We present the first x-ray images of electrically exploding wires in air and water, captured at the European X-ray Free-Electron Laser (EuXFEL). These images reveal current shunting in a copper wire during its explosion in air, and the development of electrothermal (and possibly magnetohydrodynamic) instabilities in copper and aluminum wires exploding in water. The experiments were conducted at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography instrument (SPB/SFX) at EuXFEL, where fine metallic wires were driven by a pulsed-power generator with a current rise time of ∼1.1 μs and a peak amplitude of ∼28 kA. EuXFEL enabled MHz x-ray radiography of the wires using 20 keV photons and a narrow bandwidth of ∼40 eV. Using the specific current action integral for a copper wire explosion, we provide the first quantitative estimate of the fraction of current that is shunted through the surrounding medium of an exploding wire. Fourier analysis of the electrothermal instability spectrum shows that its wavelength remains mostly independent of the wire diameter once it has exploded, and that the temperature perturbation is similar in magnitude to the average temperature in the wire.

Interactions of planar Mach 1.4 and Mach 1.5 blast waves in a water--gelatine solution, used as a water surrogate, with millimetre-scale cylindrical air bubbles in the high-Atwood-number limit (A≈-1) are investigated. Using copper-foil explosions to generate blast waves with gigapascal-scale peak overpressures, X-ray phase-contrast imaging, and compressible two-phase simulations, we resolve the sequence of events from incident-wave impact through high-speed jet propagation, water-hammer shock emission, generation of a second upstream pressure peak, and late-time vortex-pair formation. The blast-wave overpressure persists for less than the bubble-collapse timescale, placing the interaction away from the step-like shock limit, where the post-shock overpressure is effectively sustained. Consequently, the blast-driven interaction produces a thinner and slower jet, a substantially weaker water-hammer shock, and remnant lobes that evolve in a lower-pressure surrounding medium than in the corresponding step-like shock case. This separates the relevant wave interactions and remnant-lobe dynamics in space and time, allowing the mechanisms leading to the second upstream pressure peak and subsequent vortex-pair formation to be resolved. In particular, the blast-driven case exhibits delayed formation of the second upstream pressure peak, which exceeds the water-hammer pressure, and a distinct multi-stage vorticity evolution as the remnant lobes evolve into a coherent counter-rotating vortex pair. The measurements provide two-dimensional experimental benchmarks for compressible multiphase-flow solvers in the water--air regime characterized by high Atwood number and large acoustic-impedance mismatch.

A scaling framework unifying the markedly different and independently studied cylindrical and spherical shock convergence is presented. For ionizing argon, we show that the focal temperature becomes invariant to shock symmetry and initial shock conditions when scaled by the prefocus shock Mach number, after accounting for pressure effects. The resulting collapsed focal temperature–Mach number relation is governed by the thermodynamics of argon, up to an equilibrium temperature of 35 000 K. Such a scaling enables both predictive estimation of focal temperatures over a wide range of initial conditions and, conversely, determination of the parameters required to achieve a target temperature in a given medium.

We present x-ray radiographs of underwater electrically driven exploding copper foils of different thickness, captured at the European X-ray Free-Electron Laser (EuXFEL) using 20 keV (∼30 eV bandwidth) self-amplified spontaneous emission photon beams. The foils were exploded by a ∼30 kA amplitude, ∼1.1 μs rise time current pulse produced by a compact pulsed-power generator. The radiographs reveal rapid frontal expansion of foils accompanied by lateral compression. This occurs due to strong magnetic pressure at the foil edges where, due to lateral skin-effect, the temperature reaches ∼1000 K leading to a fivefold decrease in the yield strength. Furthermore, the explosion begins with the foil edges, consistent with enhanced edge heating due to lateral skin-effect. With relatively thick foils, the bulk of the foil material remains in the liquid phase, and initial longitudinal density non-uniformities, coinciding with the current direction, transform into longitudinal striations. For thinner foils which experience explosion into a plasma, spatially non-uniform density structures appear at the edges of the foil and transverse the current direction. These density modulations, which can be estimated by x-ray attenuation, may be associated with the electrothermal instability (ETI); however, the linear theory of ETI growth does not appear to be applicable at the time of observation.

This work investigates the formation of supersonic water jets produced by exploding conical wire arrays and their impact on aluminum targets of different thicknesses. Experiments are performed using the pulsed power driver at beamline ID19 of the European Synchrotron Radiation Facility (ESRF), with the wire arrays driven by a 95 kA electrical discharge with a current rise time of ∼550 ns. Jet formation is diagnosed using multi-frame enhanced phase-contrast x-ray radiography at a pulse repetition rate of 5.68 MHz. Jet velocities in the range of 1450 − 1820 m/s are achieved, and the radiographs suggest a strongly density-depleted, possibly hollow jet core surrounded near its base by denser liquid set into motion during jet formation. For a jet impacting a thick aluminum target, radiographs show a high-density stagnation region at the impact position and radial water splashing caused by redirection of the incoming liquid flow along the target surface, followed by atomization of the spreading liquid. Axisymmetric compressible multiphase Navier–Stokes simulations estimate a peak impact pressure of ∼1.4 GPa, associated with initial water-hammer loading. In separate jet penetration experiments on thin aluminum foils, the material deformation rate decreases with increasing foil thickness, and foil perforation is observed up to a target thickness of 0.3 mm, consistent with analytical estimates based on a shear-failure criterion.

The interaction between cylindrically converging shock waves (SWs) in a water–gelatine solution and a coaxial cylindrical air bubble is studied experimentally and numerically. Two configurations are considered: (i) an azimuthally symmetric, cylindrically converging SW of Mach 1.35 impinging on a coaxial cylindrical bubble, and (ii) a semicylindrical converging SW of Mach 1.45 (corresponding to half of the cylindrical front), interacting with the same target. Shock waves are generated by exploding wire arrays driven by a high-voltage pulsed power system at beamline ID19 of the European Synchrotron Radiation Facility, delivering currents up to 130kA with rise times of 0.35 and 0.55 µs to the cylindrical and semicylindrical wire loads, respectively. X-ray radiography is conducted at a pulse repetition rate of 5.68 MHz using two synchronised high-speed cameras. Numerical hydrodynamic simulations are performed using a compressible multiphase Navier–Stokes solver. A Gilmore-type model for compressible cylindrical bubble pulsation provides an independent analytical estimate of the interface evolution. In the cylindrical SW configuration, the bubble collapse in experiments exhibits Richtmyer–Meshkov instability spikes. The cylindrically converging shock is analysed with Guderley’s solution and Whitham’s approximation using a real-gas equation of state, predicting Mach 14.1 near the focus. In the semicylindrical configuration, momentum focuses into a single supersonic jet with a speed of 885 ± 30 m s−1, producing localised high-pressure regions, coherent vortices and complex internal Mach reflections. Experiments, simulations and theory are consistent in collapse time, interface motion and overall flow dynamics.

Focusing shocks are created underwater by exploding 10- μ 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- μ 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.

Blast waves resulting from underwater electrical wire explosions (UEWEs) are characterized using a high-speed camera and a hydrophone. The UEWEs are created by discharging a 10 µF pulsed power generator that delivers currents up to 170 kA to copper wires on a microsecond timescale, thereby driving their rapid phase transitions from solid to plasma. The trajectory of the resulting cylindrical blast waves is captured by a 5-Mfps high-speed camera, which forms part of a z-type shadowgraphy system. Pressure profiles of the blast waves are measured with a fiber optic hydrophone at 6, 8, and 10 mm away from the exploding copper wires of 150, 400, and 500 µm in thickness. Good agreement is found between these experimental results and simulations, which couple a zero-dimensional (0D) magnetohydrodynamic model for the wire expansion and a one-dimensional (1D) Euler model for the blast wave propagation. The simulations provide experimentally inaccessible insight into the first microseconds of the explosion, including the wire's thermodynamic and electrical properties, and the energy transfer dynamics between the wire and water. This reveals how wire diameter affects the transfer of electrical energy to the blast wave with 150 µm wires leading to underdamped electrical dynamics that generate slower blast waves and lower pressures than 400 and 500 µm wires. Overall, the experiments demonstrate blast pressures up to 500 MPa measured at 6 mm from the 500 µm wire and Mach numbers reaching 1.92 at 3 mm from the explosion center.

Convergence of cylindrical shock in argon is studied both experimentally and numerically. Shock tube experiments are conducted, where a planar shock is first transformed to a cylindrical shape and then converged to its focal axis. Numerical simulations of the converging shock using equations of state for an ideal gas and a real gas (SESAME 5173 model) are conducted and compared. High temporal resolution data of cylindrical shock convergence is presented. When comparing the trajectories of the converging shock of initial shock Mach number (M-S) of 4.63, the convergence exponent (alpha) in experiments is found to be 0.833. This alpha value in experiments is higher than the value obtained from computations with argon treated as an ideal gas but agrees well with the real gas computations. It is revealed that the form of convergence varies with different M-S. An asymptotic approach of alpha toward the self-similar solution for high M-S is attributed to an earlier transition of shock motion to self-similarity, while a significantly higher alpha observed at lower M-S is attributed to the negative influence of upstream nonuniformities and weaker initiation of the shock. It is found that even before the shock reflection, real gas effects are significant enough to affect the convergence of the shock and limit the extreme conditions predicted by the ideal gas computations. For an M-S of 4.63, the maximum temperature reached is 9250 K before reflection, leading to 0.12% of the argon gas undergoing the first stage of ionization.

Two interacting supersonic water jets and collisions of a water jet with an aluminum target are studied experimentally and by hydrodynamic simulations. Supersonic water jets form, when shocks generated by underwater electrical explosions of conical wire arrays converge. The arrays are supplied by a similar to 250kA, similar to 1 mu s rise time current pulse. Underwater explosion of two conical arrays placed face to face produces jets propagating in air with velocities of similar to 2.5 x 10(3) m/s leading to hot plasma formation at a temperature of similar to 2200-3000 K, pressure similar to 1.7 x 10(10) Pa, and density > 10(29) m(-3). When a single array explodes underwater in front of an aluminum target, the collision of the jet with the target produces a local pressure of similar to 3 x 10(10) Pa on the surface of the target.