Parametrization of the Driven Betatron Oscillation

TL;DR

This paper introduces a new parameterization for driven betatron oscillations caused by an AC dipole, enabling more accurate interpretation of beam optics measurements in synchrotrons.

Contribution

It presents a novel amplitude function to describe AC dipole-induced phase space ellipses, improving the accuracy of optical parameter measurements.

Findings

New amplitude function effectively describes driven oscillations.

Application to Tevatron data demonstrates improved measurement accuracy.

Reduces misinterpretation of optical parameters caused by AC dipole effects.

Abstract

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 coherent motion, the 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 the free oscillation. If not properly accounted for, this difference can lead to a misinterpretation of the actual optical parameters, for instance, of 6% or more in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the linear optics parameters 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. Beam position data taken under the influence of an AC dipole, with this new interpretation in mind, can lead to more precise measurements of the normal Courant-Snyder parameters. This new parameterization of the driven motion is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.