Calculation of axisymmetric current systems using the model of an axially magnetized cylinder

A method for calculating the inductive and power parameters of complex coaxial axisymmetric current systems based on a cylinder model is proposed. The method is based on the equivalence of the energies of coils and equal-sized cylinders with equal densities of their surface currents. The inductances, mutual inductances and ponderomotive forces in the coil system are calculated from the mutual energy and 3D fields of the cylinders. It is shown that the volume-average demagnetizing factor of a cylinder is equivalent to the Nagaoka coefficient for the inductance of coils of finite length. From the analysis of the correlation between the energy densities of the cylinder and the demagnetization energy, the criterion of a “short coil” is determined. The correspondence of the results obtained by the cylinder model to the calculations by current models is established. A method for calculating interlayer mechanical stresses, mutual radial and axial forces and stresses in a system of coaxial coils (cylinders) is presented. An example of using a cylinder model for calculating the inductance of a rectangular coil is given.