Experiments and modeling of x-ray radiography of millimeter diameter solid Al wires with laser-produced broadband x rays are reported. Experiments were performed using the 50-TW Leopard short-pulse laser in a laser and pulsed power chamber at the Nevada Terawatt Facility. To characterize broadband x rays and demonstrate a radiographic capability, bremsstrahlung, escaping electrons, and radiograph images of Al wires were simultaneously measured. The angularly resolved x-ray spectra are modeled by comparing measured bremsstrahlung signals in the range between 10 and ∼500 keV with hybrid particle-in-cell simulations. Transmission of Al wires from the radiograph images is further simulated with a Monte Carlo code. The measured transmission profiles of Al wires with three different diameters agree with calculations when a simulated x-ray spectrum composed of line emissions and bremsstrahlung is used with a source size of 600 ± 200 μm. Transmission calculations with only 22 keV Ag Kα or an exponential x-ray spectrum do not reproduce the measurement, suggesting that the accurate determination of an x-ray source spectrum, as well as the inclusion of the photon sensitivity of the detector, is critical in transmission calculations to infer the density of an object. The laser-based broadband x-ray radiography that was developed has been successfully implemented in a pulsed power chamber for future laser-pulsed-power coupled experiments.
Using the analogy between hydrodynamic and electrical current flow, we study how electrical current density j redistributes and amplifies due to two commonly encountered inhomogeneities in metals. First, we consider flow around a spherical resistive inclusion and find significant j amplification, independent of inclusion size. Hence, even μm-scale inclusions can affect performance in applications by creating localized regions of enhanced Joule heating. Next, we investigate j redistribution due to surface roughness, idealized as a sinusoidal perturbation with amplitude A and wavelength λ. Theory predicts that j amplification is determined by the ratio A/λ, so that even “smooth” surface finishes (i.e., small A) can generate significant amplification, if λ is correspondingly small. We compare theory with magnetohydrodynamic simulation to illustrate both the utility and limitations of the steady-state theory.
Inhomogeneities in a current-carrying conductor promote non-uniform heating and expansion through the complex feedback between current density, electrical resistivity, Ohmic heating, temperature, and hydrodynamics. Three-dimensional-magnetohydrodynamic (3D-MHD) simulations suggest that μm-scale resistive inclusions or voids seed local overheating and through hydrodynamic explosion generate continuously growing craters which become several times larger than the initial perturbation. The ejected mass is the genesis of an electrothermally driven plasma filament which develops at lower current than plasmas on uniform surfaces adjacent to the defect. This result suggests that 1D or even 2D treatments are largely inadequate for detailed prediction of plasma formation. To test computational predictions, z-pinch experiments driven to 1 MA studied ultra-high-purity aluminum rods which were then machined to include pairs of quasi-hemispherical voids or “engineered defects (ED)” on the current-carrying surface. ED are the dominant current-density perturbation and reproducibly drive local overheating which can be compared with 3D-MHD simulation. Data from high-resolution-gated imagers of visible surface emissions confirm many simulation predictions, including the surface topography of local overheating, and the propensity for neighboring ED to prematurely source plasmas which then connect to form a plasma filament. Results also provide conditional support of theory which suggests heating similarity; that is, heating is independent of ED size for geometrically scaled ED.
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