Using copper-foil explosions to generate underwater focusing shocks of different geometries

Focusing shocks are created underwater by exploding 10- $\mu$ m-thick copper foils with circular and polygonal geometries. Their symmetry and trajectory are characterized to assess this technique's potential contributions to fundamental and applied investigations of nonlinear wave propagation and high-energy-density phenomena. The foils are exploded using a pulsed power generator which delivers kiloamp currents in microseconds. Current and voltage time traces of the explosions are recorded concurrently with high-speed shadowgraph images of the shocks. The electric waveforms of the explosions of different foil geometries resemble each other, showing peak resistive voltages, currents, and powers around 10 kV, 300 kA, and 2.5 GW, respectively. By extracting the shocks' trajectories through statistical analysis of the shadowgraph images, it is found that circular foils, whether free standing or attached to the inside of a plastic shell, create shocks which accelerate up to Mach 1.7. Comparable Mach numbers are achieved by exploding a circular wire array of 32 100- $\mu$ m-diameter copper wires, indicating that foil designs perform similarly to this traditional design. In contrast, free-standing polygonal foils create shocks which travel at a constant near-sonic speed, seemingly behaving as non-interacting weak planar shocks. This contradicts the theoretically predicted reshaping and acceleration of such shocks; manufacturing imperfections are suspected to cause this unexpected behavior. Alternate designs in which foils are attached to polygonal plastic shells are tested and found to create shocks which do reshape and accelerate.