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For a
particular particle, the deviation from an idea orbit will
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undergo
“pseudo-harmonic”
oscillation as a
function of the
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path along the
orbit:
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Lateral deviation
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in
one plane
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The
“betatron function” b(s) is
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effectively
the local
wavelength
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and also defines the beam
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envelope.
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Closely spaced strong quads -> small b
-> small
aperture
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Sparsely spaced weak quads -> large b -> large aperture
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b(s) is has the fundamental cell periodicity
of the lattice
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length
of one, e.g., FODO cell
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However,
in general the phase (and therefore particle motion) does not, and indeed
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must not, follow the periodicity of the ring…
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