Optimum Cavity Detuning under Reactive Beam Loading with Accelerated Beams

Compensating reactive beam loading for a beam with long trains and gaps requires excess RF power. To minimize the peak RF power for such a beam in coast, the cavity has to be detuned to half the value corresponding to minimum for a beam without gaps, the so-called 'half-detuning'. Since this simple relation only holds for a beam in coast, we generalize this optimization, now handling also fast accelerated beams as may be found in rapid cycling injectors.