Linear coupling and tune adjustment for the 500 MeV cyclotron

The horizontal and vertical betatron tunes vary during acceleration in TRIUMF 500 MeV cyclotron, leading the beam to cross the linear coupling resonance nu(r) - nu(z) = 1 multiple times. This results in a measurable transfer of betatron amplitude between the horizontal and the vertical planes. In this paper, we report the observation of an unanticipated crossing of this resonance which cannot be understood from the tune diagram derived from the original magnetic field survey of the cyclotron. We present how we have resolved this conundrum and the technique we have developed to measure the vertical tune, which is particularly challenging in a cyclotron. To correct the deleterious effects of this particular crossing, rather than canceling the resonance driving term, a new strategy was adopted whereby the vertical tune is adjusted locally and pushed away from the resonance line. This is accomplished using the axial field of trim coils, while also maintaining the overall isochronism of the machine.