Surface current density distribution measurements of an electrically exploded foil via B-dot probe array data inversion

Measurements are presented of the current per unit length as a function of the transverse distance from the center of a water-tamped 80 μm Al foil that narrows to a central width of 15.2 cm as it explodes into warm dense matter by Ohmic heating. Current is delivered from a 36 μF capacitor bank charged to 30 kV and discharged to a peak current of 342 kA in 2.0 μs. The distribution is calculated by the linear regularized inversion of signals from an array of B-dot probes distributed long the foil's central half-width. The probes are far enough away from the foil (1 cm) to be noninvasive and mechanically undisturbed during the time of interest. These results are compared to 3-D MHD ALEGRA simulations of the geometry externally coupled to a two-loop lumped circuit model representing the driver. Surface current density is strongly peaked at the foil edges for low-current calibration tests, where conductivity is essentially constant. It's broadly peaked in the center at peak current for the full energy shot, though, due to the foil fusing first at the edges, which subsequently reduces current density there relative to the center by the time of peak current. There is broad agreement in this regard between the experiment and ALEGRA using thermal and electrical conductivity model SNL Sesame 293731. ALEGRA calculates that current peaks 0.5 μs earlier, though, and with 50 kA higher current. This may be due to error in the conductivity tables or effects not well-modeled, such as an electro-thermal instability that results in higher total resistance, but with a distance scale too small for the present simulation to represent. This work is a revision of that presented at IPPC 2015.