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

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

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 (!) 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

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

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

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

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

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

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: resistivity could not be implemented in numerical calculations (in Comsol), so instead 10^-14 Ohm*m is used

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  Mesh size: mm 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 sec

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

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

Non shunted studies Daniel Molnar 13

RQ/RB non shunted 14 Daniel Molnar

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

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

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

Safe operating currents for Dipole lines 18 Daniel Molnar

Safe operating currents for the Quadrupole lines 19 Daniel Molnar

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]

RB shunt with smaller holes 21 Daniel Molnar

RQ shunt with smaller holes 22 Daniel Molnar

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

RQ Side-shunt type_a, dimensions and results 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

Electrically redesigned versions Courtesy of P. Fessia Daniel Molnar 25

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

Time constant of the circuit 27 Daniel Molnar

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

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

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

Thanks 31 Daniel Molnar

Backups 32 Daniel Molnar

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

RQ shunts summary 34

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

RQ/RB below shunt 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

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

QP3 and Comsol 4.1 example Daniel Molnar 38

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

Extreme case: full length non stabilized cable 40

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

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

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

Defect look-a- like 44

Magnetic models, mesh quality 45

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

Modeled RQ side shunts 47

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