The Numerical Calculation of the Three Dimensional Electrical Field in the Central Region of a Cyclotron

To provide detailed and accurate electric fields in the ion source-puller region and at the dee dummydee gap for a cyclotron, a relaxation method solution of Laplace's equation has been used. A conventional difference equation with variation in mesh size and relaxation factor as well as different schemes for boundary corrections have been developed to achieve roughly 1 percent accuracy for a three-dimensional domain with 106 mesh points. Although the computation requires considerable computer time, it is much less expensive than electrolytic tank analogue methods for measuring field distributions around complex electrode configurations.