Nonlinear Effects of Focusing Bars Used in the Extraction Systems of Superconducting Cyclotrons

Sets of rectangular iron bars are used in combination with electostatic deflectors to focus and bend the beam along its path out of the cyclotron field. Since the design of this system was based on conventional orbit computations that include only linear vertical motion, additional studies have been undertaken to evaluate the nonlinear effects on the phase space of the extracted beam. These studies are carried out with a special orbit code that uses exact equations of motion, and treats the main cyclotron field correctly to fourth order in z. In addition, the rectangular focusing bars are assumed to be uniformly magnetized so that the resultant field can be calculated exactly on and off the median plane using simple formulas. Some preliminary results from this orbit code are presented here that show how the final radial and vertical phase space properties depend on the initial emittance values, and how they are changed by possible small displacements of the focusing bars.