Experiments with Supersonic Beams as a Source of Cold Atoms

temperature and pressure, permits the velocity to be related to the temperature at
any point along the flow. Using the relations cP = γ
γ−1
flow velocity of
w =
2 γ kBTres
γ − 1 m
1 − T
Tres
= γ
2
γ − 1
kBTres
m
kB Pa ,and m Pb =
P
1 −
Pres
Ta
Tb
γ
γ−1
gives a
γ−1
γ
, (2.22)
where Tres and Pres are the temperature and pressure in the reservoir respectively.
Assuming that the gas is expanding into vacuum, where there is negligible pressure,
the maximum flow velocity in a supersonic expansion is
w = 2 γ kBTres
. (2.23)
γ − 1 m
This maximal velocity is slightly greater than the average velocity of a gas molecule
in the reservoir.
2.2 The Supersonic Beam as a Bright General Source of Cold
Atoms and Molecules
While this discussion has illustrated many of the properties of adiabatic ex-
pansion in 1D, the reality is that physical flows are expanding in three dimensions.
Much of the discussion above still holds, however the details of the expansions change.
A detailed discussion of adiabatic expansion in 3D may be found in [8]. Since the sit-
uation in 3D is significantly more complicated, numerical simulations are often used
to model the beam [27]. One change that must be addressed is that as the gas ex-
pands the regime returns to free molecular flow and collisions between gas molecules
cease, to good approximation. A simple, yet useful, model divides the expansion
region in two. Near the nozzle, the gas is assumed to be a continuous medium and
still collisional, while outside of this region, collisions are assumed to no longer take
place. This is known as the sudden freeze model, and the surface of this division is
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