Beam-loading stability in synchrotrons with a higher rf harmonic

摘要

This work is an attempt to extend Robinson's stability studies to include a higher rf harmonic. Using an equivalent circuit model, the stability of the ''0-mode'' coherent dipole oscillation of bunched beams is studied for synchrotrons or storage rings, with rf systems operated at the fundamental and a higher harmonic, i.e., a 2nd and 3rd harmonic. Analytical expressions of the stability criteria are derived from the linearized equations. Numerical examples of stability are given for fully nonlinear cases. (ERA citation 17:029069)