Topology Optimization of the Pole Shape in Passive Magnetic Channel Using MMA Method

Passive magnetic channel is a kind of beam focusing elements in a cyclotron. It consists of several soft iron bars that are magnetized by the main field in a cyclotron. In this paper, we proposed a topology optimization method to design the pole shape in passive magnetic channel, this method does not require any fixed geometry pattern or initial design. The nonlinear static magnetic finite-element analysis model is used to calculate the objective magnetic field function. Persuade iron material with variable density is used to describe the iron distribution during the iteration. Method of Moving Asymptotes (MMA) is used to optimize the control variable of iron density distribution on magnetic channel cross-section. In three numerical examples, magnetic channels for a 250 MeV superconducting cyclotron is provided, where the design goal is to provide the given magnetic field gradient and bending angle. The relationship between the design goal and the pole shape pattern is discussed. It reveals that magnetic channel pattern with only 2 iron bars is possible for some design goals.