Beam dynamics design studies of a superconducting radioactive ion beam postaccelerator

The HIE-ISOLDE project at CERN proposes a superconducting upgrade to increase the energy range and quality of the radioactive ion beams produced at ISOLDE, which are currently postaccelerated by the normal conducting radioactive ion beam experiment linac. The specification and design choices for the HIE-ISOLDE linac are outlined along with a comprehensive beam dynamics study undertaken to understand and mitigate the sources of beam emittance dilution. The dominant cause of transverse emittance growth was attributed to the coupling between the transverse and longitudinal motions through the phase dependence of the rf defocusing force in the accelerating cavities. A parametric resonance induced by the coupling was observed and its excitation surveyed as a function of transverse phase advance using numerical simulations and analytic models to understand and avoid the regions of transverse beam instability. Other sources of emittance growth were studied and where necessary ameliorated, including the beam steering force in the quarter-wave resonator and the asymmetry of the rf defocusing forces in the solenoid focusing channel. A racetrack shaped beam port aperture was shown to improve the symmetry of the fields in the high-$\ensuremath{\beta}$ quarter-wave resonator and reduce the loss of acceptance under the offset used to compensate the steering force. The methods used to compensate the beam steering are described and an optimization routine written to minimize the steering effect when all cavities of a given family are offset by the same amount, taking into account the different velocity profiles across the range of mass-to-charge states accepted. The assumptions made in the routine were shown to be adequate and the results well correlated with the beam quality simulated in multiparticle beam dynamics simulations. The specification of the design tolerances is outlined based on studies of the sensitivity of the beam to misalignment and errors, with particular emphasis on the phase and amplitude stability required for the independently phased quarter-wave resonators.