Particle dynamics in storage rings with barrier rf systems

The stability of particle motion in a barrier rf system is studied. Parametric resonance strength functions for the barrier rf system with rf phase and voltage modulations are derived. We find that higher order parametric resonances of the barrier rf system are important. Tolerance of the rf phase modulational errors in the barrier rf system in the Fermilab Recycler, a cooling storage ring to recycle unused antiprotons from the Tevatron and to store newly produced cooled antiprotons, is analyzed. A constraint on the rate of bunch compression utilizing the barrier rf system is derived. copyright 1997 The American Physical Society