Optimization of sector geometry of a compact cyclotron by random search and matrixmethods

We have developed two iterative techniques to optimize the pole profile of the hill of a cyclotron magnet. One of the optimization method is based on random search technique and in another method we have found out the unknown parameters by using the matrix method. In both these methods we have approximated the sector shape by a polynomial function of radius and the coefficients of polynomial are optimized to get the isochronous magnetic field. Compared with the previous shimming scheme, this method gives smooth pole shape of the hill and takes less computation time for optimization. The proposed optimization method has been used to design the magnet of a high current compact cyclotron where valleys are deep and the effect of fringe field is dominant at lower radii; however, it can be used for the low flutter magnet geometry as well. In the random search method we can also give the constraint on the coil current of the magnet.