Cyclotron Matching Injection Optics Optimization∗

Injection from an external ion source into a cyclotron results in unavoidable emittance growth when the cyclotron’s first turn radius is small compared with the pole gap. In such a congested geometry, the injected beam first has the two transverse directions coupled on entering the axial magnetic field of the cyclotron, then transverse and longitudinal phase spaces are coupled by the inflector. Generally, to avoid loss, the beam is focused tightly through the inflector. It thus arrives at the first turn strongly mismatched because the vertical focusing in such a cyclotron is rather weak (vertical tune < 0.3). Space charge exacerbates the mismatch because it depresses the vertical tune further. Emittance growth from all these effects can be calculated using the full Sacherer 6D envelope formalism commonly used in transport lines. We develop the technique to include cyclotrons and in particular the transverse optics of the rf gaps, and apply it to the re-design of the TRIUMF 300 keV vertical injection line.