Coupling effects at the [formula omitted] resonance in a three-sector superconducting cyclotron

Abstract

The fourth-order resonance ν z = 3 4 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 Z 4 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.