Abstract
It is shown that the sixth-order 6σ=720° (or 6∶2) resonance is manifested for high-intensity beams of linear accelerators through the space charge potential when the depressed phase advance per cell σ is close to and below 120° but no resonance effect is observed for σ above 120°. Simulation studies show a clear emittance growth by this resonance and a characteristic sixfold resonance structure in phase space. To verify that this is a resonance, a frequency analysis was conducted and a study was performed of crossing the resonance from above and from below the resonance. Canonical perturbation is carried out to show that this resonance arises through perturbation of strong 2σ=360° (2∶1) and 4σ=360° (4∶1) space charge resonances. Simulations also show that the space charge 6σ=360° (or 6∶1) resonance is very weak.
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