Realistic modeling of microwave instability effects on the evolution of the beam energy-phase distribution in proton synchrotrons

Some situations in which microwave instability can set the effective limit to accelerator performance have been examined by particle tracking simulation. The emphasis has been on the practicability of testing alternative parameters by numerical experiment for processes with multiple time scales which would not be tractable analytically. It is not possible to exhibit here the evolution of the instability to lend intuitive support for the interpretations offered nor to make thorough comparison with analytic results. Little space has been devoted either to fundamental questions of dynamics or details or numerical method. The modeling approach may have practical benefit if it leads designers to evaluate the overall growth of emittance in a process instead of considering only the instability threshold