2017 08 07 Benson Cryogenics - University of Chicago08/07/2017 Benson | Cryogenics Dilution...

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


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


Cooling to 4K

Liquid He

Mechanical Coolers• Stirling Cooler

• Gifford-McMahon Cooler

• Pulse Tube Cooler

4


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.)


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


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

7

Tem

pera

ture

Entropy

Heat-in

Heat-out


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)

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Stirling Coolers

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• 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


Pulse Tube Cooler: OPTC

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Orifice Pulse Tube Cooler


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


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


Pulse Tube Coolers

Cryomech PT405

• Relatively new technology (~2002)

• No cold moving parts

• 40W @ 40K, 1.5W @4k

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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

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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


Cooling to below 1K

He3 Sorption Refrigerator

Dilution Refrigerator

Adiabatic Demagnetization Refrigerator (ADR)

16


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

17

1 atm (1e5 Pa) boiling point: 3.2K Critical point: 3.3 K


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.

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Multistage He3 Sorption

• Cooling Power:

– 60uW at 350mK

– 1.5uW at 270mK19

Simon Chase He4-He3-He3 (He10) fridge - Used for SPT-SZ, SPTpol



• 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



21Betts

Janis Dilution Refrigerator

• Cooling Power: – 10uW at 15mK – 100 uW at 200 mK


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


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)


Thermal Contraction, Screws + Washers, and Thermal Conduction

24


Thermal Contraction

25NIST 2000: http://www.cryogenics.nist.gov/Papers/Cryo_Materials.pdf

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


Thermal Contraction

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• 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


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


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.


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.


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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https://www.amazon.com/Experimental-Techniques-Properties-Superconductor-Critical-Current/dp/0198570546


Extras

32


aàb: isothermal compression

bàc: isobaric cooling

càd: isothermal expansion

dàa: isobaric heating

Gifford-McMahon (GM) cooler: Idealized Cycle

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GM coolers

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• 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


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.

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