Vacuum Systems Why much of physics sucks. Winter 2011 UCSD: Physics 121; 2011 2 Why Vacuum? Anything...

Vacuum SystemsVacuum Systems

Why much of physics sucksWhy much of physics sucks

Winter 2011

UCSD: Physics 121; 2011

2

Why Vacuum?Why Vacuum?

• Anything cryogenic (or just very cold) needs to get rid Anything cryogenic (or just very cold) needs to get rid of the airof the air– eliminate thermal convection; avoid liquefying air

• Atomic physics experiments must get rid of Atomic physics experiments must get rid of confounding air particlesconfounding air particles– eliminate collisions

• Sensitive torsion balance experiments must not be Sensitive torsion balance experiments must not be subject to airsubject to air– buffeting, viscous drag, etc. are problems

• Surface/materials physics must operate in pure Surface/materials physics must operate in pure environmentenvironment– e.g., control deposition of atomic species one layer at a time

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Measures of pressureMeasures of pressure

• The “proper” unit of measure for pressure is Pascals The “proper” unit of measure for pressure is Pascals (Pa), or N·m(Pa), or N·m-2-2

• Most vacuum systems use Torr insteadMost vacuum systems use Torr instead– based on mm of Hg

• Atmospheric pressure is:Atmospheric pressure is:– 760 Torr– 101325 Pa– 1013 mbar– 14.7 psi

• So 1 Torr is 133 Pa, 1.33 mbar; So 1 Torr is 133 Pa, 1.33 mbar; roughlyroughly one milli- one milli-atmosphereatmosphere

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Properties of a vacuumProperties of a vacuum

VacuumVacuum PressurePressure

(torr)(torr)

Number Number Density (mDensity (m-3-3))

M.F.P. M.F.P. (m)(m)

Surface Collision Surface Collision Freq. (mFreq. (m-2-2·s·s-1-1))

Monolayer Monolayer Formation Formation Time (s)Time (s)

AtmosphereAtmosphere 760760 2.72.710102525 77101088 3310102727 3.33.31010-9-9

RoughRough 101033 3.53.510101919 0.050.05 4410102121 2.52.51010-3-3

HighHigh 101066 3.53.510101616 5050 4410101818 2.52.5

Very highVery high 101099 3.53.510101313 5050101033 4410101515 2.52.5101033

UltrahighUltrahigh 10101212 3.53.510101010 5050101066 4410101212 2.52.5101066

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Kinetic TheoryKinetic Theory

• The particles of gas are moving randomly, each with The particles of gas are moving randomly, each with a unique velocity, but following the Maxwell a unique velocity, but following the Maxwell Boltzmann distribution:Boltzmann distribution:

• The average speed is:The average speed is:

• With the molecular weight of air around 29 g/mole With the molecular weight of air around 29 g/mole (~75% N(~75% N22 @ 28; ~25% O @ 28; ~25% O22 @ 32), 293 @ 32), 293 K:K:– m = 291.6710-27 kg– <v> = 461 m/s– note same ballpark as speed of sound (345 m/s)

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Mean Free PathMean Free Path

• The mean free path is the typical distance traveled The mean free path is the typical distance traveled before colliding with another air moleculebefore colliding with another air molecule

• Treat molecules as spheres with radius, Treat molecules as spheres with radius, rr• If (the center of) another molecule comes within 2If (the center of) another molecule comes within 2rr of of

the path of a select molecule:the path of a select molecule:• Each molecule sweeps out cylinder of volume:Each molecule sweeps out cylinder of volume:

V = 4r2vt– in time t at velocity v

• If the volume density of air molecules is If the volume density of air molecules is nn (e.g., m (e.g., m33):):– the number of collisions in time t is

notZ = 4nr2vt

• Correcting for relative molecular speeds, and Correcting for relative molecular speeds, and expressing as collisions per unit time, we have:expressing as collisions per unit time, we have:

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Mean Free Path, cont.Mean Free Path, cont.

• Now that we have the collision frequency, Now that we have the collision frequency, ZZ, we can , we can get the average distance between collisions as:get the average distance between collisions as: = v/Z

• So thatSo that

• For air molecules, For air molecules, rr 1.75 1.751010-10-10 m m• So So 6.8 6.8101088 m = 68 nm at atmospheric pressure m = 68 nm at atmospheric pressure• Note that mean free path is inversely proportional to Note that mean free path is inversely proportional to

the number density, which is itself proportional to the number density, which is itself proportional to pressurepressure

• So we can make a rule for So we can make a rule for = (5 cm)/(P in mtorr) = (5 cm)/(P in mtorr)

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Relevance of Mean Free PathRelevance of Mean Free Path

• Mean free path is related to thermal conduction of airMean free path is related to thermal conduction of air– if the mean free path is shorter than distance from hot to

cold surface, there is a collisional (conductive) heat path between the two

• Once the mean free path is comparable to the size of Once the mean free path is comparable to the size of the vessel, the paths are ballisticthe vessel, the paths are ballistic– collisions cease to be important

• Though not related in a 1:1 way, one also cares Though not related in a 1:1 way, one also cares about transition from bulk behavior to molecular about transition from bulk behavior to molecular behaviorbehavior– above 100 mTorr (about 0.00013 atm), air is still collisionally

dominated (viscous) is about 0.5 mm at this point

– below 100 mTorr, gas is molecular, and flow is statistical rather than viscous (bulk air no longer pushes on bulk air)

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Gas Flow RatesGas Flow Rates

• At some aperture (say pump port on vessel), the flow At some aperture (say pump port on vessel), the flow rate israte is

S = dV/dt (liters per second)

• A pump is rated at a flow rate:A pump is rated at a flow rate:Sp = dV/dt at pump inlet

• The mass rate through the aperture is just:The mass rate through the aperture is just:Q = PS (Torr liter per second)

• And finally, the ability of a tube or network to conduct And finally, the ability of a tube or network to conduct gas isgas is

C (in liters per second)

• such thatsuch thatQ = (P1 P2)C

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Evacuation RateEvacuation Rate

• What you care about is evacuation rate of vesselWhat you care about is evacuation rate of vessel• SS = = QQ//PP11

• but pump has but pump has SSpp = = QQ//PP22

• QQ is constant (conservation of mass) is constant (conservation of mass)• QQ = ( = (PP11 PP22))CC, from which you can get:, from which you can get:

1/S = 1/Sp + 1/C

• So the net flow looks like the “parallel” combination of So the net flow looks like the “parallel” combination of the pump and the tube:the pump and the tube:– the more restrictive will dominate

• Usually, the tube Usually, the tube isis the restriction the restriction– example in book has 100 l/s pump connected to tube 2.5 cm

in diameter, 10 cm long, resulting in flow of 16 l/s– pump capacity diminished by factor of 6!

P1

P2

Q

Q

Q

C

pump: Sp

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Tube ConductanceTube Conductance

• For air at 293 K:For air at 293 K:• In bulk behavior (> 100 mTorr):In bulk behavior (> 100 mTorr):

C = 180PD4/L (liters per second)– D, the diameter, and L, the length are in cm; P in Torr– note the strong dependence on diameter!– example: 1 m long tube 5 cm in diameter at 1 Torr:

• allows 1125 liters per second

• In molecular behavior (< 100 mTorr):In molecular behavior (< 100 mTorr):C = 12D3/L

– now cube of D– same example, at 1 mTorr:

• allows 0.1 liters per second (much reduced!)

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Pump-down timePump-down time

• Longer than you wishLonger than you wish– Viscous air removed quickly, then long slow process to

remove rest

– to go from pressure P0 to P, takes t = (V/S)ln(P0/P)

– note logarithmic performance

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Mechanical PumpsMechanical Pumps

• Form of “positive Form of “positive displacement pump”displacement pump”

• For “roughing,” or getting the For “roughing,” or getting the the bulk of the air out, one the bulk of the air out, one uses mechanical pumpsuses mechanical pumps– usually rotary oil-sealed

pumps

– these give out at ~ 1–10 mTorr

• A blade sweeps along the A blade sweeps along the walls of a cylinder, pushing walls of a cylinder, pushing air from the inlet to the air from the inlet to the exhaustexhaust

• Oil forms the seal between Oil forms the seal between blade and wallblade and wall

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Lobe Injection PumpsLobe Injection Pumps

• Can move air very rapidlyCan move air very rapidly• Often no oil sealOften no oil seal• Compression ratio not as Compression ratio not as

goodgood

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Turbomolecular pumpsTurbomolecular pumps

• After roughing, one often goes After roughing, one often goes to a turbo-pumpto a turbo-pump– a fast (24,000 RPM) blade

achieves a speed comparable to the molecular speed

– molecules are mechanically deflected downward

• Work only in molecular regimeWork only in molecular regime– use after roughing pump is

spent (< 100 mTorr)

• Usually keep roughing pump on Usually keep roughing pump on exhaustexhaust

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CryopumpingCryopumping

• A cold surface condenses volatiles (water, oil, etc.) A cold surface condenses volatiles (water, oil, etc.) and even air particles if sufficient nooks and crannies and even air particles if sufficient nooks and crannies existexist– a dessicant, or getter, traps particles of gas in cold

molecular-sized “caves”

• Put the getter in the coldest spotPut the getter in the coldest spot– helps guarantee this is where particles trap: don’t want

condensation on critical parts– when cryogen added, getter gets cold first

• Essentially “pumps” remaining gas, and even Essentially “pumps” remaining gas, and even continued outgassingcontinued outgassing

• Called cryo-pumpingCalled cryo-pumping

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Ion PumpIon Pump

• Ionize gas molecules, deposit ions on Ionize gas molecules, deposit ions on chemically active surface, removed by chemically active surface, removed by chemisorptionchemisorption

• Best use is for Ultra-High Vacuum Best use is for Ultra-High Vacuum applications (10applications (10-11-11 Torr) Torr)

• Current is proportional to pressure (pump is Current is proportional to pressure (pump is also a pressure gauge)also a pressure gauge)

• No moving parts, but efficient only at very No moving parts, but efficient only at very low pressureslow pressures

slide courtesy O. Shpyrko

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Residual Gas Analyzer Residual Gas Analyzer (mass spectrometer)(mass spectrometer)

• Electronic “nose”, sniffing inside the Electronic “nose”, sniffing inside the chamberchamber

• Can detect partial pressure down to Can detect partial pressure down to 1010-14-14 Torr Torr

• Useful as a He leak-detectorUseful as a He leak-detector• Measures mass-to-charge ratio by Measures mass-to-charge ratio by

ionizing a molecule and accelerating it ionizing a molecule and accelerating it in EM fieldin EM field


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Example of RGA spectra, He:Ne mixture 10:1Example of RGA spectra, He:Ne mixture 10:1


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Typical problems in achieving UHV:Typical problems in achieving UHV:

• Actual Leaks (valves, windows)Actual Leaks (valves, windows)• Slow pump-down times Slow pump-down times • ““Virtual” leaksVirtual” leaks• Outgassing – bulk and surfacesOutgassing – bulk and surfaces

Solutions:Solutions:• Leak-testingLeak-testing• Re-design of vacuum chamberRe-design of vacuum chamber• Bake-outBake-out• CryopumpingCryopumping


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DewarsDewars

• Evacuating the region Evacuating the region between the cold/hot wall between the cold/hot wall and the ambient wall and the ambient wall eliminates convection and eliminates convection and direct air conductiondirect air conduction

• Some conduction over the Some conduction over the lip, through materiallip, through material– minimized by making thin

and out of thermally non-conductive material

• Radiation is left, but Radiation is left, but suppressed by making all suppressed by making all surfaces low emissivity surfaces low emissivity (shiny)(shiny)

• Heat paths cut Heat paths cut holds holds temperature of fluidtemperature of fluid

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Liquid Nitrogen DewarLiquid Nitrogen Dewar

• Many Dewars are passively cooled via liquid nitrogen, at 77 KMany Dewars are passively cooled via liquid nitrogen, at 77 K

• A bath of LNA bath of LN22 is in good thermal contact with the “inner shield” of is in good thermal contact with the “inner shield” of

the dewarthe dewar• The connection to the outer shield, or pressure vessel, is The connection to the outer shield, or pressure vessel, is

thermally weak (though mechanically strong)thermally weak (though mechanically strong)– G-10 fiberglass is good for this purpose

• Ordinary radiative coupling of Ordinary radiative coupling of ((TThh44 TTcc

44) = 415 W/m) = 415 W/m22 is cut to a is cut to a

few W/mfew W/m22

– Gold plating or aluminized mylar are often good choices

– bare aluminum has 0.04

– gold is maybe 0.01

– aluminized mylar wrapped in many layered sheets is common (MLI: multi-layer insulation)

– MLI wants to be punctured so-as not to make gas traps: makes for slooooow pumping

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Dewar ConstructionDewar Construction

• Cryogen is isolated from Cryogen is isolated from warm metal via G-10warm metal via G-10– but in good thermal contact

with inner shield

• Metal joints weldedMetal joints welded• Inner shield gold-coated or Inner shield gold-coated or

wrapped in MLI to cut wrapped in MLI to cut radiationradiation

• Windows have holes cut into Windows have holes cut into shields, with vacuum-tight shields, with vacuum-tight clear window attached to clear window attached to outsideoutside

• Can put another, nested, Can put another, nested, inner-inner shield hosting inner-inner shield hosting liquid helium stageliquid helium stage

vacuumport

cryogenport

pressure vessel/outer shield

inner shield

cryogen (LN2)tank

perforated G-10cylinder

science apparatus

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Cryogen LifetimeCryogen Lifetime

• Note that LNNote that LN22 in a bucket in a room doesn’t go “poof” in a bucket in a room doesn’t go “poof”

into gasinto gas– holds itself at 77 K: does not creep to 77.1K and all

evaporate– due to finite “heat of vaporization”

• LN2 is 5.57 kJ/mole, 0.81 g/mL, 28 g/mol 161 J/mL

• L4He is 0.0829 kJ/mol, 0.125 g/mL, 4 g/mol 2.6 J/mL

• H2O is 40.65 kJ/mol, 1.0 g/mL, 18 g/mol 2260 J/mL

• If you can cut the thermal load on the inner shield to If you can cut the thermal load on the inner shield to 10 W, one liter of cryogen would last10 W, one liter of cryogen would last– 16,000 s 4.5 hours for LN2

– 260 s 4 minutes for LHe

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Nested ShieldsNested Shields

• LHe is expensive, thus the need for nested shieldingLHe is expensive, thus the need for nested shielding• Radiative load onto He stage much reduced if Radiative load onto He stage much reduced if

surrounded by 77 K instead of 293 Ksurrounded by 77 K instead of 293 K (2934 44) = 418 W/m2 (774 44) = 2.0 W/m2

– so over 200 times less load for same emissivity– instead of a liter lasting 4 minutes, now it’s 15 hours!

– based on 10 W load for same configuration at LN2

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Coolest place on earth:Coolest place on earth:

• Antarctica -89 °C, or 183KAntarctica -89 °C, or 183K• San Diego: Dilution fridges San Diego: Dilution fridges

Mayer Hall (Maple, Goodkind), NSB (Butov) ~300 mKMayer Hall (Maple, Goodkind), NSB (Butov) ~300 mK• Cambridge, MA: Sub-500 picoKelvin achieved in Cambridge, MA: Sub-500 picoKelvin achieved in

Ketterle group at MITKetterle group at MIT

See “See “Cooling Bose-Einstein Condensates Below 500 Picokelvin”Cooling Bose-Einstein Condensates Below 500 Picokelvin”

ScienceScience 301, 5639 pp. 1513 - 1515 (2003) 301, 5639 pp. 1513 - 1515 (2003)


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Adiabatic Magnetization CoolingAdiabatic Magnetization Cooling


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Photos: Displex Cryostat insertPhotos: Displex Cryostat insert


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Photos: Ultra High Vacuum chamberPhotos: Ultra High Vacuum chamber


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Photos: Turbomolecular “Turbo” PumpPhotos: Turbomolecular “Turbo” Pump


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Photos: Dilution RefrigeratorPhotos: Dilution Refrigerator


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Photos: Dilution RefrigeratorPhotos: Dilution Refrigerator


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Helium Flow CryostatHelium Flow Cryostat


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AssignmentsAssignments

• Read 3.1, 3.2, 3.3.2, 3.3.4, 3.4: 3.4.1 (Oil-sealed and Read 3.1, 3.2, 3.3.2, 3.3.4, 3.4: 3.4.1 (Oil-sealed and Turbomolecular, 3.4.3 (Getter and Cryo), 3.5.2 (O-Turbomolecular, 3.4.3 (Getter and Cryo), 3.5.2 (O-ring joints), 3.6.3, 3.6.5ring joints), 3.6.3, 3.6.5– applies to both 3rd and 4th editions

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Vacuum Systems Why much of physics sucks. Winter 2011 UCSD: Physics 121; 2011 2 Why Vacuum? Anything...

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