1.7) )), m); return (mdc); } Field Model

8. Nominal ramp configuration Field Model

9. Field Model

10. FiDeL: Harmonics Field Model

11. Geometric MDC Saturation Residual Field Model

12. Generate static harmonics Generate static harmonics Field Model

13. Delphine Jacquet Nicholas Hoibian Field Model

14. MAIN QUADRUPOLES FiDeL similarly leading to: kqd := -0.008442106796 kqf := 0.008802591259 p(t) Etc, etc… Field Model

15. Bottura & Sammut – Cham XIV Field Model

16. Decay std – normalization parameters E, T0, T1, T,P0,P1, P – fitting parameters Field Model

17. Snapback – Q’ • Fit snapback: • I(t) – MB current at time t • Iinjection – injection value of current • b3 and Iare fitting constants • b3 and Iare correlated Sextupole compensation during snap-back in collaboration with FNAL – Luca Bottura Field Model

18. Implementation Field Model

19. Implementation Suggestion • Field Model interpolates and extrapolates data from measured data • Fitting parameters stored on LSA database, entry and adjustment by magnet team • Powering history naturally on LSA database • Mathematical formulation of FiDeL in Java • On-line invocation to produce: • Transfer functions • Normalised harmonic coefficients • On-line invocation at start of each fill (if necessary): • Decay • Snapback • Details to be discussed. Field Model

20. Deliverables • Sector Test: • Transfer functions [MB, MQ, MQY, MQM, MQX etc…] • DC components • Decay prediction • Cycling prescription – deGauss & Nominal • Commissioning: • As above plus snapback • b3++ lower priority as per Massimo’s talk yesterday See Luca Bottura’s presentation - Thursday Field Model

21. Conclusions • Based on magnet measurements FiDeL provides a robust parameterized formulation of: • DC and AC components • Transfer Functions • DC harmonics • Decay • Snapback • Amenable in implementation within LSA • Java/Oracle • v0.01 prototype in place. • Details to be finalized with aim of having v1 of final implementation in place for sector test. Field Model