Optimal design of magnetic systems

Abstract

The methods and the algorithms of the magnetic system design, producing the fields with a required distribution (the inverse problem of magnetostatics), are considered. The mathematical statement of the problem is reduced to the expansion of a given function into Fourier series on a non-orthonormal basis. The basis functions are the fields of the sections of a magnetic system, and the coefficients of the expansion are the components of the magnetization vector of the sections (the vector synthesis). The algorithms proposed to solve the problem take into account the physical constraints on the magnetization distribution of the assembly sections. The application of the vector synthesis guarantees the maximum possible efficiency of magnet utilization in an assembly. The combination of the vector synthesis and the geometrical one, at which the distribution of the magnetization of the assembly sections is fixed, but the optimal basis is selected, ensures the minimization of the mass of the magnets used. The algorithms suggested for solving the synthesis problem are also effective in the presence of a ferromagnetic armature in the system. The examples of syntheses of the magnetic systems, producing the plane–parallel and the axisymmetric fields under the constraints on the magnetization distribution, are given.