A potential vector field solution in superconducting magnets, part I: Method of calculation

An analytical method is presented for calculating values and distribution of the magnetic field in superconducting dc magnets composed of cylindrical or saddle type coils in cylindrical symmetry. The method takes into account the actual length and finite thickness of the coils as well the presence of radial and axial ferromagnetic yokes. The magnetic field is determined by carrying on an expansion of the current density distribution of the coils with Fourier series: for each term of the expansion, the corresponding components of the flux density are obtained by means of the calculation of the magnetic potential vector. The resultant magnetic field is determined by applying the principle of superposition of the effects by summing up the harmonic fields; as the magnet contains ferromagnetic materials, one or more suitable constant values of permeability for such materials must be chosen.