Analytical Calculation of the Magnetic Vector Potential of an Axisymmetric Solenoid in the Presence of Iron Parts

This paper presents an analytical calculation method for the computation of the magnetic vector potential of an axisymmetric solenoid in the presence of an iron shield and a ferromagnetic core. The proposed method can be used as a fast analytical computation technique for accelerating the design optimization process of the solenoid systems. In this paper, the analysis of the current carrying coil in the presence of the ferromagnetic materials is treated as a boundary value problem. The solution approach is based on partitioning the solution domain into distinct regions. The general form of the solution to Maxwell's equation in each region along with the corresponding boundary conditions is obtained using the Fourier analysis and the separation of variables. The final solution to the boundary value problem is constituted by considering the continuity of the magnetic vector potential, as well as the magnetic field, on the interfaces between the regions. Finally, the proposed analytical computation method is applied on an electromagnetic actuator. The magnetic vector potential is computed over the entire solution domain, and the result is compared with that of the finite-element method.