Synchrotron beam-loading stability 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 ''O-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 or 3rd harmonic. Analytical expressions of the stability criteria are derived from the linearized circuit equations. Numerical solutions of the fully nonlinear equations are provided to compare with the analytical results. Simple feedback model for stabilization is discussed.