Dynamic behavior of the S2C2 magnetic circuit

1. Dynamic behavior of the S2C2 magnetic circuit FFAG13 September 2013 WielKleeven

2. The New IBA Single Room Proton Therapy Solution: ProteusONE High quality PBS cancer treatment: compact and affordable 12.8 m Synchrocyclotron with superconducting coil: S2C2 New Compact Gantry for pencil beam scanning 30.4 m Patient treatment room

3. S2C2 overview General system layout and parameters • A separate oral contribution on the field mapping of the S2C2 will be given by Vincent Nuttens (TU4PB01) • Several contributions can be found on the ECPM2012-website

4. Overview Some items to be adressed • Goal of the calculations • Different ways to model the dynamic properties of the magnet • What about the self-inductance of a non-linear magnet • Magnet load line and the critical surface of the super-conductor • Transient solver: eddy current losses and AC losses • A comparison with measurements • Study of full ramp-up/ramp-down cycles • Temperature dependence of material properties • A multi-physics approach and a qualitative quench model

5. Efforts to learn more on the superconductingmagnet Coil and cryostat designed and manufactured by the Italiancompany ASG • For the comingyears, the proteus®one and as part of that, the S2C2, willbe the number®oneworkhorse for IBA • Succes of thisprojectisessential for the future of IBA • A broadunderstandingisneededto continuouslyimprove and developthis new system • The S2C2 is the first superconducting cyclotron made by IBA. • The superconductingcoilwas for a large part designed by ASG but of course by takingintoaccount the iron design made by IBA/AIMA. This was an interactive process • For usmanythingshave to belearned, regarding the specialfeatures of this machine. • Some items understudynow, or to bestudiedsoon are: • Fast warm up of the coil for maintenance • Cold swap of cryocoolers for maintenance • The presentstudy on the dynamics of the magnet must beseen as a learning-processand any feedback of this workshop isverywelcome

6. Different models for the S2C2 magnetic circuit • Opera2D/Opera3D static solver • Opera2D transient solver • Opera2D transient solver coupled to an external circuit • Semi-analyticalsolution of a lumped-element circuit model • Multi-physics solution of a lumped element circuit with temperature-dependent properties

7. Magnetic circuit-modeling OPERA3D full model withmanydetails • Long and tediousoptimizationprocess • Yokeironstronglysaturated • Influence of externalironsystems on the internalmagneticfield • Stray-field => shielding of rotco and cryocoolers • pole gap < => extraction system optimization • Influence of yokepenetrations • Median plane errors • Magnetic forces ITERATIVE PROCESS WITH STRONG INTERACTION TO BEAM SIMULATIONS

8. The static Opera2D model What information canweobtain • The magnetload line with respect to the superconductorcritical surface • Magneticfield distribution on the coil • Maximum field on the coil vs main coilcurrent • Compare withcriticalcurrentsatdifferenttemperature • The static self-inductance of the magnet • Fromstoredenergy • From flux-linking • The dynamic self-inductance of the magnet • Essential for non-linearsystemslike S2C2

9. What do wegetfrom Opera2D staticsolver Load line relative to critical surface maximum coilfield Magnetload line and criticalcurrents (from ASG) maximum coilfieldduringramp up

10. The static self-inductance of the magnet • The static self-inductance of the magnet • From the storedenergy: L • From flux-linking: • Flux for a single wirein the coil: • Relation withvectorpotential: • Total flux over coil: • Self of one coilfrom flux-linking: • 2ndmethodallows to finddifferencebetweenupper and lowercoil • Can becalculateddirectly in Opera2D

11. Self-inductance fromstoredenergy Calculatedwith Opera2D staticsolver

12. Static self from flux-linking Asymmetrymayinduce a quench? => probably not; DV=0.3 mV istoosmall Introduces a voltage differencebetweenupper and lowercoilduringramp Small vertical symmetry in the model 0.3 mV

13. What do wegetfrom the 2D transientsolver? Eddy currents and relatedlosses Losses Currentdensity profiles Apply a constant ramp rate of 2.7 Amps/min to the coils

14. Eddy currentlosses duringrampup and quench • Duringramp-up • Eddy currentlosses in the former (max about 1.5 W) are important becausetheycontribute to the heat-balance • Losses in iron and cryostat walls are (of course) negligible • During a quench • Whencurrentdecaycurveisknown, losses in former, iron and cryostat wallscanbecalculatedwithOPERA2D transientsolver • In the former: up to 15 kWatt • In the iron: up to 8 kWatt • The yokelosses help to protect the coil

15. Opera2d transientsolvercoupledto external circuit PSU drive programmed as in real live • Cyclotron `impedance´iscalculated in real time by the transientsolver • Circuit currents are calculated in real time by the Opera2D-circuit solver • Allows to study full dynamicbehaviour of the magnetic circuit duringramp up • Quenchstudyis of qualitative value onlyand has not been done in Opera2D

16. The full ramp-up/ramp-down cycle Default PSU-ramping for the S2C2 Used in the OPERA2D external circuit simulations

17. A full ramp-up and ramp-down cycle Coilcurrentcompared to dump current • It isseenthat for a given PSU current the magneticfield in the cyclotron isdifferent for ramp-up as compared to ramp-down • This is due to the fact the dump-current changes signwhenramping down • Highercoilcurrents in down ramp coil down up Dump (x10)

18. Tierod-forces duringramp-up and ramp-down Seems to be in agreement withpreviousslide • Larger forces during down ramp • However: • Current split between dump and coilcan not explaincompletely the difference in forces • ironhysteresisalsoseems to play an important role

19. AC lossesduringramp-up From Martin Wilson course on superconductingmagnets • Hysteresislosses (W/m3) • Couplinglosses (W/m3) • Tooldeveloped in Opera2D-Transient solverthatintegratesabove expressions in coil area Jc(B) => criticalcurrentdensity df=> filament diameter lsup=> fraction of NbTimaterial lwire=> fraction of wire in channel rt=> resitivityacrosswire p => pitch of the wire dB/dt => B-time derivative in coil

20. Critical surface => Bottura formula Needed for AC lossescalculation Bottura formula (reducedtemperature) (reducedfield) criticalfieldatzerocurrent a,b,g,C0 => fitting coefficients

21. Critical surface => Botturaformula (2)

22. Critical surface => S2C2 wire

23. AC lossesobtainedwith OPER2D transientsolver Initial results => maybecanbeimproved • Hysteresislossessomewhatlargerthaneddycurrentlosses • Couplinglossesverysmall

24. A lumpedelement model of the circuit Turns out to givevery good predictions • Primary circuit • PSU • Coilself-inductance • Coilresistance (onlywithquench) • Dump resistor • Secondary circuit • Former self-inductance • Former resistance • Perfectmutualcoupling (k=1) • Ideal transformer SOLVED IN EXCEL

25. Compare bothmodelswithexperiment Voltage on the terminals of the coilsduringramp-up Blue: measured Black:OPER2D transient-circuit model Red: analyticallumpedelementmodel • Perfectmatch with OPERA2D • Not a good match withlumpedelement model

26. The concept of dynamic self-inductance Important for non-linearmagnets • Definition of self-inductance: • Faraday’slaw: • Combine: • For a non-linear system the dynamic self must beused in lumpedelement circuit simulations

27. S2C2 self-inductance A large differencebetweenstatic and dynamic self

28. Compare bothmodelswithexperiment Voltage on the terminals of the coilsduringramp-up Blue: measured Black:OPER2D transient-circuit model Red: analyticallumpedelement model withstatic self Green: analyticallumpedelementwithdynamic self An almostperfect match isobtained

29. Compare both circuit-models Resistivelosses in the former duringramp-up Blue:OPER2D transient-circuit model Red: analyticallumpedelement model Very good agreement betweenbothmodels

30. Further applications of lumpedelement model Introduce a kind of « multiphysics » • Resistors in model becometemperature-dependent • Introduceadditionalequations for temperature change • R(T) => resistance => • r(T) => resistivity • Cv(T) => specificheat Sincethis simple model workssowell: canwe push it a little bit further?

31. Specificheat of copper and aluminium Veryaccuratefittingis possible

32. Electricalresistivity of copper and aluminium Samekind of fittingis possible

33. A qualitative model for quenchbehavior Based on (« multi-physics ») lumpedelement model • Five different zones with four differenttemperatures in the cold mass • Uppercoilsuperconducting zone (T0) • Uppercoilresistive zone heated by resistiveloss(T1) • expandingdue to longitudinal and transverse quench propagation • Resistive former heated by eddycurrentlosses(T2) • Lowercoilsuperconducting zone (T0) • Lowercoilresistive zone heated by resistiveloss(T3) • expandingdue to longitudinal and transverse quenchpropagation • Start quench in uppercoil • Lowercoilwillquenchwhen former temperatureabovecriticaltemperature • ADIABATIC APPROXIMATION => no heat exchange between zones

34. Model for quench propagation From Wilson course • Introduce the fraction f=fl*ft of the coilthat has becomeresistive • fl => Longitudinal propagation (fast 10 m/sec): • ft =>Transverse propagation (slow  20 cm/sec): J => currentdensity G => mass density Cv => specificheat q0 => base temperature qt => contact temperature L0 => Lorentz number

35. Maximum temperature in the coil Occursat position where the quenchstarted Resistiveloss per m3equalsincrease of enthalpy per m3 WhereJiscurrentdensity and gis mass density Allows to calculateTmaxalsofrom a measureddecaycurve

36. Solution of quench module in Excel Severaldifferentialequations are integrated in parallel • 1 equation for the circuit current (slide24) • 3 equations for the averagetemperatures in resistive zone of bothcoils and in the coil former (slide30) • 1 equation for the maximum temperature in the coil (slide35) • 2 equations for the longitudinal and transverse quench propagation in the uppercoil (slide34) • 2 equations for the longitudinal and transverse quench propagation in the lowercoil (slide34) • Dynamic self isfitted as function of coilcurrent • Materialproperties are fitted as function of temperature • All circuit properties (currents,voltages,resistances,losses) are obtained

37. Currentdecay and quench propagation • After 50 seconds main coilcurrentalreadyreducedwith a factor 10 • Atthat time, about 25% of bothcoils have becomeresistive

38. Cold mass temperaturesduring the quench Lowercoilquenches about 0.1 seconds later • Tmax 170 K • Tcoil  120 K • Tform  40 K

39. Ohmiclossesduring the quench Ironlossesmaybeobtainedfrom Opera2D transientsolver

40. Voltages during the quench Large internal voltages in resistive zones mayoccur

41. Conclusions • Manythingshaveto belearned; thisisonly a start on one aspect • For learningwe have to startdoing • For examplestudy of the quenchproblemwill force us to learn: • More about materialproperties • More about heat transport in the cold mass • More about mechanical/thermal stress in the coldmass • Multi-physicsapproach • …. • A precisequenchstudyneeds to bedonewith 3D finiteelement codes • Quench model in Opera3D? • Comsol ?