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. 24.01.06 Field Model

MAIN DIPOLES Transfer Function DC components AC components 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 24.01.06 Field Model

MAIN DIPOLES Cold Measurement Join databases: measurements, installation and LSA Measurements for all magnets to be installed in 7-8 24.01.06 Field Model

Mathematical formulation describing field and field errors 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 24.01.06 Field Model

FiDeL- Field 24.01.06 Field Model

Geometric MDC Saturation Residual Data from cold test of magnets to be installed in sector 7-8 (65 magnets 130 apertures) Residual 24.01.06 Field Model

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); } 24.01.06 Field Model

Nominal ramp configuration 24.01.06 Field Model

24.01.06 Field Model

FiDeL: Harmonics 24.01.06 Field Model

Geometric MDC Saturation Residual 24.01.06 Field Model

Generate static harmonics 24.01.06 Field Model

Delphine Jacquet Nicholas Hoibian 24.01.06 Field Model

FiDeL similarly leading to: MAIN QUADRUPOLES FiDeL similarly leading to: kqd := -0.008442106796 kqf := 0.008802591259 p(t) Etc, etc… 24.01.06 Field Model

Bottura & Sammut – Cham XIV 24.01.06 Field Model

Decay std – normalization parameters E, T0, T1, T,P0,P1, P – fitting parameters 24.01.06 Field Model

Snapback – Q’ Fit snapback: I(t) – MB current at time t Iinjection – injection value of current b3 and I are fitting constants b3 and I are correlated Sextupole compensation during snap-back in collaboration with FNAL – Luca Bottura 24.01.06 Field Model

Implementation 24.01.06 Field Model

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. 24.01.06 Field Model

See Luca Bottura’s presentation - Thursday 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 24.01.06 Field Model

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. 24.01.06 Field Model