Particle dynamics inside a quasi-isochronous storage ring

Quasi-isochronous alpha-like bucket can be important in providing ultra short bunches. The instability of a bunch inside the bucket is found to be severely affected by rf phase modulation. The synchrotron tune drops to zero at the bucket edge very rapidly, indicating the possibility of a thick chaotic layer due to overlapping of resonance islands. The approach to chaos comes from a sequence of bifurcation into 2:1 parametric resonances. When quantum excitation is included in addition to radiation damping, the instability is worsened. The steady-state particle distribution in the longitudinal phase space is Gaussian in the phase coordinate and non-Gaussian in the momentum coordinate, unless the bunch is small. The size of the bunch is governed only by the ''thermal Energy'' E-th = D-2/2A, where D and A are, respectively, the normalized diffusion and damping coefficients. The quantum lifetime of the particle bunch, for the D and ii that have been enhanced by the smallness of the phase-slip factor, is studied and turns out to be much longer than expected. Phase modulation tends to enhance quantum diffusion at high frequencies, but leads to stochastic resonances instead at low frequencies.