Experiments with Supersonic Beams as a Source of Cold Atoms

The method chosen for measuring the field is the Faraday effect. Some materi-
als (called Faraday rotators) rotate the plane of polarization of light when a magnetic
field in the direction of propagation of the light is present. The angle of rotation
of linearly polarized light passing through a Faraday rotator in the presence of a
magnetic field in the propagation direction is
ψ =
z2
z1
vB(z)dz, (4.31)
where v is the Verdet constant of the material, B is the field in the direction of
propagation, and x1 and x2 are the coordinates of material boundaries. For a constant
field this simplifies to
ψ = vBd, (4.32)
where d is the length of the Faraday rotator. Importantly, since this is an optical
process, the effect takes place on time scale much shorter than the coil switching
time, and has even been resolved in the femtosecond domain [85]. The Faraday
rotator used to measure the field in the coilgun coils is a terbium gallium garnet
(TGG) crystal, which has a Verdet constant at room temperature of −134 rad/T/m
for 633 nm wavelength light, where the sign indicates the direction of rotation. For a
negative Verdet constant, the rotation will be in the direction opposite the direction
of current in a coil around the crystal creating a magnetic field. This is independent
of the direction of propagation of the light.
A schematic drawing of the Faraday rotation measurement setup is shown in
figure 4.25. Polarized light from a Helium-Neon laser passes through a polarizing
beamsplitter cube, which sets the polarization angle of the light. This angle can
be further adjusted using a λ/2 plate, which is the next element in the setup. The
light is then focused by an 83 mm focal length lens down to a waist of 40 μm inthe
center of the coil. The TGG crystal is inserted into the bore of the coil, and care is
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