Modelling and design of permanent magnet multipoles for beam transport and focusing. I. Selection of optimal design and parameters

The design and specification choices are described for a PM quadrupole used to enable beam transport in a cyclotron. First an analytic study with a simplified 2D model is performed to give initial values for magnet configuration and performance. Characteristics of PM blocks and cylinders are analysed. Then a 3D parametrized model is used to solve the direct magnetostatic problem and accurately define quad specifications. Simulations are carried out with KOMPOT electromagnetic code utilizing the differential formulation. The regularization method is applied to solve the inverse problem. Magnetic characteristics, dimensions and shapes of the PM units and iron parts are determined in order to reach the specified field gradient. Possible correction of the resulting the ideal specification is discussed with respect to additional constraints put by practical implementation. Candidate PM materials are proposed. Simulated field maps are presented. The method described may serve as a basis for virtual prototyping and be integrated into end-to-end design and construction of magnet systems.