Abstract
This paper describes a method for design of a phase-locked radio frequency (rf) control system to accelerate bunched beams in synchronism with rf. A set of transfer functions of an ion synchrotron system for suppressing phase oscillation Δφ and radial displacement ΔR of the bunched beams are derived by the use of classical control theory. The mathematical models of the beam dynamics are the same as Schnell employed previously (W. Schnell: CERN68-27, 1968) as the standpoint of the equivalent resonant circuits for the rf phase-locked beam control systems.
From the above transfer functions, the types of Δφ and ΔR controls can be determined. A simple method to obtain their control parameters is also presented. The results of simulations show the usefulness of our design technique.
