Recent Advances in Modeling Helical FCGS

Helical explosively driven magnetic flux compression generators (FCGs) have been intensively investigated for more than four decades, because of their ability to amplify electrical current and magnetic energy with high gain and relatively small size. Whereas coaxial-geometry FCGs have lent themselves to reasonably accurate modeling, helical FCGs have always been considered "anomalously lossy," with calculated performance invariably exceeding observed performance - often by factors of two or more in peak output current. With the advent of the analytically derived Kiuttu contact resistance model (KCRM), it has become possible to approximately account for the losses in the vicinity of the contact point between armature and stator without resorting to any empirical tuning factors. Such factors have generally been required by other modeling and simulation codes to achieve agreement with experimental data. Since its introduction, the KCRM has been extended to include the region immediately in front of the contact point as well, thus improving its accuracy. Another key element in modeling the performance of helical FCGs is proper accounting of the proximity effect between adjacent turns of the solenoidal stator winding. This effect alters the magnetic field and current density distributions from their isolated, approximately locally uniform distributions, leading to an effective increase in flux diffusion rates. In order to quantitatively assess this effect, we have run a number of two- dimensional quasi-magnetostatic simulations for varying stator geometries and extracted simplified approximations that can be used in one-dimensional diffusion calculations. We have also examined the details of the circuit model definition (i.e., flux-based from Faraday\´s Law, or the diffusion equation, and energy-based from Poynting\´s Theorem). The generator equation, derived from the circuit model, involves lumped-element approximations for resistance and inductance, and we have shown t- hat the combination of inductance and resistance, which yields experimental current and time derivative of current, is not unique, and that each lumped element must be consistently defined. We have incorporated these various models and effects into the CAGEN (1&1/2-D) modeling code. As a result, we have been able to accurately calculate the performance of a wide variety of FCGs without using any additional adjustment factors. Representative results, as well as descriptions of the models, will be presented.