Correction of dispersion and the betatron functions in the CEBAF accelerator

During commissioning of the CEBAF accelerator, correcting dispersion, momentum compaction and betatron beam envelopes was essential for robust operation. To speed up the diagnostic process we developed a method which allows one to track and correct the machine optics on-line. The method is based on measuring the propagation of 30 Hz modulated betatron oscillations. Compared to the usual methods of dispersion or difference orbit measurement, synchronous detection of the beam displacement, as measured by beam position monitors, offers significantly improved speed and accuracy. The beam optics of the accelerator was altered to decrease lattice sensitivity at critical points and to simplify control of the betatron function match. The calculation of the Courant–Snyder invariant from signals of each pair of beam position monitors was used for a correction of the betatron functions.