Coupling resonance correction and avoidance for the TRIUMF 500 MeV cyclotron

The linear coupling resonance v(r) - v(z) = 1 in a cyclotron is driven by the first harmonic in the radial gradient of the radial magnetic field. In the TRIUMF 500 MeV cyclotron, this resonance is encountered multiple times. When the circulating beam is off-centred radially passing through the resonance, the radial betatron oscillation can be converted into vertical oscillation, which can cause beam losses and radio-activation. We investigated this resonance with goal to correct it by using the available harmonic correction coils. Moreover, we improved the cyclotron vertical tune measurement by using trim coils to create a flat-top radial field, and thus confirmed an extra v(r) - v(z) = 1 coupling resonance passage as this is unexpected from the historical tune diagram. To avoid this passage, the local vertical tune is adjusted to stay farther away from the resonance line by using the trim coils axial field, but at the cost of a local excursion in isochronism. After the correction and the avoidance of this resonance, both the coherent and incoherent vertical oscillations are decreased, thus helping to reduce the machine tank spills under high intensity operation. In this paper, we present the results of calculations and simulations as well as measurements that we undertook.