Space-Charge Forces in Strong-Focusing Synchrotrons

Abstract

A new principle, strong focusing, has recently been put forward as the basis for the design of synchrotrons, particularly proton synchrotrons in the energy range above about 10 Bev. In this new proposal the field gradient index, $n$, is alternatively positive and negative and has a numerical value of some thousands as opposed to conventional, weak-focusing synchrotrons and betatrons, where $0<n<\mathrm{}1\mathrm{}$. The object of this note is to examine the effect of space-charge forces in strong-focusing synchrotrons on the stability of the radial and axial motion of the particles being accelerated.