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

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

3. Protect, Enhance and Save Lives - 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. Protect, Enhance and Save Lives - 4 - 1. Goal of the calculations 2. Different ways to model the dynamic properties of the magnet 3. What about the self-inductance of a non-linear magnet 4. Magnet load line and the critical surface of the super-conductor 5. Transient solver: eddy current losses and AC losses 6. A comparison with measurements 7. Study of full ramp-up/ramp-down cycles 8. Temperature dependence of material properties 9. A multi-physics approach and a qualitative quench model Overview Some items to be adressed

5. Protect, Enhance and Save Lives - 5 -  For the coming years, the proteus®one and as part of that, the S2C2, will be the number®one workhorse for IBA  Succes of this project is essential for the future of IBA  A broad understanding is needed to continuously improve and develop this new system  The S2C2 is the first superconducting cyclotron made by IBA.  The superconducting coil was for a large part designed by ASG but of course by taking into account the iron design made by IBA/AIMA. This was an interactive process  For us many things have to be learned, regarding the special features of this machine.  Some items under study now, or to be studied soon are: 1. Fast warm up of the coil for maintenance 2. Cold swap of cryocoolers for maintenance  The present study on the dynamics of the magnet must be seen as a learning-process and any feedback of this workshop is very welcome Efforts to learn more on the superconducting magnet Coil and cryostat designed and manufactured by the Italian company ASG

6. Protect, Enhance and Save Lives - 6 - 1. Opera2D/Opera3D static solver 2. Opera2D transient solver 3. Opera2D transient solver coupled to an external circuit 4. Semi-analytical solution of a lumped-element circuit model 5. Multi-physics solution of a lumped element circuit with temperature- dependent properties Different models for the S2C2 magnetic circuit

7. Protect, Enhance and Save Lives - 7 - Magnetic circuit-modeling OPERA3D full model with many details  Long and tedious optimization process  Yoke iron strongly saturated  Influence of external iron systems on the internal magnetic field  Stray-field => shielding of rotco and cryocoolers  pole gap extraction system optimization  Influence of yoke penetrations  Median plane errors  Magnetic forces ITERATIVE PROCESS WITH STRONG INTERACTION TO BEAM SIMULATIONS

8. Protect, Enhance and Save Lives - 8 - 1. The magnet load line with respect to the superconductor critical surface  Magnetic field distribution on the coil  Maximum field on the coil vs main coil current  Compare with critical currents at different temperature 2. The static self-inductance of the magnet  From stored energy  From flux-linking 3. The dynamic self-inductance of the magnet  Essential for non-linear systems like S2C2 The static Opera2D model What information can we obtain

9. Protect, Enhance and Save Lives - 9 - What do we get from Opera2D static solver Load line relative to critical surface maximum coil field Magnet load line and critical currents (from ASG) maximum coil field during ramp up

10. Protect, Enhance and Save Lives - 10 - The static self-inductance of the magnet

11. Protect, Enhance and Save Lives - 11 - Self-inductance from stored energy Calculated with Opera2D static solver

12. Protect, Enhance and Save Lives - 12 - Static self from flux-linking Asymmetry may induce a quench? => probably not;  V=0.3 mV is too small Small vertical symmetry in the model Introduces a voltage difference between upper and lower coil during ramp 0.3 mV

13. Protect, Enhance and Save Lives - 13 - What do we get from the 2D transient solver? Eddy currents and related losses Current density profiles Losses Apply a constant ramp rate of 2.7 Amps/min to the coils

14. Protect, Enhance and Save Lives - 14 - 1. During ramp-up  Eddy current losses in the former (max about 1.5 W) are important because they contribute to the heat-balance  Losses in iron and cryostat walls are (of course) negligible 2. During a quench  When current decay curve is known, losses in former, iron and cryostat walls can be calculated with OPERA2D transient solver  In the former: up to 15 kWatt  In the iron: up to 8 kWatt  The yoke losses help to protect the coil Eddy current losses during ramp up and quench

15. Protect, Enhance and Save Lives - 15 - Opera2d transient solver coupled to external circuit PSU drive programmed as in real live  Cyclotron `impedance´is calculated in real time by the transient solver  Circuit currents are calculated in real time by the Opera2D-circuit solver  Allows to study full dynamic behaviour of the magnetic circuit during ramp up  Quench study is of qualitative value only and has not been done in Opera2D

16. Protect, Enhance and Save Lives - 16 - The full ramp-up/ramp-down cycle Default PSU-ramping for the S2C2 Used in the OPERA2D external circuit simulations

17. Protect, Enhance and Save Lives - 17 - A full ramp-up and ramp-down cycle Coil current compared to dump current  It is seen that for a given PSU current the magnetic field in the cyclotron is different for ramp-up as compared to ramp-down  This is due to the fact the dump-current changes sign when ramping down  Higher coil currents in down ramp up down coil Dump (x10)

18. Protect, Enhance and Save Lives - 18 - Tierod-forces during ramp-up and ramp-down Seems to be in agreement with previous slide  Larger forces during down ramp  However:  Current split between dump and coil can not explain completely the difference in forces  iron hysteresis also seems to play an important role

19. Protect, Enhance and Save Lives - 19 -  Hysteresis losses (W/m 3 )  Coupling losses (W/m 3 )  Tool developed in Opera2D-Transient solver that integrates above expressions in coil area AC losses during ramp-up From Martin Wilson course on superconducting magnets J c (B)=> critical current density d f => filament diameter sup => fraction of NbTi material wire => fraction of wire in channel  t => resitivity across wire p=> pitch of the wire dB/dt=> B-time derivative in coil

20. Protect, Enhance and Save Lives - 20 - Critical surface => Bottura formula Needed for AC losses calculation

21. Protect, Enhance and Save Lives - 21 - Critical surface => Bottura formula (2)

22. Protect, Enhance and Save Lives - 22 - Critical surface => S2C2 wire

23. Protect, Enhance and Save Lives - 23 - AC losses obtained with OPER2D transient solver Initial results => maybe can be improved  Hysteresis losses somewhat larger than eddy current losses  Coupling losses very small

24. Protect, Enhance and Save Lives - 24 - A lumped element model of the circuit Turns out to give very good predictions  Primary circuit  PSU  Coil self-inductance  Coil resistance (only with quench)  Dump resistor  Secondary circuit  Former self-inductance  Former resistance  Perfect mutual coupling (k=1)  Ideal transformer SOLVED IN EXCEL

25. Protect, Enhance and Save Lives - 25 - Compare both models with experiment Voltage on the terminals of the coils during ramp-up Blue: measured Black:OPER2D transient-circuit model Red: analytical lumped element model Perfect match with OPERA2D Not a good match with lumped element model

26. Protect, Enhance and Save Lives - 26 - The concept of dynamic self-inductance Important for non-linear magnets

27. Protect, Enhance and Save Lives - 27 - S2C2 self-inductance A large difference between static and dynamic self

28. Protect, Enhance and Save Lives - 28 - Compare both models with experiment Voltage on the terminals of the coils during ramp-up Blue: measured Black:OPER2D transient-circuit model Red: analytical lumped element model with static self Green: analytical lumped element with dynamic self An almost perfect match is obtained

29. Protect, Enhance and Save Lives - 29 - Compare both circuit-models Resistive losses in the former during ramp-up Blue:OPER2D transient-circuit model Red: analytical lumped element model Very good agreement between both models

30. Protect, Enhance and Save Lives - 30 - Further applications of lumped element model Introduce a kind of « multiphysics » Since this simple model works so well: can we push it a little bit further?

31. Protect, Enhance and Save Lives - 31 - Specific heat of copper and aluminium Very accurate fitting is possible

32. Protect, Enhance and Save Lives - 32 - Electrical resistivity of copper and aluminium Same kind of fitting is possible

33. Protect, Enhance and Save Lives - 33 -  Five different zones with four different temperatures in the cold mass 1. Upper coil superconducting zone (T 0 ) 2. Upper coil resistive zone heated by resistive loss (T 1 )  expanding due to longitudinal and transverse quench propagation 3. Resistive former heated by eddy current losses (T 2 ) 4. Lower coil superconducting zone (T 0 ) 5. Lower coil resistive zone heated by resistive loss (T 3 )  expanding due to longitudinal and transverse quench propagation  Start quench in upper coil  Lower coil will quench when former temperature above critical temperature  ADIABATIC APPROXIMATION => no heat exchange between zones A qualitative model for quench behavior Based on (« multi-physics ») lumped element model

34. Protect, Enhance and Save Lives - 34 -  Introduce the fraction f=f l *f t of the coil that has become resistive 1. f l => Longitudinal propagation (fast  10 m/sec): 2. f t =>Transverse propagation (slow  20 cm/sec): Model for quench propagation From Wilson course J => current density G => mass density C v => specific heat  0 => base temperature  t => contact temperature L 0 => Lorentz number

35. Protect, Enhance and Save Lives - 35 - Resistive loss per m 3 equals increase of enthalpy per m 3 Where J is current density and  is mass density Allows to calculate T max also from a measured decay curve Maximum temperature in the coil Occurs at position where the quench started

36. Protect, Enhance and Save Lives - 36 - 1. 1 equation for the circuit current (slide 24) 2. 3 equations for the average temperatures in resistive zone of both coils and in the coil former (slide 30) 3. 1 equation for the maximum temperature in the coil (slide 35) 4. 2 equations for the longitudinal and transverse quench propagation in the upper coil (slide 34) 5. 2 equations for the longitudinal and transverse quench propagation in the lower coil (slide 34) 6. Dynamic self is fitted as function of coil current 7. Material properties are fitted as function of temperature 8. All circuit properties (currents,voltages,resistances,losses) are obtained Solution of quench module in Excel Several differential equations are integrated in parallel

37. Protect, Enhance and Save Lives - 37 - Current decay and quench propagation  After 50 seconds main coil current already reduced with a factor 10  At that time, about 25% of both coils have become resistive

38. Protect, Enhance and Save Lives - 38 - Cold mass temperatures during the quench Lower coil quenches about 0.1 seconds later  T max  170 K  T coil  120 K  T form  40 K

39. Protect, Enhance and Save Lives - 39 - Ohmic losses during the quench Iron losses may be obtained from Opera2D transient solver

40. Protect, Enhance and Save Lives - 40 - Voltages during the quench Large internal voltages in resistive zones may occur

41. Protect, Enhance and Save Lives - 41 -  Many things have to be learned; this is only a start on one aspect  For learning we have to start doing  For example study of the quench problem will force us to learn: 1. More about material properties 2. More about heat transport in the cold mass 3. More about mechanical/thermal stress in the coldmass 4. Multi-physics approach 5. ….  A precise quench study needs to be done with 3D finite element codes  Quench model in Opera3D?  Comsol ? Conclusions