Experiments with Supersonic Beams as a Source of Cold Atoms

the coil can instead be switched before it arrives at this position. This is illustrated
in figure 4.6(b). In this case, the particles that are ahead of the synchronous atom in
the bunch are slowed more, and thus will be pushed back towards the center of the
bunch. Similarly, particles which are behind the center of the bunch are slowed less
than the synchronous particle and catch up. This creates a region of phase stability,
where the bunch remains in phase with the coil pulses for the entire coil sequence.
This also reduces the necessary accuracy of the timing sequence for the coil pulses,
as slight deviations in coil timing are sel-correcting. A slight error in coil timing may
mean that the bunch is slowed slightly more(less) than predicted by a particular coil,
but because the bunch was slowed more(less), the next coil in the coilgun slows it
less(more) because the bunch is farther(closer) from(to) the peak field when the coil
is switched. This makes the coilgun quite robust against small timing errors.
A brief comment on notation is useful at this point. When producing the
timing sequence, the numerical simulation of the synchronous atom switches each coil
at a pre-defined position in that coil. This position can also be referred to as a phase
angle using the following conversion. The midpoint between two coils is considered
to be a phase angle of 0 ◦ and switching when the synchronous atom or molecule is in
the center of a coil is labeled 90 ◦ , with intermediate positions linearly converted to
an angle. This convention comes from previous work with particle accelerators, and
the concept of phase stability is similar to that found in colliders [76, 77], and the
pulsed electric field decelerator [15, 78]. The concept of phase stability in the coilgun
is discussed in [21, 25, 69–71].
4.3.2 Electromagnetic Coils as a Waveguide
While the longitudinal stability of the slowed bunch of particles is addressed
in the previous section, the transverse behavior of particles in the coilgun also has a
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