Asymptotic method for calculation of electromagnetic fields and forces in systems with spatial conductors configurations

An appointed class of 3-dimensional electromagnetic field created by large cross-section curved conductors is considered. It was established that problems formulation in the accompanying coordinate system by using asymptotic method allows considerably simplify the calculations of 3-dimensional electromagnetic fields, electrodynamics forces and energy parameters. The solutions of the problem for an arbitrary spatial contour configuration have been obtained on conditions that the ratio of the typical cross-section dimension to the typical contour dimension is a small parameter. The principal geometrical factors: contour configuration, curvature and generalized twist of axes, as well as shape and size of conductor cross-section are taken into account. It is shown that the general 3-dimensional problem is reduced to more simple 2-dimensional problems for the rectilinear conductor of the same cross-section placed into external field. The intensity of this field is determined by geometry of conductor axis. On the basis of this theoretical approach the effective calculation technique has been developed for investigation and optimization of complicated electromagnetic systems. The magnetic systems with screw conductors with helical and toroidal configurations have been considered. It was obtained the geometry configurations provided that the linear density force is minimal.