1. Hervé Allain, R. van Weelderen (CERN)
Thermal model for Nb3Sn Inner Triplet quadrupoles - 140 mm aperture option
Hervé Allain, R. van Weelderen (CERN)
4th September 2012

2. Overview General aspect Cases considered – proposed features
Coil insulations
Typical to be expected T-map for a coil with cooling at 1.9 K up to 2.05 K
Parametric study
Main observations
Proposed features

3. Coil cooling principle
Heat from the coil area (green) and heat from the beam pipe (purple) combine in the annular space between beam pipe and coil and escape radially through the magnet “pole” towards the cold source  “pole, collar and yoke” need to be “open”
Heat Conduction mechanism in the coil packs principally via the solids, except for dedicated helium channels deliberately machined in the midplane
Longitudinal extraction via the annular space is in superfluid helium, with T close to Tλ and with magnets up to 7 m long not reliable  “pole, collar and yoke” need to be “open”
≥ 1.5 mm annular space

4. Feature Value comments
Superfluid helium cooling, 140 mm aperture, 2 cases considered: 3.7 mm cold bore + 7 mm W inserts 3.7 mm cold bore + 2 mm beam screen + 6 mm W absorbers Proposed features
Feature
Value
comments
Annular gap
1.5 mm
Safest choice for cooling and pressure rise due to quench
(to be verified)
collar open
2 %
Can be lower in steady state
Dynamic to be verified
Yoke open
Titanium piece open
4 %
More investigation needed with the real holes
Aluminium collar keys
Midplane open
Beam screen actively cooled by helium channels
4 x 4.5 – 4.7 mm ID or
8 x ~ 3.4 mm ID
estimated for ~ 400 W total
2 heat exchangers
68 mm ID
calculated for ~ 500 W total
Some Materials thermal properties need to be measured

5. Coil magnet configuration assumed for calculations
Naked coil in He II bath assumed for calculations to evaluate the best case
Inner coil layer
Outer coil layer 1 2
1 & 2: superfluid helium
0.5 mm G-10
Cable: 0.15 mm G-10 insulated
Coil magnet configuration assumed for calculations
Inner coil layer
Cold
bore
Outer coil layer
Collars 1 2 3 4
1) 1.5 mm annular space
2) 50 µm kapton + 25 µm stainless steel 50 % filled
3) 200 µm G-10
4) 0.5 mm kapton
0.5 mm G-10
Cable: 0.15 mm G-10 insulated
2-3-4 have been homogenized to form one mono layer
Lack of some material thermal properties: need to be measured

6. Energy deposition 2D map for Q1 at peak power
Courtesy of F. Cerutti and L. Salvatore

7. Same heat load on the coil (~16 W/m)
Corresponding Energy deposition used for the model on the coil
1) 3.7 mm cold bore + 7 mm W inserts
2) 3.7 mm cold bore + 6 mm W inserts + Beam Screen
Same heat load on the coil (~16 W/m)
peak at 4.6 mW/cm3
Difference between 1 and 2: heat load on the cold bore -> 55.6 W/m2 for 1 and 6.8 W/m2 for 2
Absorbed by the heat exchanger

8. Simulated T-distribution
He II channels in midplane (4 % open)
coils in a He II bath at 1.9 k
coils in magnet configuration - HX at 1.9 k
T He II midplane
Midplane He II channels
closed
1 side open
2 sides open
T max (K) coils in a He II bath at 1.9 k
2.243
2.075
2.069
T max (K) coils in magnet configuration - HX at 1.9 k
3.265
2.396
2.377
ΔT (K)
1.022
0.321
0.308
Dangerous:
T max He II midplane ~ 2.06 K
Too close to TLamda
Safe: T max He II midplane ~ 1.93 K
~ Maximum effective
thermal conductivity of He II

9. Parametric study (1/2) Variation of the heat exchanger temperature
Midplane 4 % open, 2 sides open
Annular space: 1.5 mm

10. Parametric study (2/2) Remark: Variation of the midplane % open
2 sides open
THX = 2.05 K
Annular space: 1.5 mm
Remark:
BS, if ≤ 2 % open
no BS , if ≤ 3 % open
He II -> He I in the
midplane -> too dangerous

11. Main Observations Midplane opened:
Midplane open means He II channels in the midplane which communicate with the annular space and He II in space between laminations (NEED OF A WAY FOR THE HEAT TO GO TO THE HEAT EXCHANGER)
Temperature field : 500 mK < Tmax coil – THX
7 mm W insert or 6 mm W insert + beam screen:
1 side open  Tmax HeII midplane over Tlamda (except for very low HX temperatures)
2 sides open  assures functionality up to 2.05 K
Safest choice: midplane > 7 % open (transits from He II to He I for Midplane ≤ 4 %)
Caution: midplane taken open to He II homogeneously, more investigations needed with the real channels and experiments must be planned to assess the efficiency of the chosen geometry and design

12. Proposed features Feature Value comments Annular gap 1.5 mm
Safest choice for cooling and pressure rise due to quench
(to be verified)
collar open
2 %
Can be lower in steady state
Dynamic to be verified
Yoke open
Titanium piece open
4 %
More investigation needed with the real holes
Aluminium collar keys
Midplane open
7 %
(≈ 35 µm for a 500 µm midplane spacing)
Assures functionality up to 2.05 K
Beware of slit compression, actual size needs experimental validation
Beam screen actively cooled by helium channels
4 x 4.5 – 4.7 mm ID or
8 x ~ 3.4 mm ID
estimated for ~ 400 W total
2 heat exchangers
68 mm ID
calculated for ~ 500 W total
Some Materials thermal properties need to be measured

13. References
“Investigation of Suitability of the Method of Volume Averaging for the Study of Heat Transfer in Superconducting Accelerator Magnet Cooled by Superfluid Helium”, H. Allain, R. van Weelderen, B. Baudouy, M. Quintard, M. Prat, C. Soulaine, Cryogenics, Available online 14 July 2012.