Axion Relics Thermal – mechanical simulation for a flange UHV 114/63 1D with copper gasket

Mechanical simulation goal Simulate the deformation occurring on the copper gasket The entity of the force characterizes and affect the thermal contact coefficient. Required force  6.125 kN for each bolt  9.8 Nm/bolt  8 bolt  49 kN Bolt size M8x50 Conclusion Thermal contact copper gasket – ss flange plastically deformed  approximated as perfect contact Applied Force 49 kN 1 - 2 micrometres of def. room temperature copper RRR 50 Copper tube FIXED constraint Copper tube and Flange bonded

Thermal simulation goal To calculate the temperature distribution for the component connecting the copper cavity to the magnet through the flange UHV 114/63 Inner copper cavity simulation for different heat loads: 10 mW 15 mW 20 mW 2 K MLI insulated Heat Load Material used: AISI 316 L for the tube and flanges Copper RRR 50 Surrounding T = 70 K

Thermal simulations results I Heat load 15 mW Tmax 10.7 K Heat Load T max 20 mW 12.7 15 mW 10.7 10 mW 9.4

Solutions A Aim: to keep the copper cavity temperature as low as possible. The requested temperature is 2.0 K Three mm-thick copper pipe added to make a thermal bridge from the helium sink up to the copper cavity Solution: One thermal contact: Copper bridge – 316L tube  Extrapolated value: 1 W/Km2 and 3 W/Km2 [“Thermal boundary resistance of mechanical contact btw solids at sub-ambient temperatures” – E. Gemlin et al.]

Thermal simulations II Solution: Two thermal contact considered btw copper and 316L tubes 2 K 15 mW MLI insulated 5 mW

Thermal simulations results II Heat load 15 + 5 mW Tmax 6.98 K Tmax 6.92 K Kcopper-ss tube 1 W/m2K Kcopper-ss tube 3 W/m2K Tmax – copper bridge 3.01 K Tmax – copper bridge 3.66 K Copper bridge to actively cool the electronic support

Solution B outer copper ring plus bayonet

Liquid He II Copper ring Cold clamps to attach cabling. To be modelled

Thermal simulations Solution: Copper cylinder attached to the cold part. Di = 58 and De = (68, 80, 84, 100)mm copper strip attached to it and working as a cold bridge for the measuring part. thickness (6, 10, 14, 28); width 25 mm. (Ω = 150, 250, 350, 700 mm2) Thermal contact btw copper bayonet and copper measuring part: 20 mW

Thermal simulations Solution: Copper cylinder attached to the cold part. Di = 58 and De = (68, 80, 84, 100)mm copper strip attached to it and working as a cold bridge for the measuring part. thickness (6, 10, 14, 28); width 25 mm. (Ω = 150, 250, 350, 700 mm2) Thermal contact btw copper bayonet and copper measuring part: 20 mW Kcopper-ss tube 1 W/m2K KSS tube - Copper sink 200 W/m2K [2] 2 K KCopper sink - copper strip 385 W/m2K [2] KCopper cavity- copper strip 385 W/m2K [2] 20 mW [2] “Thermal boundary resistance of mechanical contact btw solids at sub-ambient temperatures” – E. Gemlin et al. Table 1 and Table 2 Cu/Apiezon/Cu (385 – 3300) W/m2K Force of 450 N Temperature range (1.6 – 6) K Cu/SS 1280 W/m2K Force of 9.8 kN Temperature range (326/335) K

Thermal simulations results Heat load 20 mW Sim. IV : Tmax 4.77 K Copper ring 58/68 mm Copper strip 6 mm thick Sim. V : Tmax 3.93 K Copper ring 58/80 mm Copper strip 10 mm thick Sim. VI : Tmax 3.48 K Copper ring 58/84 mm Copper strip 14 mm thick Sim. VII : Tmax 2.92 K Copper ring 58/100 mm Copper strip 28 mm thick

Thermal simulations Solution: Copper cylinder attached to the cold part. Di = 58 and De = 80 mm copper strip attached to it and working as a cold bridge up to the measuring part (cross section: 10 x 49 mm2 = 490 mm2) Thermal contact btw copper bayonet and copper measuring part: 10 mW

Thermal simulations results Heat load 10 mW Sim. VIII : Tmax 2.55 K Copper ring 58/80 mm Copper strip 10 mm x 49 mm Heat load 20 mW Sim. VIII : Tmax 3.08 K Copper ring 58/80 mm Copper strip 10 mm x 49 mm

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