Residual pressure can thwart the best cryogenic design
Each gas molecule collision carries ~kT from the “hot” exterior to the cold interior.
1 milliTorr = 3.5x10¹³/cm³
Gas atoms leaving the “hot” surfaces have velocities of order
300 m/s
1 / 2 many collisions/second/gas atom v avg
=

8kT
 m
 at high pressures energy transfer “limited” by short mean free paths

Mean free path
 =
5 cm
P mTorr
Monolayer formation time t =
2.5
× 10 − 3
P mTorr sec

Consider 1 mTorr residual pressure in an instrument with
100 cm² of warm surface area separated from a cold surface by 1 cm.
5 x 10^{15} gas atoms making 10,000 transits between warm and cold each second.
kT = 4 x 10^{-14} ergs/collision
~0.2 Watts of heat loss

Heat loss due to gas conduction can be used to advantage in sensing pressure (at relatively high pressures).

A pump has a capacity to remove a fixed volume per unit time, S, the pump's “speed” in liters/sec.
Gas flow, Q, at the pump inlet is S times the ambient pressure (torr-liters/s)
The pump must draw this volume through a pipe which limits the flow.
In analogy to electronic circuitry, a pipe has a “conductance,” C
¿
A pressure difference (i.e. “voltage”) across the conductance leads to a gas flow, Q =  P * C
Flow through the system is uniform leading to a relationship for net pumping speed in terms of pump
1
S system
=
1
S pump

1
C pipe

Like electrical conductances, series pipe conductances add inversely while parallel conductances add directly.
1
C series
=
1
C
1

1
C
2
 ...
C para
= C
1
 C
2
 ...
Pipe conductance depends on whether the flow is “viscous”
(collision dominated) or “molecular”
(large mean free path).
Conductance improves subtantially with increasing pipe diameter.
C viscous
= 180
D 4
L
P torr liters s − 1
C molecular
= 12
D 3
L liters s − 1
1
S system
=
1
S pump

1
C pipe

Time required to pump out a fixed
“clean” volume no outgassing – only removal of original gasses volume, V start pressure Po, final pressure P pump speed S (liters/s) assumed constant over pressure range, but in practice, S may change as pressure falls t = 2.3
V
S ln
P o
P

The “clean” system is an idealization. Real world systems adsorb gasses from the environment while open and evolve these gasses at low pressures.
For example, stainless steel will outgas 10^{-7} torrliters/s/cm² after one hour at vacuum.
This outgassing rate will drop by a factor of 10 after a day.
Systems can be “baked” to remove adsorbed gasses (if practical).
Aluminum, mylar insulation, copper... are all worse adsorbers.
Keep systems open to atmosphere as little as possible.
Machining oil, fingerprints, adhesives, .... are examples of other nasty outgassing candidates.
Outgassing ceases from components at cryogenic temperature.

Mechanical/compression pumps
Simple example – piston pump
(a bicycle pump in reverse)
Pull air into an expanding volume and force it out through a different port
Rotary vane pumps
An off-center rotating cylinder moves two spring-loaded
“vanes” around a cylindrical volume.
Gas is drawn in on one side and expelled through the other.
Oil seals the pump
Typical speed – 200 l/s

Ideal for rough pumping
Atmospheric pressure down to
about 1mTorr.
Not practical for high vacuum applications partial pressure of oil limits ultimate pressure back-streaming of oil at lowest pressures can contaminate instrument trajectories become ballistic when mean free paths become small a cryogenic “cold trap” will protect against back-flow of oil

Higher vacuums can be achieved by impelling gasses through the system with fan blades.
rotation speeds are of order 50,000 r.p.m. fan blades are nearly supersonic
With a small conventional pump to reduce outlet pressure to < 1 mTorr line pressures of 10¯³ mTorr can be achieved.
The outlet pump is critical. Outlet pressures > 1 mTorr produce a precipitous drop in compression ratio.
compression ratios also depend strongly on gas being pumped –
10^7 for N2 but 10^2 for H2.
These pumps are “oil-free”

Stream of heavy molecules created by heating/boiling an oil
(or mercury) and driving the vapor through downwardly directed pipes.
The flow entrains gas atoms which get compressed and removed (by an auxiliary pump at the outlet).
Will not begin to operate until mean free pathos exceed internal dimension (otherwise thermalizing collisions redirect the flow) requires a good forepump with a cryogenic trap
Losing vacuum on the outlet is
“very bad”

Stream of heavy molecules created by heating/boiling an oil
(or mercury) and driving the vapor through downwardly directed pipes.
The flow entrains gas atoms which get compressed and removed (by an auxiliary pump at the outlet
Will not begin to operate until mean free pathos exceed internal dimension (otherwise thermalizing collisions redirect the flow).
requires a good forepump with a cryogenic trap
Losing vacuum on the outlet is
“very bad”

A few thousand volts are applied across a stainless steel anode and a titanium cathode.
Field emission produces electrons which stream from cathode to anode focused by a magnetic field.
Ambient gas atoms are ionized by electron collision.
– The electric field embeds these gas atoms in the titanium anode.
Titanium atoms sputtered off the anode coat the other surfaces providing additional adsorption of other gasses.
Pumping capacities are a few liters/s. Ultimate pressures are in the microTorr range.
By measuring the anode current, ion pumps are their own vacuum gauges.

Due to lack of gas conduction, thermocouple gauges are insensitive at low pressures.
The precise current measuring capability of an ion gauge permits measurement to substantially lower pressure.
The principle is the same as in the ion pump. In fact, ionization gauges also “pump” by the nature of their operation.

Surfaces have an affinity of gas atoms/molecules
Every material is characterized by a binding energy,thus a Boltzmann factor determines the population of adsorption sites.
Low temperatures = effective adsorption
Some materials, activated charcoal and zeolite for example, have substantial surface area per unit mass and thus have substantial capacity for gas adsorption of order 500 square meters / gram!
In fact, there is a class of “sorption” pump based entirely on this principle, which, when cryogenically cooled, can obtain exceptionally low pressures.
–
–
50 g of zeolite can pump a 1 liter volume from atmospheric pressure to 10 millitor in
20 minutes.
adsorption can maintain an already
“roughed” volume at 0.001 milliTorr.
Zeolite – one of many forms
Zeolite mineralogy

Gas condensation onto cryogenic metallic surfaces will substantially improve dewar vacuum but is condensation onto a detector good???
pump thoroughly before cooling if you care.
Pressure will drop substantially on introduction of cryogens due to
“freezing out” of most gas molecules.
Including sorption “getter” material
(charcoal or zeolite) will maintain a low ambient vacuum while the system is cold.
Getter material must be “recharged” by heating to drive off adsorbed gas
– charcoal is “baked out” at room temperature; zeolite must be heated to about 300C.

O-rings (“low” vacuum) and copper gaskets (“high” vacuum) seal surfaces which must be disassembled and re-assembled.
O-rings are available in stock sizes with precise machining specifications for the grooves depending on application.
Outgassing from o-ring material and o-ring vacuum grease renders them less effective than grease-free all metal UHV seals for the highest vacuum applications.
Parker O-ring Handbook
Making UHV seals

Nobody’s perfect... vacuum systems (sometimes) leak
hairs/scratches on o-ring surfaces cracks in ceramic/glass feedthroughs dysfunctional welds leaky valves and seals incompetence
A “leak-checker” provides a robust means of detecting even small leaks.
Combine a high-quality vacuum pump with a helium mass spectrometer.
Spray helium gas on the outside of the instrument while watching the signal.
Can precisely identify the location of a leak.

A typical astronomical instrument must maintain about one cubic meter at a pressure of <0.1 milliTorr.
The Large Hadron Collider at CERN is 27 kilometers in circumference and contains two beam pipes that must be held <10^{-9} millitorr for months at a time.
The accelerator uses hundreds of superconducting magnets which must be cooled to <4K.
700,000 liters of superfluid liquid helium (superfluid to minimize distribution losses and improve energy transfer).
200 kilometers of cryogenic piping, 40,000 junctions, 1700 cryogenic valves...