Experiments with Supersonic Beams as a Source of Cold Atoms

The same effect is also responsible for the creation of eddy currents in materials near
a coil. These currents must be accounted for when computing the time dependence
of the magnetic fields.
The switching of a coil can also be examined by looking at the voltage and
current in the coil as a function of time. The problem can be simplified by approxi-
mating the coil as an ideal resistor in series with an ideal inductor. The voltage across
this circuit is
V = IR + L dI
, (4.26)
dt
where L is the inductance of the coil and R is the resistance of the coil. For instan-
taneously switched drive voltages, the current when switching the coil on is
I(t) = V
R
1 − e −tR
L
and similarly the current when switching the coil off is
, (4.27)
I(t) = V −tR
e L . (4.28)
R
To achieve fast switching times, it is desirable to have either high resistance, or low
inductance. Because high currents are also needed to produce large magnetic fields,
high resistance is unfavorable, and thus low inductance is an important aspect of the
coil design. Similarly, greater applied voltages can produce larger dI , both for turn
dt
on and for turn off, but this requires the electronics driving the coil to be capable of
withstanding these large voltages.
4.3 Principle of Operation
As described in section 4.1, the energy levels of atoms or molecules with a
non-zero magnetic moment undergo a shift in a magnetic field. This energy level
shift results in a change in the potential energy of the atom or molecule. As an
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