1 K thermal model for QUBIC For Technological Demonstrator (T.D.) J.P. Thermeau, M. Piat QUBIC Collaboration Meeting, January 18/19, Milano

Schematic representation QUBIC Collaboration Meeting, January 18/19, Milano

QUBIC Collaboration Meeting, January 18/19, Milano 1K stage To 4K stage 6 Tie rods Thermal conduction from 4.2K to 1K 1K stage QUBIC Collaboration Meeting, January 18/19, Milano

Tensile tests of the carbone fiber tubes All experiments are made at SACM/IRFU/DSM, CEA Saclay Possibility to make the tensile tests at room temperature and low temperature (77K and 4.2K) QUBIC Collaboration Meeting, January 18/19, Milano

Tensile tests of the carbon fiber tube QUBIC Collaboration Meeting, January 18/19, Milano

Mechanical tests of the tie rods First design T (K) Force Max (N) E (GPa) Tests n°1 with pin 300 13 000 120 Tests n°2 25 000 110 Tests n°3 77 1 300 Tests n°4 33 000 85 Tests n°5 16 000 78 Second design T (K) Force Max (N) E (GPa) Test n°6 300 71 000 120 Tests n°7 77 36 000 82 tests n°8 4.2 28 000 81 QUBIC Collaboration Meeting, January 18/19, Milano

Carbon fiber tube physical properties With the current design of the 1K stage the maximum forces applied to the carbon tube are about 800 N  Last design of the tie rods with carbon fiber tube is validated. Characteristics of the carbon fiber tube: 60%(volum) of fiber, 40% DP406 resin 80% of fiber at 12°, 10% at 45°, 10% at 90° E theorical = 111 GPa at 300K external diameter: 32mm, internal diameter: 30mm The coefficient of thermal expansion was measured: axial: -0.014% from 80K to 280K radial: 0.12% from 80K to 280K The thermal conduction properties will be measured in february at APC. - Replace SS304 by CF, the thermal leaks through the tie rods are reduced by a factor 2.5 - Decrease the thickness of CF tube, the thermal leaks through the tie rods are reduced by a factor 2 QUBIC Collaboration Meeting, January 18/19, Milano

QUBIC Collaboration Meeting, January 18/19, Milano 0.3K stage 0.3K stage 2 x 8 Tie rods Thermal conduction from 1K to 0.3K 1K stage QUBIC Collaboration Meeting, January 18/19, Milano

Sub-Kelvin cryogenic scheme QUBIC Collaboration Meeting, January 18/19, Milano

Sub-Kelvin static thermal losses 1K Stage 6 Tie rods (epoxy/carbon-fiber): 0.32 mW 2 Precooling thermal switches (52 µW/K): 0.33 mW Instrumentation wires: 15 µW Thermal radiation through instrumentation window: 1 µW Thermal radiation (=0.1), 4.2K1K: 6 µW Total:  0.7 mW 0.3K Stage 16 Tie rods (epoxy/carbon-fiber): 17 µW Instrumentation wires: 6 µW Thermal radiation through instrumentation window: 1 µW Thermal radiation: (=0.1), 1K0.3K: <<1 µW Total:  25 µW QUBIC Collaboration Meeting, January 18/19, Milano

1K stage Thermal model Cool down from 4.2K to 1K 1. 2. Assumptions: Cooling capacity Thermal conduction Precooling thermal switches Thermal conduction Tie rods Energy stored in materials removed during the cooling Cool down of liquid helium 2. Assumptions: mHe = 1.5 mol 4He = 6g 4He. P1Kfridge = Cooling capacity of 1K fridge is constant = 6mW at 0.9K KPC : Conductance (W/K) of thermal switches is constant Thot: 1K stage temperature at the starting cooling Material = 115 kg of aluminum  60J at 4.2K QUBIC Collaboration Meeting, January 18/19, Milano

QUBIC Collaboration Meeting, January 18/19, Milano Cooling of the 1K stage Assumptions for the cooling from 4.2K to 1K Remove energy 4.2K -> 1K:  60J Constant cooling capacity: 6mW at 0.9K Thermal losses (Tie rods, instrumentation, …): 0.35mW Others losses (precooling switches): 2 x 52W/K Cooling time from 4.2K to 1K:  4.5 h Steady state at 1K (static thermal losses): Energy available in the 1K fridge 1.65 g LHe:  32J 1K fridge temperature: 0.8K with 0.7mW Cooling time at 0.8 K:  12h QUBIC Collaboration Meeting, January 18/19, Milano

1K stage thermal model Warm up of 1K stage during the pump regeneration cycle 1. Thermal conduction Precooling thermal switches Thermal conduction Fridge thermal switch Thermal conduction Tie rods Energy needed to increase the material temperature Assumptions: Thot4K: Temperature of 4K refrigerator is constant ThotF: 1K fridge temperature is constant Thot: 1K stage temperature at the end of the regeneration sequence Tcold: 1K stage temperature at the starting of the regeneration sequence KPC, KF: Conductances (W/K) of thermal switches (precooling and fridge) are constant Material = 115 kg of aluminum QUBIC Collaboration Meeting, January 18/19, Milano

Dynamic cooling of the 1K stage Assumptions for the warm-up Thot4K: Temperature of 4K refrigerator is constant = 4.2K ThotF: Temperature of 1K fridge is constant = 6K KPC: Conductance of precooling thermal switches: 52W/K KF: Conductance of ridge thermal switch: 530W/K Thermal losses (Tie rods, instrumentation, …): 0.35mW Warm-up time of 1K pump: 3 h (data given by Andy) When the regeneration sequence is finished:  What is the helium available quantity for the cooling sequence ? Assumptions for the cool-down The available quantity of helium is 80% of the initial filling quantity = 4.8 g Thot4K: Temperature of 4K refrigerator is constant = 4.2K P1Kfridge: cooling capacity is constant = 6 mW at 0.9K KPC: Conductance of precooling thermal switches: 52W/K Thermal losses (Tie rods, instrumentation, …): 0.35mW QUBIC Collaboration Meeting, January 18/19, Milano

Initial cooling of the 1K stage Initial cooling of 1K stage First step: from room temperature to 4.2K  cooling using the cryo-refrigerator 4K and the ON state of the precooling switches Second step: from 4.2K to 1K  cooling using the 1K refrigerator and the 1K fridge switch Cooling down from 300K to 4.2K Energy stored in materials removed during the cooling Thermal conduction Precooling thermal switches = Cooling capacity Assumptions: Cooling capacity = thermal conduction of the thermal switches The 4K refrigerator operates at 4.2K during the initial cool-down sequence QUBIC Collaboration Meeting, January 18/19, Milano

Initial cooling of the 1K stage - 115 kg aluminum  20 x106 J to remove during the cool-down - 2 precooling thermal switches : 2 x 69 mW/K Initial cool-down from 300K to 4.2K : High quantity of energy to extract, Cooling capacity limited by the ON state of the thermal switches, Cooling time very long  2 weeks Investigate others solutions to improve the cooling capacity, - mechanical heat switch - exchange gas in vacuum vessel, …. Obtain the cryogenerator cooling capacity in function of the temperature., QUBIC Collaboration Meeting, January 18/19, Milano

QUBIC Collaboration Meeting, January 18/19, Milano Summary 1/2 1K Static thermal losses: Thermal budget  0.7 mW Half of this budget is the contribution of the thermal switches. Other half of the budget is due to the losses through the tie rods 0.3K Static thermal losses: Thermal budget  25 µW (16 tie rods and instrumentation) 1K Dynamic analysis: Current operating time at 1K: Steady state at 1K: 15h Regeneration cycle (warm-up + cooling): 5h Operating ratio: 15/20 = 0.75 One Fridge thermal switch seems enough to cool the 1K stage from 4.2 K to 1K What is the helium available quantity for the cooling sequence ? QUBIC Collaboration Meeting, January 18/19, Milano

QUBIC Collaboration Meeting, January 18/19, Milano Summary 2/2 1K Dynamic analysis: The duration of the 1K stage initial cool-down is too long > 10 days The current ON state of the precooling thermal switches is not enough to allow the initial cooling of the 1K stage fast enough from the room temperature to the 4.2K. The OFF state of the precooling thermal switches has: a small impact on the cool-down duration from 4.2K to 1K. a strong impact on the duration of the steady state at 1K Is it possible to increase the ON conductance value of the precooling switch without increase OFF conductance value ? ON state > 140 mW/K OFF state  50 µW/K Investigate others solutions to improve the cooling capacity during the initial cooling down. Is it possible to reduce the OFF conductance of the 1K fridge switch ? ON state = 100 mW/K  T switch = 7 mK if the cooling power = 0.7mW (steady state) OFF state = 100 µW/K  the steady state duration increases. QUBIC Collaboration Meeting, January 18/19, Milano