Cryogenics (Benson)

Cryogenics

Bradford Benson

August 7, 2017 How cold?

Detector Noise BOLOMETERS • Ground-based: 300mK Photon “Shot” • Balloon borne: 100mK Noise SQUIDS To keep • Niobium (Nb) circuitry, NEPbolo < NEPload superconducting at < 9.3 K

from the South LC Boards: Pole, need detector • Aluminum traces (SPT-3G), temperatures superconducting at < 1.2 K < ~300 mK • Nb used for SPT-SZ, SPTpol

Richards 08/07/2017 Benson | Cryogenics 2 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

08/07/2017 Benson | Cryogenics 3 Cooling to 4K

Liquid He

Mechanical Coolers • Stirling Cooler • Gifford-McMahon Cooler • Pulse Tube Cooler

08/07/2017 Benson | Cryogenics 4 Liquid Helium

• Stable temperature • Electrically quiet • Low vibration • Reliable • Low cost for occasional use – ~$10 / Liter ($6000 / 0.5W- mo.) 1 atm boiling point: 4.2 K Critical pont: 5.2K Can pump to get to 1-1.5K http://www.britannica.com/ 08/07/2017 Benson | Cryogenics 5 Liquid Helium: Cons

• 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 08/07/2017 Benson | Cryogenics 6 Mechanical Cooling: Carnot Cycle

• Do “work” on a gas to remove heat from a system in a reversible process: Heat-in • 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 Temperature in state b

Heat-out – W = Work done on the system Qc = Heat taken from the system Entropy –

08/07/2017 Benson | Cryogenics 7 Stirling coolers: Idealized Cycle • Warm compression space separated by a regenerator • Regenerator is high heat capacity, porous material that aàb: isothermal compression supports T gradient, (e.g., lead spheres, copper screens)

bàc: isochoric cooling

càd: isothermal expansion

dàa: isochoric heating

08/07/2017 Benson | Cryogenics 8 Stirling Coolers Stirling Cooler from Janis

• 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 08/07/2017 Benson | Cryogenics 9 Pulse Tube Cooler: OPTC

Orifice Pulse Tube Cooler

08/07/2017 Benson | Cryogenics 10 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

Weisend 2006 08/07/2017 Benson | Cryogenics 11 Pulse Tube: DIPTC

Double Inlet Pulse Tube cooler

• Additional parameter to adjust pressure/ﬂow phase • Regenerator bypass • Creates multiple equilibria • Cryomech PTC’s are DIPTC’s

08/07/2017 Benson | Cryogenics 12 Pulse Tube Coolers

• Relatively new technology (~2002) • No cold moving parts • 40W @ 40K, 1.5W @4k

Cryomech PT405

08/07/2017 Benson | Cryogenics 13 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

08/07/2017 Benson | Cryogenics 14 Regenerators

Volumetric Specific Heats • 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 optimization àComputer 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.

ter Brake 08/07/2017 Benson | Cryogenics 15 Cooling to below 1K

He3 Sorption Refrigerator

Dilution Refrigerator

Adiabatic Demagnetization Refrigerator (ADR)

08/07/2017 Benson | Cryogenics 16 He3

• Relatively expensive ($3K/liter) – Use in closed cycles • Requires pumped He4 bath to condense (critical temp 3.3 K) Base temperature of 1 atm (1e5 Pa) boiling point: 3.2K • Critical point: 3.3 K ~230 mK with pumping

08/07/2017 Benson | Cryogenics 17 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.

08/07/2017 Benson | Cryogenics 18 Multistage He3 Sorption

• Cooling Power: Simon Chase He4-He3-He3 (He10) fridge 60uW at 350mK – - Used for SPT-SZ, SPTpol – 1.5uW at 270mK 08/07/2017 Benson | Cryogenics 19 Dilution Refrigerator

He3-He4 phase diagram • Finite solubility of He3 in He4 – When mixture is cooled < 0.87K, phase separation into He3-rich phase and He3-dilute phase Normal liquid He3, He4 • Remove He3 from solution in Fermi liquid He3 in superfluid He4 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 He3 Concentration change

Lounasmaa (1974) 08/07/2017 Benson | Cryogenics 20 Dilution Refrigerator

Janis Dilution Refrigerator

• Cooling Power: – 10uW at 15mK – 100 uW at 200 mK Betts 08/07/2017 Benson | Cryogenics 21 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.

Betts White 08/07/2017 Benson | Cryogenics 22 ADR: Characteristics

• Salts for ~100mK – FAA on MAXIMA • 100nW @ 100mK • 2.5 T, 6A • Metallic nuclei for <1mK – Cu: down to nK

TOPHAT ADR (PI: Steve Meyer)

08/07/2017 Benson | Cryogenics 23 Thermal Contraction, Screws + Washers, and Thermal Conduction

08/07/2017 Benson | Cryogenics 24 Thermal Contraction

NIST 2000: http://www.cryogenics.nist.gov/Papers/Cryo_Materials.pdf 08/07/2017 Benson | Cryogenics 25 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

08/07/2017 Benson | Cryogenics 26 Thermal Contraction

• 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

08/07/2017 Benson | Cryogenics 27 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

08/07/2017 Benson | Cryogenics 28 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.

08/07/2017 Benson | Cryogenics 29 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.

08/07/2017 Benson | Cryogenics 30 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

08/07/2017 Benson | Cryogenics 31 Extras

08/07/2017 Benson | Cryogenics 32 Gifford-McMahon (GM) cooler: Idealized Cycle

aàb: isothermal compression

bàc: isobaric cooling

càd: isothermal expansion

dàa: isobaric heating 08/07/2017 Benson | Cryogenics 33 GM coolers

Two stage GM • Single or double stage available • Robust, well developed technology • Cons: Vibration from moving regenerator • Widely used: – Cryopumps – DASI • Typical cooling: ARS GM cooler – 50W @ 50K, 1W @ 7K

08/07/2017 Benson | Cryogenics 34 ADR: Materials

• Require – U>kT at high ﬁelds and U

• Spin interactions prevent Bf =0 – Can achieve colder temperatures with nuclear spins.

08/07/2017 Benson | Cryogenics 35