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

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

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

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

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

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

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

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

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

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

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

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

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.