Effects of tune modulation on particles trapped in one-dimensional resonance islands

The response of particles trapped in one-dimensional resonance islands to betatron tune modulation resembles, yet is not equivalent to, that of a parametric resonant system. Experimental data obtained at Indiana University Cyclotron Facility for the fourth-order resonance islands have confirmed this characteristic feature. The beam, driven by betatron tune modulation, was observed to travel from near the center of resonance islands toward the separatrix. The experimental data are characterized by the onset of a large response at a critical modulation amplitude and frequency, which are compared with theoretical models. Possible future experiments are suggested.