EXPERIENCE WITH FIELD MODELING IN THE LHC

1. CERN, Space charge 2013 17th April 2013 EXPERIENCE WITH FIELD MODELING IN THE LHC E. Todesco CERN, Geneva Switzerland Thanks to the FiDeL team

2. CONTENTS • The approach: FiDeL, LSA, Wise • The gold mine: LHC magnets production data • Detailsof modeling and operation

3. FIDEL AND WISE • FiDeL (Field Description of the LHC) • is the conversion of fields/gradients to currents • plus the recipe to precyclemagnetsto ensurereproducibility and correct modeling • It consists of • A set of equationsdescribing the relation field(current) • Done for the main component + multipoles • So italsomodels imperfections and fielderrors • Theseequations have components • Geometric (linear) • Saturation (high fields) • Magnetizationboth of iron and of conductor (lowfields) Field & Gradients Currents

4. FIDEL AND WISE • FiDeL (Field Description of the LHC) • Each component depends on severalparameters • The functionalform of each component isspecified in [N. Sammut, L. Bottura, J. Micalef et al. Phys. Rev. STAB 012402 (2006)] • In some cases relies on a physical model, in othersitis a nonlinear fit • Saturation ismodeledthrough a double erffunction • Magnetization relies on the knownfits of the criticalcurrent

5. FIDEL AND WISE • First step (FiDeL) – magnet experts • Fit the magneticmeasurementswith the FiDeLparametrization • Extract the fit parameters • Construct a DB withtheseparametersmagnet by magnet • Associate to eachparameteruncertainties (recentdevelopment[P. Hagen, P. Ferracin]) • The resultis the summa of the knoweldge on ourmagnets

6. FIDEL AND WISE • Second step: export towards CCC – OP group • This is the need of the control room: • Currents to steer the circuits of the main magnets • Currents to steer the circuits of the correctors • The control room system (LSA) has the FiDeLparametrizationindependetelyimplemented • The DB isreducedfrommagnet to magnet to circuit to circuit • This is the LSA DB used to steer the acceleratoraccording to the optic files • Trims are alsobased on FiDeLparametrization (tune, chroma, …) • Obviously, a lot of information is not used(magnet by magnet, high ordermultipoles for whichwe have not correctors …)

7. FIDEL AND WISE • Thirdstep: export towardsmodeling– ABP group • WISE: Windows Interface for Sequence of Elements[P. Hagen] • Builds the best input for MAD or tracking codes based on ourknowledge of the magnets • It also relies on the information about alignement and geometry • It canassociateuncertaintiesto each component to account for the measurementserrors or for missing information MAD input file FiDeLparameters, uncertainties and equations WISE Sequence of magnets Geometry

8. CONTENTS • The approach: FiDeL, LSA, Wise • The gold mine: LHC magnets production data • Detail of modeling

9. THE GOLD MINE • Magneticmeasurements are the key point • Room temperature: providinggeometric • 100% of magnetsmeasured – full knowledge • Doneat the industries, in twodifferent stages (redundancy) • Operational conditions (20% dipoles, 10% quadrupoles, 100% triplet) • Doneat CERN or in US (triplet) • Phenomenology of superconductingmagnetsradicallydifferentfromresistive • Magnetization and dynamiceffects are the mostchallenging • Saturation proves to beeasier and withless variation frommagnet to magnet

10. THE GOLD MINE • Example: measurements of the triplet

11. CONTENTS • The approach: FiDeL, LSA, Wise • The gold mine: LHC magnets production data • Detail of modeling and operation

12. DETAILS OF MODELING • Each model isdevelopedwith a level of detailappropriatefor its relevance in the LHC • We do not model everything for everymagnet … • Dipoles and quadrupoles • Geometricisestimatedmagnet by magnet • Persistent and saturation component are estimatedfamily by family (i.e. one for eachmagnet type) • Alsobecausewe do not have measurementsat 1.9 K for eachmagnet • Triplet • Geometric, persistent, saturation are estimatedmagnet by magnet • Herewe have all the measurements • Correctors • Only the transferfunctionismodeled, not the multipoles • We have measurements but we do not want to complicate the model

13. DETAILS OF OPERATION • Precisionachievedcanbemeasured by the beam • Tune control duringrampiswithin0.07 [N. Aquilina, et al, PAC 2012] • Not enough for operation, but a very good starting point for the tune feedback • Precision in absolute tune is 0.1 (out of 60) – quad trasferfunctionsabsolute model within 0.15%

14. DETAILS OF OPERATION • Precisionachievedcanbemeasured by the beam • Beta beatingwithin 40% at injection, 20% at high field[R. Garcia Tomas, et al. Phys. Rev. STAB 13 (2010) 121004] • Model at injection much more difficult – not a surprise • Chromaticitycontrol within 10 units[N. Aquilina, M. Lamont] • Large contribution fromsextupolarerror in the dipole (200) on the top of nominal chromaticity (60) • Snapback (typical of scmagnets) controlled and corrected – not an issue for LHC operationat 4 TeV • Impact of octupole and decapèole on nonlinearchromaticityQ’’ and Q’’’ [E. McLean, F. Schmidt]

15. CONCLUSIONS • Weoutlined the strategyfollowed in the LHC for modellingfield vs current and expectedfielderrors • FiDeL: the best knowledge of ourmagnets and of theirnonlinearities • Built on considerable effort in measuringmagnetsduring production • WISE: creates instances of the LHC sequence of magnetswiththeirnonlinearities • Uncertainties are beingincluded in the model, sodifferent instances of the machine canbegenerated