1. ELECTRO THERMAL SIMULATIONS OF THE SHUNTED 13KA LHC INTERCONNECTIONS Daniel Molnar, Arjan Verweij and Erwin Bielert

2. Contents Daniel Molnar 2  Introduction  Interconnections and their repair  Physical description  Materials  Modeling with Comsol 4.1  Comparisons to other codes, validations  Shunted lines  Design optimizations for the shunts  Shunt concepts  Other investigations  Conclusions  Acknowledgements

3. The LHC interconnections Daniel Molnar 3  In case of a quench they should ensure the safe operation i.e. carrying the current  In the main ring there are some 10.000(!) connection btw. the dipole and quadrupole magnets  If the protection systems detect a quench,the circuit is opened and the current is decaying with a time constant Tau, 100 sec for dipoles and 30 sec for quadrupole

4. Motivation Daniel Molnar 4  The motivation is to insure the safe operation of the LHC machine at the nominal beam energy of 7TeV  The 2008 incident has shown that present splices mean a significant danger, and not capable to secure the long term operation at higher current levels Thus they need to be repaired and protected  A shunt will be added to all of them, which has to carry the current even in worst case (adiabatic) conditions

5. The ideal\designed interconnects Daniel Molnar 5 Different Cu stabilizer pieces Cross section of a well soldered cable Side view of a perfectly soldered joint

6. And the reality….. Daniel Molnar 6  A vast number of defects and lack of soldering X-raySchematics

7. Physical description  The first and main physical phenomena which describes such a runaway is the Joule heating, later other physical problems coupled with it (magneto-resistivity) 7 Daniel Molnar

8. Boundary conditions and initial values Daniel Molnar 8  Most of the following results with the assumption of adiabatic thermal boundaries(worst case)  Electrical boundary conditions: On one side J current density constraint, the other is V=0  Initial conditions: V(t=0)=0 and in most cases T(t=0)=10K, so we have already quenched the cable  Pessimism is the most important factor ! bus

9. Material properties 9 Daniel Molnar -Magneto resistivity is included in the models, simply adding a constant to the Copper’s electrical resistivity (Self Field Factor) -The superconducting cable consists Nb-Ti and Copper, with the ratio of1:1.95 -0 resistivity could not be implemented in numerical calculations (in Comsol), so instead 10^-14 Ohm*m is used

10. Modeling Daniel Molnar 10  3D model of the problem  Linear shape function for the finite elements, significant save of time  Mesh elements number: for shunted 12236, non shunted 11950  Mesh size: 0.3-0.5mm in the defects(and shunt), 10 mm for the BUS  Linear interpolation for the material properties i.e. between two known points it uses constant value, not significant simplification  The non linear solver uses a Newtonian algorithm, relative tolerance is 0.02  CPU time is typically 2000 sec, but for instance the He cooling case and quench etc. took 12000 sec

11. Modeling II.  Instead of the actual shape rectangular was used with same cross section, to be able to use rectangular mesh  Symmetries introduced when it’s possible to speed up calculations Time step: 1msec 11 Daniel Molnar

12. Comparisons, validations  The simulations carried out with Comsol, have been compared to another code QP3  Good agreement between the two results (and between measurements), within a 4-5 % difference  The difference is intrinsic to the fact that QP3 is a 1D model, while in Comsol 3D was implemented  Again we have to point out, both measurements and codes (QP3 and Comsol) show that the runaway is very fast, and in some cases non- protectable ! 12 Daniel Molnar

13. Non shunted studies Daniel Molnar 13

14. RQ/RB non shunted 14 Daniel Molnar

15. Non shunted run-away(cause of 2008 incident) Daniel Molnar 15 A runaway of a joint, notice the sharp and very fast change in the temperature

16. The shunted bus bars  The main shunt itself is the same for both quadrupole and dipole circuits  Dipole lines can have 4 shunts/ joints, for the quads just below ones  The solder is SnPb, avg. thickness 100 m m  In the calculations the RRR is 200 (pessimistic) 16 Daniel Molnar Main shunt dimensions, top/bottom and side view The main shunt soldered to the BUS

17. Description of symmetric shunt defects 50 mm 15 mm Holes Up shunt Below shunt BUS wedge U-profile BUS 17 Daniel Molnar Non stabilized cable

18. Safe operating currents for Dipole lines 18 Daniel Molnar

19. Safe operating currents for the Quadrupole lines 19 Daniel Molnar

20. Shunt designs  Naturally questions come up: do we have bigger margin for longer shunt? Or could a smaller reservoir hole for solder mean higher safety?  There are other view points than electro-thermal, such as quality control, accessibility, mechanical studies and solder quality 20 Daniel Molnar Length of Shunt[mm] Current density y component[A/m^2]

21. RB shunt with smaller holes 21 Daniel Molnar

22. RQ shunt with smaller holes 22 Daniel Molnar

23. Additional shunts for quadrupole bus bars(side shunts)  The quad buses have no possibilities for a top shunt(at least idem as below shunt )  There are two designs for side shunts  Again there are other view points than electro-thermal 23 Daniel Molnar Type_a, “bridge” Type_b

24. RQ Side-shunt type_a, dimensions and results 24 15 zlzmzr x 8mm -Summary of different designs for the “bridge” side shunt -The original design is not safe The depth is not varied Daniel Molnar

25. Electrically redesigned versions Courtesy of P. Fessia Daniel Molnar 25

26. RQ sideshunt type_b dimensions and results 26 x z=zb+zj y zb 15 zj x -Summary of different designs for the “simple” side shunt -The original design is not safe Daniel Molnar

27. Time constant of the circuit 27 Daniel Molnar

28. Magneto-resistivity  In all calculations shown before the magnetic effect is included, a constant is added to the resistivity of the Copper –Self Field Factor  One can ask what about the shunt? The current density is higher so is the magnetic field  Nice modeling problem, but practically not so significant 28 Daniel Molnar

29. Conclusions  The present shunt design could guarantee the safe long term operation of the LHC at 7TeV (13kA or more) for dipole and quadrupole lines as well  The side shunts for the quadrupoles do not mean full redundancy, although with major changes they could be safe  The safe current also strongly depends on the defect of the BUS  Also other calculations are ongoing, such as cooling to He, to investigate the margins in this case 29 Daniel Molnar

30. Acknowledgements  Many thanks to Arjan Verweij and to Erwin Bielert 30 Daniel Molnar

31. Thanks 31 Daniel Molnar

32. Backups 32 Daniel Molnar

33. Modeling in 1D and 3D  Qp3:1D  The green arrows are the current density vectors  Comsol 4.1:3D  In this case there’s a real redistribution 33 Daniel Molnar defect

34. RQ shunts summary 34

35. RB up shunt 35 -Note that the two reservoir holes are always considered to be AIR, with rectangular shape -The defect of SnPb solder is indicated by green lines, different lengths of it -also non perfect contact between wedge and U-profile Top view for up-shunt 15 Wedge U-profile

36. RQ/RB below shunt 36 15 Bottom view below shunt -The shunt is the same as for the up one -The defect of SnPb solder is indicated by green lines, different lengths of it -Also the defect is symmetric with respect to the connection of Bus and U profile

37. QP3 Comsol difference; shunt RRR 150 37 For RQ shunted calculations(0=0.5) For RB shunted calculations (0=0.5) QP3 the shunt’s RRR=150

38. QP3 and Comsol 4.1 example Daniel Molnar 38

39. Modeling considerations: geometry 39 RB (half) RQ(full) RQ(half)

40. Extreme case: full length non stabilized cable 40

41. Extreme case II) full length NSC,non symmetric SnPb defect 41

42. And a more Extreme:No Cu in the defect for RQ below shunt 42

43. The effect of the SnPb thickness  The “standard” is 100  m but, also the effect of a thicker SnPb layer under (or above) the shunt has been investigated  For an RB below shunt with 8mm of GAP in the SnPb -100  m thickness:16200 A -300  m thickness:15900 A 43

44. Defect look-a- like 44

45. Magnetic models, mesh quality 45

46. Different Time constants-same current 46 The safe current for Tau 30 sec: 16kA (also a bd case)

47. Modeled RQ side shunts 47

48. An example of usage beyond Comsol 48  Resistance as a function of time; It could carry14kA without reaching 300 K, shunted version, no void in SnPb