| A magnetic flux expansion--flux compression duality is proposed as the basic method of approach of electromechanical hypervelocity macroparticle accelerators and their electromechanical power supplies.;This duality as the method of approach is justified by the highly transient nature and rapidly changing electromagnetic structure of such devices, being an actualization of the motor--generator duality from the classical theory of electrical machinery. The characteristics of flux compression--flux expansion are shown to match reciprocally in an almost ideal manner.;For the demanding analysis and design of flux compression structures, a three-dimensional finite element method based on Galerkin technique formulation for solving parabolic differential equation with partial derivatives and, in particular, electromagnetic field diffusion is presented.;One of the original features of the formulation is the introduction of superficial currents with linear current density, ;The superficial currents are introduced in formulation as Lagrange multipliers, solenoidality of the three vectors, ;The unfolding in time of the phenomena occurring in a three-dimensional flux compression structure is illustrated by three-dimensional plots of magnetic flux density and current density.;Finally, an analytical approach of finding electromagnetic forces in magnetic flux compression--expansion converters by using the method of flux derivative is presented.;In the treatment of the magnetic flux compression--expansion in the numerical methods used in conjunction with superficial currents constraining the magnetic flux as Lagrange multipliers and, finally, in passing from generalized forces to the body forces acting locally in each element of the flux compressor, the ideal constancy of the magnetic flux was a continuous theme of this work. |
