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 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
Field Model

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

4. 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
Field Model

5. FiDeL- Field
Field Model

6. Geometric MDC Saturation Residual
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
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9.
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10. FiDeL: Harmonics
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11. Geometric MDC Saturation Residual
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12. Generate static harmonics
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13. Delphine Jacquet
Nicholas Hoibian
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14. FiDeL similarly leading to:
MAIN QUADRUPOLES
FiDeL similarly leading to:
kqd :=
kqf :=
p(t)
Etc, etc…
Field Model

15. Bottura & Sammut – Cham XIV
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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 I are fitting constants
b3 and I are correlated
Sextupole compensation during snap-back in collaboration with FNAL – Luca Bottura
Field Model

18. Implementation
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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. 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
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