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

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

3. 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

4. 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

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

6. 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

7. 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: % 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

8. 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

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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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