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

Microwave instability implies that the coupling impedance is largest at several times the RF frequency and that the decay of the wakefield is fast enough that bunches do not affect each other. This high frequency, low Q impedance is represented by a single resonance at 1.7 GHz. The parameters used are influenced by the Fermilab Main Ring and design of the Main Injector. The numerical modeling uses standard features of the code ESME. Microwave instability may be an intensity limitation during parts of the acceleration cycle where the beam is debunched or loosely bunched, perhaps at injection or high duty factor extraction. Probably of more general importance is the time near transition when the spread in circulation frequency is sharply reduced. Concrete examples are given.<>