Comparison of energy spreads induced by a longitudinal wakefield in a cavity

It is pointed out that the energy spread of a beam bunch induced in a linear accelerator can be reduced to a minimum if the amplitude and the phase of the RF voltage are optimized. The energy spread is induced by the longitudinal wakefield and by the sinusoidal profile of the accelerating voltage acting on the beam. The cavity shape, the bunch profile, and the charge in the bunch determine the wake function. In order to have an approximately constant net voltage acting across the beam bunch, the amplitude and the phase of the RF voltage are optimized. The minimum energy spread, the required RF voltage, and the required RF phase are calculated as a function of the net charge and the length of the bunch. To determine the effect of cavity shape on the minimum energy spread, the optimization was performed for several types of cavities. The optimization shows that the energy spread can be reduced by a factor of 3 for the Energy Recovery Experiment (ERX)-type cavity and the Modular Component Technology Development (MCTD)-type cavity by adjusting the amplitude and the phase of the RF voltage. This is done by increasing RF voltage and phase. However, the ERX-type cavity is superior because it requires a third of the voltage of the MCTD to attain the same energy spread.<
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