Abstract
An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam oscillations in a synchrotron. By observing this driven coherent oscillation, the linear optical parameters can be directly measured at locations of the beam position monitors. The driven oscillations 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 misinterpretations of the actual optical parameters, for instance, 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 parametrization of driven oscillations is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.
Highlights
Transverse motion of charged particles is stabilized with linear forces of quadrupole magnets and, as a result, the particles undergo oscillations around the ideal trajectory, called betatron oscillations [1]
If quadrupole magnets in an accelerator have errors, the function and betatron phase advance become different from their design values and performance of the accelerator can be degraded
Under the influence of a sinusoidally oscillating magnetic field of an AC dipole, the beam is driven by two driving terms
Summary
Transverse motion of charged particles is stabilized with linear forces of quadrupole magnets and, as a result, the particles undergo oscillations around the ideal trajectory, called betatron oscillations [1]. To observe the betatron oscillations and measure parameters such as the function or the betatron phase advance, coherent oscillations must be excited (Fig. 1). If the amplitude of its oscillating magnetic field is adiabatically ramped up and down, it can produce large coherent oscillations without decoherence or emittance growth [3] This property makes it a useful diagnostic tool of a synchrotron. Lesser driving term makes driven oscillations different from the free oscillations This difference has typically been ignored in previous analyses [5,12], it could affect interpretation of the function more than 12% in a typical operational condition of the Tevatron.
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