Harmonic method for measuring and correcting amplitude functions in the circular accelerator

Abstract

Free oscillations of particles in the ring’s focusing system with a variable gradient are described by the amplitude function (beta function) and the phase function. The gradient perturbation leads to distortions in these functions. Beta-function distortions reduce the ring acceptance, especially if the working point on the betatron frequency is close to the half-integer resonance. A new method for calculating the current in the windings of correcting quadrupole lenses is presented. The idea of this method consists of the excitation of the closed orbit distortions with the dipole magnet. A comparison of the measured values of these orbits in the pickup with calculated values for the ideal gradients presents the opportunity to calculate the resonant harmonics of the beta-function distortions and then adjust them using quadrupole correctors. The algorithm of the method and the preliminary results of applying it to the SIS 100 synchrotron are given.