MOZLR10
TRIUMF, Canada's National Laboratory for Particle and Nuclear Physics, Vancouver, Canada
From both simulations and measurements, it is known that at sufficiently high charge per bunch, the bunches in an isochronous cyclotron undergo a vortex effect whose ultimate result is that the bunches reshape into circularly-symmetric distributions in the radial-longitudinal plane. This state cannot exist for arbitrarily high charge since at some point the space charge force will overwhelm the cyclotron's radial magnetic focusing. We apply envelope equation (or ‘‘second moment'') formalism to determine (a) the particle motion frequencies (b) the self-consistent size, or turn width, and (c) the upper limit for the bunch charge for a given size of the bunch. This work is partly a review of work by Sacherer, Kleeven, and Bertrand-Ricaud, and partly a synthesis of those works. Some comparisons are made to published data for the PSI high intensity cyclotrons and new data from the TRIUMF cyclotron.
