In the theoretical study of a cyclotron, it is possible to make many simplifying approximations and obtain satisfactory results. For example, off-center orbits may be considered as circular in some cases. A method was developed to simulate cyclotron operation by calculating the trajectories of proton motion in cylindrical coordinates. Results of the calculations were then used to determine where simpler calculations may or may not be used. The conclusion is that resonant couplings between axial and radial oscillations should be studied by the calculation of proton trajectories. It is unnecessary to study electric decelerations with this method since circular orbit approximations appear to be sufficient.
Proceedings of the Iowa Academy of Science
©1963 Iowa Academy of Science, Inc.
Moses, Ronald W. Jr.
"Proton Orbits in a Small Cyclotron,"
Proceedings of the Iowa Academy of Science, 70(1), 403-414.
Available at: https://scholarworks.uni.edu/pias/vol70/iss1/67