Current Spreading in Thin Foils or Flat Current Sheets

To consider the evolution of current distribution in inhomogeneous thin conductive layers or foils, we apply an integrodifferential equation, which reduces the three-dimensional problem for the magnetic field to a two-dimensional problem, and, for the current distribution across the width of inhomogeneous conductive sheets or foils, this equation reduces the two-dimensional problem for the magnetic field to a one-dimensional problem. For homogeneous conductive layers with constant conductivity, the spatial scale of current distribution, initially concentrated in a limited area, increases proportionally to time at a rate of u = c2/4πσΔ, where σ is the conductivity of the layer material and Δ is its thickness. As an application to the problems of current transfer through electroexplosive opening switches, a current distribution across the width of a foil is considered for a periodic serpentine-type system of flat foils. It is shown that initially a current distribution corresponding to the perfect conductivity of foils is established in this system. Then, in a time on the order of s/u (2s is the width of a foil), the current distribution in the foil relaxes to a uniform distribution. Estimates show that if the foils are used as opening switches, then currents through the foils during the current transfer to the load are expected to have time to get uniformly distributed across their width; therefore, corrections for the nonuniformity of the current distribution in the switches should be small.