Analytical description of stripping foil extraction from isochronous cyclotrons

Analytical expressions are derived describing beam parameters on a stripping foil (SF) as a function of radial amplitude of betatron oscillations and of energy gain. The results computed from these expressions are in good agreement with those from numerical calculations. These results indicate the existence of a parametric relationship between radial emittance and energy spread, via the amplitude of radial betatron oscillations. This relationship enables one to generate the working diagram of expected beam parameters on a SF. Such a diagram can be particularly useful for designers of extraction systems, since it gives the relationship between quantities used as extraction system input parameters. The derived analytical expressions can make the design of cyclotrons easier and significantly reduce the need of numerical simulations.