Crossing The Phase Transition In Strong Focusing Proton synchrotrons

Two effects are observed when a intensity bunch crosses the phase transition: bunch-length oscillations are excited, and there is also a sudden increase of the longitudinal emittance. These effects may for some accelerators be an intensity limitation as important as the transverse space-charge limit at injection. The bunch-length oscillations are caused by longitudinal space-charge forces and their nature is well understood. The emittance increase is less well understood, the most important mechanism is probably a negative-mass instability which develops right after transition, but also other mechanisms play a certain role. Various cures exist to counteract these mechanisms; the most successful one is the so-called gamma /sub transition/-jump, where the transition energy is rapidly reduced by pulsing a suitable set of quadrupoles. The various mechanisms and cures are first discussed in qualitative terms, then the theory is developed, and the state of today's knowledge is discussed. (63 refs).