Experiments with Supersonic Beams as a Source of Cold Atoms

Magnetic field (T)
1.8
1.75
1.7
1.65
1.6
1.55
1.5
1.45
1.4
1.35
−4 −3 −2 −1 0 1 2 3 4
x 10 −3
1.3
Radial position (m)
(a)
Magnetic field (T)
0.7
0.65
0.6
0.55
0.5
0.45
−4 −3 −2 −1 0 1 2 3 4
x 10 −3
0.4
Radial position (m)
Figure 4.7: This figure illustrates the manner in which the magnitude of the magnetic
field varies with radial position in a 1.05 cm diameter coil. The field at the center of
the coil (z = 0) is plotted in (a). The magnitude of the field is at a radial minimum
on the axis of the coil at this axial position, which provides a focusing force to lowfield-seeking
particles. The field, as a function of radial position well outside of the
coil is plotted in (b). Here, the radial dependence of the field magnitude is at a
maximum on the axis of the coil, providing a de-focusing effect for low-field-seekers.
The interplay between the focusing effects inside the coil and the de-focusing outside
the coil is complex, and depends on the velocity of the particles passing though the
coil, as well as the switch-off timing.
large effect on the number of slowed atoms or molecules. Maxwell’s equations dictate
that there can be no free space maximum in magnetic field. Though the magnitude
of the magnetic field on the axis of a coil (z-axis) is at a maximum at center of the
coil, this cannot be a true local maximum. Instead, this point at the center of a coil
is a saddle point, and is at a minimum of the field radially. The magnitude of the
field of a coil as a function of radial position at z = 0 is plotted in figure 4.7(a). The
fact that the field is at a minimum on axis here means that low-field-seeking atoms
feel a force pushing them towards the axis of the coil, producing a focusing effect on
the beam of particles. This allows the coilgun to act as a waveguide, and can provide
a degree of transverse stability to the slowed bunch of atoms in the coilgun.
(b)
Though the magnitude of the field is radially minimal on axis at the center
of the coil, this is not true at all locations. Examining the radial dependence of
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