Envelope instability in love-energy proton synchrotrons

In this paper we investigate the limits on beam intensity in low-energy proton synchrotrons due to the instability of the beam envelope . This instability has been previously examined in the context of space charge dominated ion beams, in particular for inertial confinement fusion applications. We generalize the formalism of beam envelope evolution to include effects found in circular accelerators, i .e . curvature focusing and momentum dispersion . Several example lattices are analyzed to determine intensity limits imposed by onset of envelope instability ; it is found that the instability can occur without depressing the phase advance below 90' per cell .