Space-charge-dominated bunched beams in the frequency domain

The effect of space charge on high-phase-space-density bunched beams in an ion storage ring with electron cooling is investigated in the frequency domain for bunches in the vicinity of the local microwave instability threshold. Space charge causes a splitting of synchrotron satellites into incoherent and coherent lines. Results of measurements of the splitting and shift are compared with analytical formulas as well as with simulation of the noise spectra by multiparticle computer simulation. Coherent frequencies of the quadrupole and sextupole modes of Gaussian bunches are found to deviate slightly from the analytical mode frequencies. Consequences for the interaction with narrow-band impedances and on the possible accuracy of Delta p/p momentum-spread measurements for high-phase-space-density bunches are briefly discussed.