Thermal model for Nb 3 Sn Inner Triplet quadrupoles - 140 mm aperture option

1. 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. 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

5. Naked coil in He II bath assumed for calculations to evaluate the best case Inner coil layer Outer coil layer 2 1 1 & 2: superfluid helium 0.5 mm G-10 • Cable: 0.15 mm G-10 insulated Coil magnet configuration assumed for calculations 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 Inner coil layer Outer coil layer Cold bore Collars 2 3 4 1 2) 50 µm kapton+ 25 µm stainless steel 50 % filled 3) 200 µm G-10 4) 0.5 mm kapton 1) 1.5 mm annular space 0.5 mm G-10

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

7. Corresponding Energy deposition used for the model on the coil Same heat load on the coil (~16 W/m) peak at 4.6 mW/cm3 1) 3.7 mm cold bore + 7 mm W inserts 2) 3.7 mm cold bore + 6 mm W inserts + Beam Screen 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 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) • Variation of the midplane % open • 2 sides open • THX = 2.05 K • Annular space: 1.5 mm Remark: He II -> He I in the midplane-> too dangerous BS, if ≤ 2 % open no BS , if ≤3 %open

11. Main Observations • Midplane opened: • Midplane openmeansHe II channelsin 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  TmaxHeIImidplane 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

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.