Phase and radial beam feedbacks in the accelerating system of the U-70 synchrotron

An optimum tuning procedure of the phase and radial beam feedback loops used in the master oscillator of the accelerating system of the U-70 synchrotron at the Institute for High Energy Physics (IHEP) is described. The recent commissioning of the new digital master oscillator provided a means for using feedback gains, varying in the acceleration cycle, in the course of which the transition energy crossing occurs. This notably improved the quality of the accelerated beam handling. The characteristic equation of the closedloop system is obtained. The complex roots that determine the oscillation eigenmodes are analyzed on its basis, and this allowed one to substantiate practical recommendations on selection of parameters. Results of experiments on the accelerated proton beam with energies of 1.3–50.0 GeV are presented.