Studies of specific action integral and electro-thermal instabilities in the sub-microsecond underwater electrical explosions of shaped foils

We present the results of two studies: (1) on the specific action integral h and (2) on the electrothermal instability (ETI) during underwater electrical explosions of different material foils. Values of h were studied in experiments with the explosion of tapered (“butterfly”) foil geometries using current pulses with an amplitude of ∼300 kA and ∼400 ns rise time using the MAGEN [Kovalchuk et al., Rev. Sci. Instrum. 80, 083504 (2009)] generator at Technion. Shadow images of foils, together with strong shock waves generated in the surrounding water by their explosion and results of COMSOL [Asmedianov et al., J. Appl. Phys. 136, 133303 (2024)] numerical simulations, were used to determine the values of h. These values were found to be significantly smaller than those stated in earlier research of wire explosions in vacuum. ETI was studied with butterfly and rectangular shaped foils explosion using pulsed driver generating current pulses with an amplitude of ∼120 kA and ∼450 ns rise time and multi-frame x-ray radiography at the European Synchrotron Radiation Facility . In the case of the butterfly, x-ray radiography showed the ETI instability initially appeared at the “waist,” where later explosion starts. In the case of the rectangular foil, it was found that the ETI perturbations have a minimum wavelength and a broad spectrum of larger wavelengths.