Beams Document 2816-v5

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Parametrization of the Driven Betatron Oscillation

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Submitted by:
Ryoichi Miyamoto
Updated by:
Ryoichi Miyamoto
Document Created:
19 Jun 2007, 18:02
Contents Revised:
28 Dec 2007, 14:08
Metadata Revised:
28 Dec 2007, 14:08
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18 Sep 2007, 17:21
25 Jul 2007, 15:44
25 Jul 2007, 15:39
19 Jun 2007, 18:02
An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites
coherent transverse beam motion in a synchrotron. By observing this driven coherent motion, the
linear optical parameters can be directly measured at the beam position monitor locations. The
driven oscillation induced by an AC dipole will generate a phase space ellipse which differs from
that of free oscillations. If not properly accounted for, this difference can lead to a
misinterpretation of the actual optical parameters, typically, 6\% or more in the cases of the
Tevatron, RHIC, or LHC. This paper shows that the effect of an AC dipole on the observed linear
optics is identical to that of a thin lens quadrupole. By introducing a new amplitude function to
describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to
interpret. The introduction of this new amplitude function also helps measurements of the normal
Courant-Snyder parameters based on beam position data taken under the influence of an AC dipole.
This new parameterization of the driven motion is presented and is used to interpret data taken in
the FNAL Tevatron using an AC dipole.
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