0. Fermilab Associate Scientist Position Interview
Thermal analysis of superconducting magnets and Study of Nb3Sn conductor during heat treatment
Fermilab Associate Scientist Position Interview
April 6, 2011

1. Fermilab Associate Scientist Position Interview
OUTLINE
Thermal analysis of superconducting magnets
Motivation
Thermal model of superconducting magnets
Model validation with measurements
Quench limit calculation
Model implementation to new designs of superconducting magnets
Study of Nb3Sn conductor during heat treatment
Measurements
Results
Summary
April 6, 2011
Fermilab Associate Scientist Position Interview

2. Thermal analysis of superconducting magnets
Particles coming from proton-proton collision impact the LHC magnets
energy deposition in the coils → possible magnet quench
quench limits required for beam loss monitors → dump the beams before magnets quench
Heat flow paths and heat flow barriers identification in the magnet
quench limit of existing superconducting magnets (LHC)
feedback to the future superconducting magnet designs
New CERN quadrupole design
enhanced insulation scheme → open helium paths between the bath and the cable
LARP Nb3Sn quadrupole design
impregnated coil → no helium link between the bath and the cable
Helium cooling channels in the magnet structure
April 6, 2011
Fermilab Associate Scientist Position Interview

3. Motivation - Heat load in the LHC magnets
Particles from proton-proton collision debris
Interaction of lost protons with collimators
Physics processes – BFPP (ion beam case)
Accidental beam losses
Transient losses ~ns to ~ms
Enthalpy of the cable (metal only) (~ns)
Heat transfer to helium volume inside the cable (~ms)
Enthalpy of the cable (metal + He) (~ms)
Steady-state losses
Transfer of the heat from cable to the heat reservoir (~s)
Magnet structure and geometry of cooling channels
References:
D. Bocian, CERN AT-MTM note, EDMS
D. Bocian et al., IEEE Trans. on Appl. Supercond.,18, (2008) 112 – 115;
P.P. Granieri, (D. Bocian), et al., IEEE Trans. on Appl. Supercond.,18, (2008) 1257 – 1262;
D. Bocian et al., IEEE Trans. on Appl. Supercond.,19, (2009) 2446–2449;
R. Bruce, (D. Bocian), et al., Phys. Rev. ST Accel. Beams 12, (2009) ;
April 6, 2011
Fermilab Associate Scientist Position Interview

4. Motivation - LHC Beam Loss Protection
HEAT
DEPOSIT
IN THE COIL
MAGNET
QUENCH
BEAM
DUMP
BEAM LOSS
CYCLING
FILLING
RAMPING
SQUEEZING
~ 2h
RECOVERY
~1h – 48h
(1-3 cells ~ 5h
>14 cells ~ 48 h)
COLLISIONS
April 6, 2011
Fermilab Associate Scientist Position Interview

5. Motivation - LHC Beam Loss Protection
BLM
Beam
Loss
Monitor
HEAT
DEPOSIT
IN THE COIL
BEAM
DUMP
BEAM LOSS
CYCLING
FILLING
RAMPING
SQUEEZING
~2h
RECOVERY
~1h – 48h
(1-3 cells ~ 5h
>14 cells ~ 48 h)
COLLISIONS
April 6, 2011
Fermilab Associate Scientist Position Interview

6. Heat transport in the magnet
A heat transfer in the main dipole
Cold bore
inner layer
outer layer
Analytic considerations:
Cable insulation and helium channel around cold bore
are the most critical parameters limiting heat flow
from the magnet coil at steady state heat load
April 6, 2011
Fermilab Associate Scientist Position Interview

7. Network Model construction
Temperature
margin map
ΔT(B)
MAGNET
QUENCH
CURRENT
Heat load profile
HEAT FLOW
MODEL
Detailed
magnet
geometry
(Technical
drawings)
Material properties
at low temperature
OTHER
(non-beam induced
heat sources)
MEASUREMENTS
Model validation
Hysteresis losses
Eddy currents, etc.
(A. Verweij, R. Wolf)
Contribution is order of
1-2% of beam loss energy
during ramping
April 6, 2011
Fermilab Associate Scientist Position Interview

8. Helium in the Network Model
The volumes occupied by helium in the magnet are considered as:
narrow channels,
semi-closed volumes = inefficient inlet of fresh helium.
April 6, 2011
Fermilab Associate Scientist Position Interview

9. Network Model - Cable modeling
He channel
April 6, 2011
Fermilab Associate Scientist Position Interview

10. Network Model - coil modeling
April 6, 2011
Fermilab Associate Scientist Position Interview

11. Network Model - Validation
heat
VALIDATION
predicted
quench current
measured
END
MAGNET
EXPERIMENT
Heat source
- quench heaters
- inner heating apparatus
HEAT SOURCE
MODEL
More details:
D. Bocian, B. Dehning, A. Siemko, Modeling of Quench Limit for Steady State Heat Deposits in LHC Magnets,
IEEE Transactions on Applied Superconductivity, vol. 18, Issue 2, June 2008 Page(s):112 – 115;
D. Bocian, B. Dehning, A. Siemko, Quench Limit Model and Measurements for Steady State Heat Deposits in LHC Magnets,
accepted for publication in IEEE Transactions on Applied Superconductivity, 2009
April 6, 2011
Fermilab Associate Scientist Position Interview

12. Heating with Quench Heater
Measurements and analysis : D. Bocian
Two methods of measurement
Icoil =const, increase of IQH with a step of 0.1 A
IQH =const, wait 300 second for steady state, then ramp of Icoil
Second method is better for steady state heat transport
3 MQM, 2 MQY, MQ and MB have been tested at 4.5 K
April 6, 2011
Fermilab Associate Scientist Position Interview

13. Inner Heating Apparatus
General concept: D. Bocian and A. Siemko
Expansion rings: J. Halik
Measurements and analysis: D. Bocian
April 6, 2011
Fermilab Associate Scientist Position Interview

14. Inner Heating Apparatus
Main Dipole - MB
Main Quadrupole - MQ
MQY
MQM
April 6, 2011
Fermilab Associate Scientist Position Interview

15. Validation of the model
Larger temperature margin of magnet head!
April 6, 2011
Fermilab Associate Scientist Position Interview

16. Quench limits simulation – ion beam
Heat deposition map in the MB dipole magnet coil
Temperature map in the MB dipole magnet coil after heat load
Power peak in the coil = 24.3 mW/m
Power peak in the cold bore = 80.3 mW/m
POWER PEAK corresponds to the nominal LHC ion beam conditions (optics ver )
Peak temperature rise in the coil DT= 2.0 K
Peak temperature rise in the cold bore DT=1.4K
For nominal LHC ion beam conditions (beam optics ver )
heat deposition map for nominal LHC ion beam intensity was created by interpolation of FLUKA data to the cable strand coordinates from ROXIE (R. Bruce)
heat deposition map was implemented to Network Model
the magnet current range from injection to ultimate values (761 A to A, nominal is A) was scanned by linear scaling of heat deposition map
temperature distribution for nominal LHC ion beam conditions, corresponding to 95% of loss energy peak in the coil (23.1 mW/m) and 95% loss energy peak in the coldbore (76.3 mW/m)
quenching cable is located at the coil mid-plane
Temperature map corresponds to nominal MB current (11850 A)
April 6, 2011
Fermilab Associate Scientist Position Interview

17. Quench limits simulation – ion beam
Power peak in the coil = 24.3 mW/m and in the cold bore = 80.3 mW/m
POWER PEAK corresponds to the nominal LHC ion beam conditions
Simulation uncertainties
Process (BFPP) cross section: ~20%
Changes in the optics (e.g. beta beating) could change the spot size: ~10%
Network model: ~ 30%. This is the error on the quench limit for this beam loss distribution
On top of this, uncertainty on the energy deposition from the FLUKA simulation, could in worst case be a factor 2. Dominating uncertainty for this specific beam loss but could be less in other cases.
April 6, 2011
Fermilab Associate Scientist Position Interview

18. Fermilab Associate Scientist Position Interview
OUTLINE
Thermal analysis of superconducting magnets
Quench limit of present LHC magnets
Heat sources in the LHC magnets and beam loss protection system
Thermal model of superconducting magnet
Model validation with measurements
Quench limit numeric calculation
New designs of superconducting magnets
LHC NbTi quadrupole with enhanced insulation
Study of Nb3Sn conductor during heat treatment
Summary
April 6, 2011
Fermilab Associate Scientist Position Interview

19. LHC enhanced insulation - parameters
Cable sample – real scaling
Here: length = 115 mm (transposition pitch)
α – insulation wrapping angle,
w – insulation width
(insulation tape width + gap width)
h – cable width
(here: 15.1 mm + 2*insulation thickness),
open helium paths between the bath and the cable
Enhanced insulation scheme parametrs used in:
D. Tommasini and D. Richter „ A new cable insulation scheme improving heat transfer to superfluid helium in NbTi superconducting accelerator magnets” in Proc. 11th European Particle Accelerator Conference, Genoa, 2008
Sample length = 1 m, strand diameter = mm, cable width (bare)= 15.1 mm
1st layer
(polyimide)
2nd layer
3rd layer
(polyimide with
adhesive coating)
9 mm wide, 1 mm gap
25.4 μm thick
wrap angle α1 =71.68 deg
4 x(2.5 mm wide, 1.5 mm gap)
75 μm thick,
cross wrapped with the layers 1 and 3
wrap angle α1 =62.16 deg
55 μm thick,
50% overlap with the 1st layer
wrap angle α1 =71.90 deg
April 6, 2011
Fermilab Associate Scientist Position Interview

20. LHC enhanced insulation – analytic view
Single cable in helium bath
Max. heat flow over 1 m of cable at ΔT=0.26K, Tbath=1.9 K (units W/m)
279.10
0.035
3.8E-03
281.27
0.17
412.36
0.31
8.77
2.8E-03
0.03
0.24
26.05
0.41
0.79
HEAT/m
April 6, 2011
Fermilab Associate Scientist Position Interview

21. Layer 2 He channel length
dL1-L3
L – helium channel length in insulation layer 2,
dL1-L3 – distance between the helium channel in layer 1 and 3,
αLi – insulation wrapping angle of layer (i=1,2,3),
wins(Li) – insulation layer width (insulation tape width + gap width)
hci – cable width (15.1 mm + 2*insulation thickness),
Calculated winding angle L1 L2 L3
71.68
62.16
71.90
Helium channel length in insulation layer 2
edge L1- edge L3
middle L1- edge L3
middle L1- middle L3
dL1-L3 =
4.0 mm
4.5 mm
5.0 mm L=
5.15 mm
5.8 mm
6.44 mm
1400 chanels L2 / 1m
He L2 channel cross-section: 1.5E-3 m x 75E-6 m = 1.125E-7 m2
Superfluid helium heat flux density calculation
S is helium channel cross-section in [cm2],
l is helium channel length in [cm],
Tc is the temperatures of cold channel end in [K]
Th is the temperatures of hot channel end in [K]
April 6, 2011
Fermilab Associate Scientist Position Interview

22. Helium channels pattern
Interlayer coil edge
Inner coil edge
cable
along cable
April 6, 2011
Fermilab Associate Scientist Position Interview

23. Helium channels pattern
Inner coil edge
Interlayer coil edge
cable
along cable
April 6, 2011
Fermilab Associate Scientist Position Interview

24. Simulations – network model
along cable
April 6, 2011
Fermilab Associate Scientist Position Interview

25. Simulations (helium channels + insulation)
Measurements results from: D. Tommasini and D. Richter „ A new cable insulation scheme improving heat transfer to superfluid helium in NbTi superconducting accelerator magnets” in Proc. 11th European Particle Accelerator Conference, Genoa, 2008
April 6, 2011
Fermilab Associate Scientist Position Interview

26. Simulations (helium channels + insulation)
Measurements results from: D. Tommasini and D. Richter „ A new cable insulation scheme improving heat transfer to superfluid helium in NbTi superconducting accelerator magnets” in Proc. 11th European Particle Accelerator Conference, Genoa, 2008
Kapitza coeff.
50% of He channel cross-section
April 6, 2011
Fermilab Associate Scientist Position Interview

27. Fermilab Associate Scientist Position Interview
Conclusions
Model works
Model was validated for original ins and enhanded
In progress for Nb3Sn – optimization of cooling channels
April 6, 2011
Fermilab Associate Scientist Position Interview

28. Fermilab Associate Scientist Position Interview
OUTLINE
Thermal analysis of superconducting magnets
Quench limit of present LHC magnets
Heat sources in the LHC magnets and beam loss protection system
Thermal model of superconducting magnet
Model validation with measurements
Quench limit numeric calculation
New designs of superconducting magnets
LHC NbTi quadrupole with enhanced insulation
LARP Nb3Sn quadrupole magnets
Study of Nb3Sn conductor during heat treatment
Summary
April 6, 2011
Fermilab Associate Scientist Position Interview

29. Study of Nb3Sn conductor during heat treatment
Nb3Sn why, why reaction
Material properties change during reaction
strand / cable / coil dimension changes → tensions and stresses during reaction
Material properties E, ρ and CTE required for proper study of coil mechanical behavior
Precise measurements of Nb3Sn conductor dimensional changes
changes in length are order of tenth of a percent (not confined sample)
feedback to the future superconducting magnet designs
Nb3Sn conductor studies LARP magnet program
Strands are confined in the cable (twist pitch)
Coil and cables are confined in reaction tooling
Feedback for Nb3Sn coils R&D
Optimize reaction process, tooling and select the best material for pole
April 6, 2011
Fermilab Associate Scientist Position Interview

30. Fermilab Associate Scientist Position Interview
Motivation
During the reaction process of a Long Nb3Sn coil (part of the LARP Long Quadrupole R&D) an issue was found:
the inner layer had ~5.3 kN of longitudinal tension caused by the pole
Experimental data are required in order to understand and model this problem
Modeling of reaction process in three steps:
requires experimental data at all steps
strand dimensions changes during/after treatment
cable dimensions changes during/after treatment
coil dimensions changes during/after treatment
April 6, 2011
Fermilab Associate Scientist Position Interview

31. Fermilab Associate Scientist Position Interview
April 6, 2011
Fermilab Associate Scientist Position Interview

32. Fermilab Associate Scientist Position Interview
1,000,000
YBCO: Tape, || Tape-plane, SuperPower
(Used in NHMFL tested Insert Coil 2007)
At 4.2 K Unless
YBCO: Tape, |_ Tape Plane, SuperPower
Otherwise Stated
(Used in NHMFL tested Insert Coil 2007)
YBCO B||c
Bi-2212: non-Ag Jc, 427 fil. round wire,
YBCO B||ab
Ag/SC=3 (Hasegawa ASC-2000/MT )
100,000
Nb-Ti: for whole LHC NbTi
strand production (CERN, Boutboul '07)
Nb-Ti: Nb-47wt%Ti, 1.8 K, Lee, Naus and
1.9 K LHC
Larbalestier UW-ASC'96
Nb-Ti
Nb3Sn: Non-Cu Jc Internal Sn OI-ST RRP
10,000
1.3 mm, ASC'02/ICMC'03
Nb3Sn: Bronze route int. stab. -VAC-HP,
non-(Cu+Ta) Jc, Thoener et al., Erice '96.
Critical Current Density (non-Cu), A/mm² 
Nb3Sn: 1.8 K Non-Cu Jc Internal Sn OI-ST
2212
RRP 1.3 mm, ASC'02/ICMC'03
1,000
round wire
Nb3Al: RQHT+2 At.% Cu, 0.4m/s (Iijima et al
2002)
2223 Nb
Al: 3
Bi 2223: Rolled 85 Fil. Tape (AmSC) B||,
tape B|_
2223
RQHT
UW'6/96
tape B||
Bi 2223: Rolled 85 Fil. Tape (AmSC) B|_,
UW'6/96
100
MgB2: 4.2 K "high oxygen" film 2, Eom et Nb Sn
al. (UW) Nature 31 May '02
MgB 3 2
1.8 K
MgB2: Tape - Columbus (Grasso) MEM'06
film
MgB 2 Nb Sn 3 Nb Sn 3
tape
ITER
Internal Sn 10 5 10 15 20 25 30 35
Applied Field, T
April 6, 2011
Fermilab Associate Scientist Position Interview

33. Fermilab Associate Scientist Position Interview
WORK PLAN
Bibliography study and discussion with experts
Collection of the data and material properties for simulations (limited data available)
Experimental data collection
strand/cable sample measurement before/after heat treatment
dilatometer measurement at NHMFL
FEM simulation of the strand/cable/coil behavior during reaction
Feedback to the coil fabrication technology
Strand Model
Strand Subelement Model
Nb barier Sn
Nb+Cu Cu
April 6, 2011
Fermilab Associate Scientist Position Interview

34. Simulation plan 7h36’ 79h36’ 87h12’ 135h12’ 140h 188h 48 h 50°C/h 48 h
Temperature 400 → 640°C
Nb3Sn formation start
(Sn diffusion into Nb)
Need Nb3Sn properties
→ tuning of the model
Temperature 210 → 400°C
Continuation of Sn diffusion to Cu
(Sn melts at 238°C)
Temperature 20 → 210°C
Linear/non-linear elongation
Temperature 640 → 20°C
→ strand/cable shrinks I II
III IV V VI
VII
VIII
T [°C]
48 h
Preload on Nb (z-axis)
(Nb under tension,
Cu under compression)
640
50°C/h
48 h
400
25°C/h
~48 h
72 h
Strand/cable annealing
( 2 h at 200 °C)
Linear elongation,
Plastic deformation.
210
25°C/h
Cu6Sn5
Cu3Sn
Nb3Sn 20
7h36’
79h36’
87h12’
135h12’
140h
188h
Ch. Scheuerlein et al.,
IEEE Trans. Appl. Supercond.
VOL.18, NO. 4, 2008,
Temperature=210°C
Sn diffusion to Cu
→ Cu6Sn5 formation
Strand/cable shrinkage
Need Cu6Sn5 properties
→ tuning of the model
Temperature=400°C
Further Sn diffusion to Cu
→ Cu3Sn formation,
→ strand/cable shrinks,
→ all Sn reacted
Need Cu3Sn properties
→ tuning of the model
Temperature = 640°C
→ Strand/cable expand,
→ Plastic deformation?
→ Larger strand cross-section?
E, ρ and CTE needed for each step
April 6, 2011
Fermilab Associate Scientist Position Interview

35. Strand sample measurement
Sample preparation:
Sample length ~ 48 mm.
group 7 strand sample together
weld the ends of strands and file them.
Continous ΔL/L measurement during full Heat Treatment at NHMFL
Linear Variable Differential Transformers (LVDT)
measurement tip
furnace
measured
sample
reference
material
sample
holder
D. R. Dietderich et al., “Dimensional changes of Nb 3Sn. Nb3Al. and Bi2Sr2CaCu2O8 conductors
during heat treatment and their implication for coil design.” Adv. Cryo. Eng., vol. 44b, 1013–1020,
April 6, 2011
Fermilab Associate Scientist Position Interview

36. 54/61 strands measurement results
After a few first measurements, following questions needed to be answered:
Why strand sample elongate?
strand twist change contribution?
Why is length dependence of ΔL/L?
Before dilatometer measurements (lsample<50 mm):
Is there end effect?
STRANDS ENDS: C – crimp, F – fused, NF – not fused (as cut)
April 6, 2011
Fermilab Associate Scientist Position Interview

37. Length dependence of ΔL/L
Sample measurement
The length changes were measured from scratch to scratch
ΔL/L remains constant in the straight part of strands
In the ends ΔL/L show large end effect.
Scratches on strand surface placed:
10 mm from strand ending
10 mm + N * 50 mm form strand end (N=3)
Segmentation of rest strand length mm.
April 6, 2011
Fermilab Associate Scientist Position Interview

38. 54/61 strands measurement summary
Measured strand samples demonstrate:
Length increase by ,
Diameter increase by ,
Twist change by , (~4% of nominal twist (nt), nt=13 mm)
Diameter increase show conformance with data in:
N. Andreev, E. Barzi, D.R. Chichili, S. Mattafirri, and A.V. Zlobin
„Volume expansion of Nb-Sn strands and cables during heat treatment”
STRANDS ENDS: C – crimp, F – fused, NF – not fused (as cut)
April 6, 2011
Fermilab Associate Scientist Position Interview

39. Twist change impact on ΔL/L
Measurement of108/127 strand (#12521)
Twisted samples elongate during the heat treatment
nt- non twisted
tw - twisted
April 6, 2011
Fermilab Associate Scientist Position Interview

40. Fermilab Associate Scientist Position Interview
Conclusions
ΔL/L and twist change dependence confirmed by testing „non-twisted” strands
Strand ends can introduce „noise” in measurements
Important for measurements of short sample (< 50 mm) with dilatometer
Careful preparation and measurements of short samples
„non-twisted” strands are prefered in dilatometer measurements
twist change effect eliminated
behaves as confined strand in cable
April 6, 2011
Fermilab Associate Scientist Position Interview

41. Fermilab Associate Scientist Position Interview
SUMMARY
Both presented tasks required to be organized in form of dedicated experiments with:
Data collection and discussion with the experts
Construction of the model / design of experiment
Model validation with measurements
Results
Results of these studies have been/are used:
Reliable thermal models of superconducting magnets have been developed and used in quench limit calculations, beam optics adjustment and optimization of heat flow paths
Method of precise measurement of Nb3Sn dimensions have been developed and used for Nb3Sn strand measurements and also for recent Nb3Sn coil cross section study
April 6, 2011
Fermilab Associate Scientist Position Interview

42. Fermilab Associate Scientist Position Interview
Extra slides
April 6, 2011
Fermilab Associate Scientist Position Interview

43. Electrical equivalent
The analogy of the equivalent thermal circuit
Thermal circuit
Electrical Circuit T
[K]
Temperature V
[V]
Voltage Q
[J]
Heat
[C]
Charge q
[W]
Heat transfer rate i
[A]
Current κ
[W/Km]
Thermal Conductivity σ
[1/Ωm]
Electrical Conductivity RΘ
[K/W]
Thermal Resistance R
[V/A]
Resistance CΘ
[J/K]
Thermal Capacitance C
[C/V]
Capacitance
The analogy between electrical and thermal circuit can be expressed as:
steady-state condition Temperature rise  Voltage difference
transient condition Heat diffusion  RC transmission line
April 6, 2011
Fermilab Associate Scientist Position Interview

44. Network Model - Cable modeling
April 6, 2011
Fermilab Associate Scientist Position Interview

45. Fermilab Associate Scientist Position Interview
Detailed coil model
April 6, 2011
Fermilab Associate Scientist Position Interview

46. Insulation material properties
POLYIMIDE
κ = 2.4E-3*T+2.28E < T < 2.0 K [1]
κ = 4.638E-3*T < T < 5.0 K [2]
κ = 6.5E-3*T < T < 5.0 K [3]
G10
κ = 25.8E-3*T-12.2E < T < 2.5 K [4]
Bibliography:
B. Baudouy, „Kapitza resistance and thermal conductivity of Kapton in superfluid helium”, Cryogenics 43(2003), ,
Lawrence et al., „ The thermal conductivity of Kapton HN between 0.5 and 5 K”, Cryogenics 40 (2000), ,
Barucci et al, „Low temperature thermal conductivity of Kapton and Upilex”, Cryogenics 40 (2000), ,
B. Baudouy, J. Polinski, „Thermal conductivity and Kapitza resistance of epoxy resin fiberglass tape at superfluid helium temperature”, Cryogenics 49(2009),
April 6, 2011
Fermilab Associate Scientist Position Interview

47. Fermilab Associate Scientist Position Interview
Kapitza Resistance
Kapitza resistance reduces heat transfer in Kapton by 3÷6% and G10 by 5÷9%
Copper – He II
[4-6]
For metal – He II:
POLYIMIDE – He II
Theorerical: RK~T-2.57 Km2W-1,α=65.51 Wm-2K-3.57
RK=10.54E-3T-3 Km2W-1,α=47.43 Wm-2K-4 [1]
RK=0.7E-3*T-3 Km2W-1 [2]
G10 – He II
RK=1462E-6T-1.86 Km2W-1,hK=239 Wm-2K [3]
Bibliography:
B. Baudouy, „Kapitza resistance and thermal conductivity of Kapton in superfluid helium”, Cryogenics 43(2003) ,
Nacher PJ et al.,” Heat exchange in liquid helium through thin plastic foils”, Cryogenics 32 (1992),
B. Baudouy, J. Polinski, „Thermal conductivity and Kapitza resistance of epoxy resin fiberglass tape at superfluid helium temperature”, Cryogenics 49(2009),
A. Kashani and S.w.Van Sciver, „High heat flux Kapitza conductance of technical copper with several different surface preparations”, Cryogenics 25 (1985),
P.P. Granieri et al, „ Stability analysis of the LHC cables for transient heat depositions”, IEEE Trans. Appl. Supercond., vol. 18, No. 2 (2008).
D. Camacho et al.,”Thermal characterization of the HeII LHC heat exchanger tube”, LHC Project Report 232, 1998.
April 6, 2011
Fermilab Associate Scientist Position Interview

48. Helium properties Normal fluid and gaseous helium Superfluid helium
In case of channels inside of the cable and μ-channels which are of the order of 0.2 mm and 0.07 mm respectively, a typical nucleate boiling flux becomes much lower than that for helium bath which is W/m2 [1]. The gaseous phase in the narrow channels is described by a constant heat transfer coefficient and is of the order of 70 W/m2/K as extrapolated from [2]. The convective heat transfer in steady state mode is restricted to heat fluxes not greater than a few mW/cm2 [3] as it is only relevant for large volumes. In case of helium inside the cable and in the μ-channels this mode is negligible.
[1] S.W. Van Sciver, Helium Cryogenics.
[2] M. Nishi et all., Boiling helium heat transfer characteristics in narrow cooling channel, IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-19, NO. 3, MAY 1983.
[3] C. Schmidt, Review of steady state and transient heat transfer in pool boiling helium I.
Superfluid helium
The He II thermal resistance is calculated as follow:
where heat flow in He II is calculated according formulae [CRYOGENIE et ses applications en supraconductivite, IIF/IIR]
and X(T) is an experimental results fitting
April 6, 2011
Fermilab Associate Scientist Position Interview

49. LHC main superconducting magnets
MB – arc magnet, Tb=1.9 K
MQ – arc magnet, Tb=1.9 K
HEAT FLOW
LIMITS
heat flow barriers
cable insulation
interlayer insulation (MQM)
ground insulation
helium channel around cold bore (for temperatures above 2.16 K)
bath temperature 1.9 K
Transition HeII  HeI: helium channels are blocked = less effective heat evacuation due to the changing of heat evacuation path
bath temperature 4.5K
lower temperature margin (worst case: MQM 0.45K)
Helium channels does not play dominating role (heat conduction of He I and polyimide is the same order)
MQM – LSS magnet, Tb=1.9/4.5 K
MQY – LSS magnet, Tb=4.5 K
April 6, 2011
Fermilab Associate Scientist Position Interview

50. Heat deposits simulation
M. Sapinski – Geant 4
R. Bruce - FLUKA
proton beam
ion beam optics v
R. Bruce
R. Bruce
ion beam optics v
ion beam optics v with orbit bump
April 6, 2011
Fermilab Associate Scientist Position Interview

51. New inner triplet magnet – Heat Load
A combining particle tracking, FLUKA shower simulations in a single magnet coil
The inner triplet quadrupole FLUKA simulations were ran with a thick Beam Screen (BS) in Q1 (10.15 mm extra stainless steel shield added to the usual 2mm thick BS).
L=2.5*1034 cm-2s-1
Energy deposits in selected bin of magnet cross section with peak value. Magnet has been divided
longitudinally into 108 bins (~10 cm)
April 6, 2011
Fermilab Associate Scientist Position Interview

52. Fermilab Associate Scientist Position Interview
Summary
Quench limit at steady state for the „real” beam loss depends on the beam loss profiles
The model validation with LHC magnets was completed
The first quench level calculation for MB magnet with simulated beam loss profile are presented
Some simulation results:
Ebeam
[TeV]
Peak quench limit
[mW/cm3]
Avarage quench limit
Protons/second 7
10.2
6.2
3.5e7 5
17.5
10.6
6.0e7
0.45* 51 31
1.55e8
* The 450 GeV simulations were performed on beam loss distribution
for 7 TeV protons. This means that is is only „study case” which gives
rough estimations of quench level at injection.
April 6, 2011
Fermilab Associate Scientist Position Interview