Fourth order resonance of a high intensity linear accelerator*

For a high intensity beam, the 4/nu=1 resonance of a linear accelerator is manifested through the octupolar term of space charge potential when the depressed phase advance /sigma is close to and below 90 but no resonance effect is observed when /sigma just above 90. To verify that this is a resonance, a frequency analysis is performed and a study of resonance crossing from above and from below the resonance is conducted. It is observed that this fourth order resonance is dominating over the better known envelope instability and practically replacing it. Simulation study shows a clear emittance growth by this resonance and its stopband. One of the authors [DJ] proposed an experiment to measure the stopband of this resonance to GSI using the UNILAC.