1. Cooling aspects for Nb3Sn Inner Triplet quadrupoles and D1
Using superfluid helium (HeII) at T < 2.17 K (R. van Weelderen, CERN)
Using Supercritical Helium at ~ 4.0 K < T < ~4.5 K (J-M. Poncet, CEA)

2. Points to be addressed for Superfluid Helium
Generic cold mass requirements for cooling IT+D1
Estimated cold source temperature and T-margin for heat extraction
Generic cold mass design features for coil cooling and quench pressure protection

3. 1: Typical layout for Nb3Sn (140 mm and 120 mm aperture combined)
Magnet
length (m)
variation (m) Q1
7.445
0.255
Q1 t Q2
3.305
Q2a
6.38
0.19
Q2a to Q2b
1.775
0.135
Q2b
Q2b to Q3 Q3
Q3 to D1
8.2
D1? 15
Total
59.2
1.5
The total length variation between 140 mm or 120 mm aperture option is irrelevant for the general cooling design.
Typically a length of ~ 60 m will be considered for all cooling options.

4. 1: 2-Phase HeII heat exchanger (our « cold source »)
Sizing based on [ref 1] :
Minimum heat exchange area
Acceptable 2-phase flow ∆P
Vapour flow below 2-phase flow instability threshold of 7 m/s
Two parallel bayonet heat exchangers made out of Cu pipes passing in-interrupted (i.e. at one level) through all cold masses and interconnects
2 x ID 68 mm (500 W) or 2 x ID 86 mm (800 W)
design pressure 20 bar external

5. 1: additional generic cold mass features
Balancing heat load longitudinally will require ≈130 cm2 (500 W) – 520 cm2 (800 W) section of helium
N.B. : 800 W figure based on extrapolation from 500 W calculation. We should probably compromise on this heat load balancing and lower the 520 cm2 to a more realistic value for magnet construction.
Quench discharge will require ≥ 50 cm2 smooth pipe equivalent longitudinal passage
Cool-down and warm-up will require ≥ 50 cm2 smooth pipe equivalent longitudinal passage

6. 1: Generic cold mass requirements blue 500 W, red 800 W
2 // HX ID 68 mm - 86 mm
Free section of helium ≈130 cm2 – 520 cm2
≥ 50 cm2 smooth pipe equivalent longitudinal passage (quench, cool- down/warm-up)

7.  minimum coil temperature > 1.895 K (1.997 K)
2: Temperature in the cooling system at 500 W or 800 W (two parallel 68 mm ID / 86 mm ID bayonet heat exchangers and one 97 mm ID pumping line)
Location
T (K)
Available ∆T to Tλ (mK)
cold compressor station
1.776
394
cold compressor station - HX outlet ( < 0.5 km QRL)
1.790 (1.812)
380
(358)
HX outlet - HX inlet
1.800
(1.822)
370
(360)
HX inlet – bayonet HX outlet (60 m, 97 mm ID pumping line)
1.818
(1.874)
352
(296)
Superfluid bath in the triplet+D1
1.895
(1.997)
275
(173)
Available ∆T for radial heat extraction from coil to cold source is 275 mK (173 mK)
 minimum coil temperature > K (1.997 K)

8. 3: Coil cooling and quench pressure
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 radial through the magnet “pole” towards the cold source  “pole & collar” need to be “open” (by ≈ 4 % as a first guess)
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 need to be “open”
Due to the relative incompressible nature of HeII in order to prevent quench induced pressure built up far exceeding 20 bar around the beam pipe  “pole” & collar need to be “open”
≥ 1.5 mm annular space

9. Summary (1 of 3)
The features listed (see next page) are essential for an accelerator ready magnet and should be implemented.
Values given are qualitative, based on experience, past calculations and strongly dependent on final heat load.
Values need to be confirmed by “closing the loop” with the heat load assessment and by increasingly detailed thermal models.

10. Summary (2 of 3)
2 // bayonet heat exchangers made out of Cu pipes passing in-interrupted (i.e. at one level) through all cold masses and interconnects: 2 x ID 68 mm (500 W) or 2 x ID 86 mm (800 W), design pressure 20 bar external.
Free section of helium ≈130 cm2 – 520 cm2
≥ 50 cm2 smooth pipe equivalent longitudinal passage

11. Summary (3 of 3)
Available ∆T for radial heat extraction from coil to cold source is 275 mK (173 mK)  minimum coil temperature > K (1.997 K)
“pole & collar” need to be “open” (by ≈ 4 % as a first guess)
Free annular space between beam pipe and coil ≥ 1.5 mm

12. References
CERN-ATS , “The Cryogenic Design of the Phase I Upgrade Inner Triplet Magnets for LHC”, van Weelderen, R (CERN) ; Vullierme, B (CERN) ; Peterson, T (Fermilab), 23rd International Cryogenic Engineering Conference, Wroclaw, Poland, Jul 2010