Hervé Allain, R. van Weelderen (CERN) Thermal model for Nb3Sn Inner Triplet quadrupoles - 140 mm aperture option Hervé Allain, R. van Weelderen (CERN) WP3 – WP2 - WP10 joint meeting (26 July 2012 - CERN) Updated on 1st August 2012

Overview General aspect Cases considered - assumptions Coil insulations Typical to be expected T-map for a coil with cooling at 1.9 K

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” 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

Expected Temperature Profile in Coils Assumptions: Superfluid helium cooling, 140 mm aperture, 3 cases considered: 3.7 mm cold bore + 2.3 mm W inserts 3.7 mm cold bore + 7 mm W inserts 3.7 mm cold bore + 2 mm beam screen + 6 mm W absorbers Energy deposition maps from F. Cerutti and L. Salvatore’s calculations for the 3 cases considered at peak power deposition in Q1 1.5 mm annular gap (free space for helium) between coil and beam-pipe 0.2 % open collars and yoke 4 % open titanium piece and collar keys 2 heat exchangers 1.9 K cold source in heat exchanger All material properties have been taken temperature dependent Cable has been homogenized at the first order

Coil insulations assumed for calculations Inner coil layer Outer coil layer Cold bore Collars 1 2 3 4 5 6 4) 50 µm kapton + 25 µm stainless steel 50 % filled 5) 200 µm G-10 6) 0.5 mm kapton 1) 1.5 mm annular space 2) 200 µm G-10 3) 50 µm kapton + 25 µm stainless steel 50 % filled 0.5 mm G-10 Cable: 0.15 mm G-10 insulated 2-3 and 4-5-6 have been homogenized to form one mono layer each 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

Corresponding Energy deposition used for the model Example: 3.7 mm cold bore + 2.3 mm W inserts – heat load 33 W/m – peak at 8 mW/cm3

Simulated T-distribution (1/6) – coils in a HeII bath at 1.9 k 3.7 mm cold bore + 2.3 mm W inserts – heat load 33 W/m – peak at 8 mW/cm3 Tmax = 2.419 K

Simulated T-distribution (2/6) 3.7 mm cold bore + 2.3 mm W inserts – heat load 33 W/m – peak at 8 mW/cm3 Tmax = 3.766 K

Simulated T-distribution (3/6) – coils in a HeII bath at 1.9 k 3.7 mm cold bore + 7 mm W inserts – heat load 36.5 W/m – peak at 4.6 mW/cm3 Tmax = 2.243 K

Simulated T-distribution (4/6) 3.7 mm cold bore + 7 mm W inserts – heat load 36.5 W/m – peak at 4.6 mW/cm3 Tmax = 3.265 K

Simulated T-distribution (5/6) – coils in a HeII bath at 1.9 k 3.7 mm cold bore + 2 mm beam screen + 6 mm W inserts – heat load 15.75 W/m on the cold bore and on the coils – peak at 4.6 mW/cm3 Tmax = 2.246 K

Simulated T-distribution (6/6) 3.7 mm cold bore + 2 mm beam screen + 6 mm W inserts – heat load 15.75 W/m on the cold bore and on the coils – peak at 4.6 mW/cm3 Tmax = 3.269 K

Simulated T-distribution at peak power deposition in vertical central part of the coils for each case considered 7 mm W insert and BS+6 mm W insert have the same profile (due to identical heat load on the coils)

Main Observations - Conclusions Temperature field depends on tungsten insert thickness only: 1.365 K < Tmax-coil – 1.9 K < 1.866 K Having the tungsten insert actively cooled via the beam screen at a temperature higher than the cold mass will make the heat extraction design of the cold mass much more manageable. Titanium piece and collars keys between 2 and 4 % open, 16 mK difference on the ΔT max, 1 % absolute limit where T diverges, (bottleneck collar key, to be checked). Longitudinal distribution of openings has to be accounted for  4% remains safest design choice! Caution: titanium piece and collars keys taken open to HeII homogeneously, more investigations needed with the real holes Collars and yoke packing critical: at 0% open T in annular space moves dangerously close to Tlambda  avoid that all load passes via the inner layer and annular space Annular space taken between 0.3 and 1.5 mm, 30 mK on the ΔT max. Longitudinal distribution of openings + quench pressure build-up and helium discharge have to be accounted for  1.5 mm remains safest design choice! Thermal Material properties to be measured Simulations done with two heat sinks: need to investigate if the heat exchanger can absorb all the heat load

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.