Coupling effects at the νz = 34 resonance in a three-sector superconducting cyclotron

The fourth-order resonance νz = 34 often occurs in the pre-extraction region of three-sector superconducting cyclotrons, and acceleration through this resonance can deform the vertical (and radial) phase space of the beam. The phase-space properties near the resonance have been explored using an improved version of the Z4 Orbit Code and magnetic field data from the K1200 superconducting cyclotron at this laboratory. The orbit code results have been compared with those obtained from a standard theoretical analysis based on an expansion of the Hamiltonian. This comparison shows that relatively good agreement can be obtained if and only if certain third-order coupling effects are included in the theory. These effects are associated with particular coupling resonances that are not very far from the operating point.