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Bradford Benson
August 7, 2017
Cryogenics
Benson | Cryogenics08/07/2017
How cold?
BOLOMETERS• Ground-based: 300mK• Balloon borne: 100mK
SQUIDS• Niobium (Nb) circuitry,
superconducting at < 9.3 K
LC Boards:• Aluminum traces (SPT-3G),
superconducting at < 1.2 K• Nb used for SPT-SZ,
SPTpol
2Richards
To keep NEPbolo < NEPload
from the South Pole, need detector temperatures < ~300 mK
Detector Noise
Photon “Shot” Noise
Benson | Cryogenics08/07/2017
Outline
• Cooling to 4K• Cooling from 4K to below 1K• History of Pulse Tube Cooler, He3 fridge
development for CMB bolometers• Contact Resistance and Thermal
Contraction, Screws+Washers
3
Benson | Cryogenics08/07/2017
Cooling to 4K
Liquid He
Mechanical Coolers• Stirling Cooler
• Gifford-McMahon Cooler
• Pulse Tube Cooler
4
Benson | Cryogenics08/07/2017
Liquid Helium
1 atm boiling point: 4.2 KCritical pont: 5.2KCan pump to get to 1-1.5K
5http://www.britannica.com/
• Stable temperature • Electrically quiet • Low vibration • Reliable • Low cost for occasional
use – ~$10 / Liter ($6000 / 0.5W-
mo.)
Benson | Cryogenics08/07/2017
Liquid Helium: Cons
6
• Dewar manufacture – Superfluid welds – Size / Weight for long-term
operation • Availablility
– Must be shipped to remote locales
• Must be continually replenished – Technician on-hand
Helium transfer for ACBAR, i.e., outside at the South Pole
Benson | Cryogenics08/07/2017
Mechanical Cooling: Carnot Cycle• Do “work” on a gas to remove heat
from a system in a reversible process:• Isothermal expansion (b->a): Do
work on a gas • Adiabatic expansion (a->d)• Isothermal compression (d->c): Gas
does work by cooling surroundings• Adiabatic compression (c->b): End
in state b
– W = Work done on the system– Qc = Heat taken from the system
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Tem
pera
ture
Entropy
Heat-in
Heat-out
Benson | Cryogenics08/07/2017
Stirling coolers: Idealized Cycle
aàb: isothermal compression
bàc: isochoric cooling
càd: isothermal expansion
dàa: isochoric heating
• Warm compression space separated by a regenerator
• Regenerator is high heat capacity, porous material that supports T gradient, (e.g., lead spheres, copper screens)
8
Benson | Cryogenics08/07/2017
Stirling Coolers
9
• Cannot separate compression from expansion space
àMiniaturization – Used to cool IR detectors – High critical Temperature (Tc)
superconducting devices (e.g., cell phone towers, IR cameras)
• Typical cooling: – ~1W at 80K
x20
Stirling Cooler from Janis
Benson | Cryogenics08/07/2017
Pulse Tube Cooler: OPTC
10
Orifice Pulse Tube Cooler
Benson | Cryogenics08/07/2017
Pulse Tube: Flow Phase
For a simple 1-D model with no turbulence
We require enthalpy flow for cooling. It can be calculated for any point along the tube
Applying mass conservation and ideal gas law
Assuming sinusoidal pressure and velocity fluctuations, yields:
àMass flow and pressure must be in phase for Cooling
11
Weisend 2006
Benson | Cryogenics08/07/2017
Pulse Tube: DIPTC
• Additional parameter to adjust pressure/flow phase
• Regenerator bypass
• Creates multiple equilibria
• Cryomech PTC’s are DIPTC’s
12
Double Inlet Pulse Tube cooler
Benson | Cryogenics08/07/2017
Pulse Tube Coolers
Cryomech PT405
• Relatively new technology (~2002)
• No cold moving parts
• 40W @ 40K, 1.5W @4k
13
Benson | Cryogenics08/07/2017
Loss Mechanisms
• Non Isothermal Expansion/Compression• 1-10% efficiency is standard• Thermal losses
– (Conduction along walls, etc.)• Regenerator Dead volume
– Wastes compression work• Regenerator efficiency
– Cool all gas to cold T• Pressure oscillation damping
– Decreases refrigeration effect
14
Benson | Cryogenics08/07/2017
Volumetric Specific Heats
Regenerators
• The Regenerator is a solid, porous material. Requires low flow resistance, but good heat contact with gas; which are conflicting requirements.
• Ultimate limit to achievable T– Material Heat capacity
• Difficult optimizationàComputer modeling of geometry and
operation• Traditional materials (e.g., lead spheres,
copper sheets), have mostly been replaced with magnetic materials (e.g., ErNi) in the ~1990s: temperatures went from ~10 to 4 K.
15ter Brake
Benson | Cryogenics08/07/2017
Cooling to below 1K
He3 Sorption Refrigerator
Dilution Refrigerator
Adiabatic Demagnetization Refrigerator (ADR)
16
Benson | Cryogenics08/07/2017
He3
• Relatively expensive ($3K/liter)– Use in closed cycles
• Requires pumped He4 bath to condense (critical temp 3.3 K)
• Base temperature of ~230 mK with pumping
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1 atm (1e5 Pa) boiling point: 3.2K Critical point: 3.3 K
Benson | Cryogenics08/07/2017
He3 Sorption
1. Switch is opened.
2. Heat applied to charcoal pump (30-50K). Liquid is condensed in boiler.
3. Switch is closed.
4. Charcoal cools. Boiler cools to 300mK.
18
Benson | Cryogenics08/07/2017
Multistage He3 Sorption
• Cooling Power:
– 60uW at 350mK
– 1.5uW at 270mK19
Simon Chase He4-He3-He3 (He10) fridge - Used for SPT-SZ, SPTpol
Benson | Cryogenics08/07/2017
Dilution Refrigerator
• Finite solubility of He3 in He4
– When mixture is cooled < 0.87K, phase separation into He3-rich phase and He3-dilute phase
• Remove He3 from solution in He4
– He3 is diluted as it flows across phase boundary between He3-rich and He3+He4 mixture
– This process is endothermic, causes a calculable enthalpy change
20Lounasmaa (1974)
He3-He4 phase diagram
He3 Concentration
Fermi liquid He3 in superfluid He4
Normal liquid He3, He4
Benson | Cryogenics08/07/2017
Dilution Refrigerator
21Betts
Janis Dilution Refrigerator
• Cooling Power: – 10uW at 15mK – 100 uW at 200 mK
Benson | Cryogenics08/07/2017
Adiabatic Demagnetization Refrigerator
1. Switch is closed
2. B field is turned on. Spins in paramagnet align.
3. Switch is opened.
4. B adiabatically reduced to ~zero, lowering temperature.
22Betts White
Benson | Cryogenics08/07/2017
ADR: Characteristics
• Salts for ~100mK
– FAA on MAXIMA
• 100nW @ 100mK
• 2.5 T, 6A
• Metallic nuclei for <1mK
– Cu: down to nK
23
TOPHAT ADR (PI: Steve Meyer)
Benson | Cryogenics08/07/2017
Thermal Contraction, Screws + Washers, and Thermal Conduction
24
Benson | Cryogenics08/07/2017
Thermal Contraction
25NIST 2000: http://www.cryogenics.nist.gov/Papers/Cryo_Materials.pdf
Benson | Cryogenics08/07/2017 26
Thermal Contraction• Most materials have done
>95% of their contraction by 77 K
• Contraction (ΔL/L) for some common materials at 4 K: Aluminum: 4.1 mils per inch Brass: 3.8 mils per inch Copper: 3.3 mils per inch Stainless Steel: 3.0 mils per inch
Benson | Cryogenics08/07/2017
Thermal Contraction
27
• Screws loosen if the part they go through shrinks more than the screw. • Stainless steel (SS) screws are preferred from strength perspective, but they shrink less than
most common materials. • Typically use brass screws through copper parts (brass weaker, so don’t strip the screws!)• If you use SS screws, make sure to use belleville (conical) washers
• Most materials have done >95% of their contraction by 77 K
• Contraction (ΔL/L) for some common materials at 4 K: Aluminum: 4.1 mils per inch Brass: 3.8 mils per inch Copper: 3.3 mils per inch Stainless Steel: 3.0 mils per inch
Benson | Cryogenics08/07/2017 28
Thermal Conduction• OFHC Copper is by far best common thermal conductivity cryogenic material
• e.g., Most common Aluminum alloy (Al-6061) is ~400x less conductive at 4K • Conductivity can vary significantly across aluminum alloys:
• e.g., Al-1100 is a “soft” aluminum with much better conduction, but harder to machine / tap-screws
Benson | Cryogenics08/07/2017 29
Contact Resistance• Thermal contact resistance across
interfaces with bolts often dominates thermal gradient
• Oxide layer on material forms a barrier• Rules of thumb:
1) Gold plating: doesnt oxidize, and is “soft” material which improves contact
2) Clean-oxide via scotch-brite or sand-paper every time you dis-assemble• In addition, always use Apeizon-N
grease; a very light layer can fill micro-roughness of material’s surface
3) Use belleville washers to increase clamping force between materials.
Benson | Cryogenics08/07/2017 30
Heat Loading Between Stages• Radiative:
• Typically dominates loading on 1st stage (i.e., 50 or 77 K), often reduced via gold-plating or reflective super-insulation
• Can also be important for coldest stages (i.e., 0.25 K), where ~uW loads cause bigger problems
• Mechanical supports:• Need low-thermal conductivity, strong supports• From 300-4 K; G10 is most common and typically
best strength-to-conductivity ratio. Stainless steel, and carbon fiber (CF) are also common.
• Sub-4 K: CF, Vespel, Kevlar are common materials
• Wiring:• Need low-thermal conductivity wiring between
stages.• From 300-4 K, Manganin (with Cu-Ni cladding) wire.
Phosphor bronze wire used by lakeshore, but has higher conductivity. Sub-4K use NbTi.
Benson | Cryogenics08/07/2017
Useful References
• Radebaugh 2009, “Cryocoolers: the state of the art and recent developments”, http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=901013
• de Waele, 2011 “Basic Operation of Cryocoolers and Related Thermal Machines”, https://link.springer.com/article/10.1007%2Fs10909-011-0373-x
• Gmelin 1999 et al., “Thermal boundary resistance of mechanical contacts between solids at sub-ambient temperatures”, http://iopscience.iop.org/article/10.1088/0022-3727/32/6/004/meta
• http://www.cryogenics.nist.gov/MPropsMAY/material%20properties.htm
• Ekin 2006, “Experimental Techniques: Cryostat Design, Material Properties”, https://www.amazon.com/Experimental-Techniques-Properties-Superconductor-Critical-Current/dp/0198570546
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Benson | Cryogenics08/07/2017
Extras
32
Benson | Cryogenics08/07/2017
aàb: isothermal compression
bàc: isobaric cooling
càd: isothermal expansion
dàa: isobaric heating
Gifford-McMahon (GM) cooler: Idealized Cycle
33
Benson | Cryogenics08/07/2017
GM coolers
34
• Single or double stage available
• Robust, well developed technology
• Cons: Vibration from moving regenerator
• Widely used: – Cryopumps – DASI
• Typical cooling: – 50W @ 50K, 1W @ 7KARS GM cooler
Two stage GM
Benson | Cryogenics08/07/2017
ADR: Materials
• Require– U>kT at high fields and U<kT at starting temp and low
field.– Entropy of lattice small
• Spin interactions prevent Bf =0– Can achieve colder temperatures with nuclear spins.
35