Theoretical and experimental beam studies for the Michigan state university cyclotron

Abstract

Numerical orbit studies using Michigan State University cyclotron fields have been performed to determine the validity of use of the separated longitudinal equations of motion under conditions obtained in actual cyclotron operation. These results have been applied in a systematic study of phase measurement procedures using frequency and trim coil detuning. Direct experimental measurements were performed to determine the phase and phase width of the beam, as well as the betatron oscillation frequencies v r and v z , as a function of radius. From the phase history data the radial dependence of the rf dee voltage has been obtained, and the nominal initial phase ϕ 0 has been determined to be +20° ± 1° for the MSU central region geometry. Use of necessary computer calculations with this result gives an rf starting time τ 0 of −28° ± 1° for maximum beam intensity. Results of experimental measurements are compared with pre-computed orbit behavior where possible.