The Application of Kiuttu’s Formulation to Study Coaxial Flux Compression Generators

A class of flux compression generators (FCGs) is based on the compression of the cross-sectional area of a coaxial geometry where the current flows along the outer conductor and returns through the inner conductor. This compression causes an increase in current since magnetic flux must be conserved. Kiuttu's inductive electric-field formulation is a powerful tool for the conceptual design of coaxial FCGs. The usefulness of this formulation is demonstrated in this paper for a simplified geometry using a finite-element partial differential equation solver (FlexPDE) for calculation of the inductive electric field. A time-varying applied current or a moving surface creates the nonconservative electric field. Losses due to diffusion of magnetic flux into conducting surfaces can also be accounted for and modeled in this setting. This analytical-computational approach serves as an important step in validating the magnetohydrodynamic (MHD) portion of the complex multiphysics parallel Lawrence Livermore code, Arbitrary Lagrangian-Eulerian (ALE3D). The nonintuitive boundary conditions involved in solving the otherwise straightforward partial differential equations are described in detail and illustrated in a simple model. The physical parameters used in the simulations are not based on a specific design.