Abstract
We study the dynamics of transverse oscillations near the linear coupling resonance excited by a pair of skew quadrupoles at the Laborat\'orio Nacional de Luz S\'{\i}ncrotron UVX electron storage ring through the analysis of the beam profile. Transverse coherent oscillations were excited with a fast kicker and the profile of the oscillating beam was observed by focusing visible synchrotron radiation from a bending magnet onto a fast charge-coupled device camera. Using a single resonance approximation, we calculated the border of the time-averaged transverse beam profile as a function of the complex coupling coefficient $\ensuremath{\kappa}$, which characterizes the distribution of coupling fields along the storage ring. A least-squares fit of the calculated beam profile border to the experimentally obtained isointensity contours provided a new method to determine both the modulus and the phase of $\ensuremath{\kappa}$. The values obtained for the modulus are in good agreement with those from the conventional normal mode tune separation technique, and the values obtained for the phase of $\ensuremath{\kappa}$ agree with calculations based on the model lattice and the known skew quadrupole distribution.
Highlights
Coupling between the horizontal and vertical motion is widely recognized as an important performance limitation in storage rings used as synchrotron radiation sources or as colliders
Linear coupling may be caused by tilted quadrupoles, vertical closed orbit deviations in sextupoles, and solenoidal fields in detectors, whereas nonlinear coupling may be produced by interaction with the electric fields of ions trapped in the electron beam [3] as well as by space charge or beam-beam forces [4]
Close to a resonant condition, the dynamics of linear coupling can be described by a single complex parameter: the coupling coefficient k
Summary
Coupling between the horizontal and vertical motion (betatron coupling) is widely recognized as an important performance limitation in storage rings used as synchrotron radiation sources or as colliders. Coupling produces betatron tune shifts and vertical dispersion, reduces the dynamic aperture [1], and increases the vertical emittance (with a corresponding decrease in light source brilliance or collider luminosity [2]). Other techniques to measure coupling usually involve transversely exciting the beam and observing the resulting coherent oscillations. Observations of coherent oscillations on a turn-by-turn basis at two different locations in the storage ring have allowed the experimental determination of both the modulus and the phase of k from a Hamiltonian description of the coupled dynamics [8,9,10]
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