No abstract

Synchrotron motion with rf phase modulation was studied experimentally. Poincarb maps in the resonant precessing frame were obtained from the experimental data and compared with the tori of the resonant Hamiltonian. Our experimental data revealed island structure in longitudinal phase space. Experimental results for synchrotron motion excited by phase modulation at the third harmonic of the synchrotron frequency are also reported. '

No abstract

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.

We investigate effects of quantum fluctuation, potential well distortion, quantum lifetime, and Touschek lifetime of the quasi-isochronous ͑QI͒ dynamical system. The Fokker-Planck equation is employed to study the equilibrium bunch distribution. The quantum lifetime in the moderate damping regime is compared with analytical formulae. The effects of harmonic radio-frequency phase modulation on equilibrium distribution function, quantum lifetime reduction, and the occurrence of stochastic resonance are studied. The formula for the Touschek lifetime for the QI dynamical system is derived and studied.