Experiments with Supersonic Beams as a Source of Cold Atoms

As the pressure in the gas reservoir is increased, the mean free path decreases
accordingly. When the pressure is high enough, the mean free path will decrease to
the point that d>λ. When this condition is met, the gas enters the continuum regime
near the nozzle and can be treated as a compressible fluid. The principle advantages
of this regime are the greatly decreased temperature of the atoms in the beam, and
increased brightness due to higher reservoir pressures, larger nozzle diameter, and
increased directionality of the beam.
2.1.1 Steady State Gas Flow in 1D
To examine what can be expected in the d>λregime, it is instructive to
examine the flow of an ideal gas through passages with changing cross-sectional area
(this is presented in detail in [8–10] and the discussion here follows the presentation
in [8]). To do this effectively, some of the basic thermodynamic properties of ideal
gases are needed. To start with, the ideal gas law (equation 2.1) can be expressed as
P = ρkBT
m
, (2.4)
where ρ is the density of the gas. Letting eint be the internal energy of the gas per unit
mass, the heat transfered to an unchanging quantity of an ideal gas, dq, at constant
pressure is
and the enthalpy per unit mass is
dq =deint + P d
1
, (2.5)
ρ
h = eint + P
ρ = eint + kBT
. (2.6)
m
Using equation 2.5 and equation 2.6, along with the fact that the internal energy of
an ideal gas depends only on the temperature, produces
dq =dh− 1
dP. (2.7)
ρ
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