ELECTRO THERMAL SIMULATIONS OF THE SHUNTED 13KA LHC INTERCONNECTIONS

Daniel Molnar, Arjan Verweij and Erwin Bielert

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Contents

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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

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The LHC interconnections

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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

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Motivation

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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

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The ideal\designed interconnects

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Different Cu stabilizer

pieces

Cross section of a well soldered

cable

Side view of a perfectly soldered joint

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And the reality…..

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A vast number of defects and lack of soldering

X-ray Schematics

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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)

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Boundary conditions and initial values

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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= 𝐼0𝐴∗exp൬−𝑡𝜏൰ −𝑛ሬԦ⋅ 𝐽Ԧ= 𝐽0 ∗exp൬−𝑡𝜏൰ V= 0

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Material properties

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-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

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Modeling

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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

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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

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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 !

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Non shunted studies

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RQ/RB non shunted

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Non shunted run-away(cause of 2008 incident)

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A runaway of a joint, notice the sharp and very fast change in the temperature

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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 mm In the calculations the RRR is 200 (pessimistic)

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Main shunt dimensions, top/bottom and side

view

The main shunt soldered to the BUS

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Description of symmetric shunt defects

50 mm

15 mm

Holes Up shunt

Below shunt

BUSwedgeU-profile

BUS

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Non stabilized

cable

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Safe operating currents for Dipole lines

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Safe operating currents for the Quadrupole lines

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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

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Length of Shunt[mm]

Curr

en

t densi

ty y

co

mponent[

A/m

^2]

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RB shunt with smaller holes

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RQ shunt with smaller holes

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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

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Type_a, “bridge”

Type_b

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RQ Side-shunt type_a, dimensions and results

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zl zm

zr

x

8mm

-Summary of different designs for the “bridge” side shunt-The original design is not safe

The depth is not varied

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Electrically redesigned versions

Courtesy of P. Fessia

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RQ sideshunt type_b dimensions and results

xz=zb+zj

y

zb

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zj

x

-Summary of different designs for the “simple” side shunt-The original design is not safe

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Time constant of the circuit

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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

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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

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Acknowledgements

Many thanks to Arjan Verweij and to Erwin Bielert

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Thanks

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Backups

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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

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defect defect

34RQ shunts summary

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RB up shunt

-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 betweenwedge and U-profile

Top view for up-shunt 15

WedgeU-profile

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RQ/RB below shunt

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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

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QP3 Comsol difference; shunt RRR 150

For RQ shunted calculations(0=0.5)

For RB shunted calculations (0=0.5)

QP3 the shunt’s RRR=150

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QP3 and Comsol 4.1 example

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Modeling considerations: geometry

RB (half)

RQ(full)

RQ(half)

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Extreme case: full length non stabilized cable

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

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

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The effect of the SnPb thickness

The “standard” is 100 mm 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 mm thickness:16200 A

-300 mm thickness:15900 A

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Defect look-a-like

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Magnetic models, mesh quality

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Different Time constants-same current

The safe current for Tau 30 sec:16kA(also a bd case)

47Modeled RQ side shunts

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An example of usage beyond Comsol Resistance as a function of time; It could

carry14kA without reaching 300 K, shunted version, no void in SnPb