The electrothermal instability (ETI) is a Joule-heating-driven instability that promotes runaway temperature in conductors driven to high current density, altering the 3D evolution of the expansion and phase state of the metal. Most metals include complex distributions of imperfections (voids, resistive inclusions) which seed ETI. To simplify comparison with modeling and theory, experiments examined growth of ETI from relatively void/inclusion free, 99.999% pure, diamond-turned, 1.00 mm-diameter aluminum rods. Surfaces included a variety of deliberately machined and well-characterized perturbations, including 10-micron-scale quasi-hemispherical voids, or “engineered” defects (ED), and sinusoidal patterns of varying wavelength and amplitude. Such perturbations were studied in isolation and colocation to evaluate which defect type drove more rapid heating. First, the emission evolution of axially vs. azimuthally oriented ED pairs of identical size and spacing was studied; individual defects initially evolve independent of pair orientation, but at higher current density, pair orientation dictates global plasma evolution. Next, heating similarity, the hypothesis that heating is independent of ED size, was evaluated in experiments with scaled 12, 24, and 48-micron diameter ED. Data from 12 and 24-micron ED demonstrate similarity, exhibiting brightest emission regions above and below the ED, which later source plasma filaments. Surprisingly, the evolution of 48-micron diameter ED is qualitatively different, with brightest emissions forming on both sides of the ED and plasma filaments sourced from the divot center. This may be consistent with similar temperature evolution driving identical expansion velocity, with the ejected material therefore traversing a smaller extent of the larger defects. Next, epoxy coatings were added to select loads to evaluate the effect of hydrodynamic tamping. Reduced expansion of the metal delays surface plasma formation, thus elongating the stage where the azimuthally correlated version of ETI is expected to grow. Indeed, strata formation between azimuthally separated ED is dominant for dielectric coated surfaces. Finally, 24-micron diameter ED have been machined into sinusoidally-perturbed surfaces of varying amplitudes (0.191 – 3.05 microns) and wavelengths (24-48 microns). Maximum theoretical current density amplification (j/j₀) for the sinusoids ranges from 1.05 to 1.5, while the maximum ED-driven j/j₀ is 1.5. ED alter the periodic heating of sinusoidal emissions more than 100 microns from the divot center. Experimental data and comparisons with 3D simulation will be discussed.

Increased interest in z-pinch rotation resulted from the recent observations of such rotation appearing spontaneously in z pinches with the imposed Bz field.¹ It motivated our theoretical and numerical stability analysis of supersonic implosions of rotating magnetized z-pinches. The conservation of angular momentum density ρΩr in the imploding plasma flow will naturally create dΩ/dr <0, which is a condition for magnetorotational instability (MRI). This instability is well known in astrophysics,² particularly as a major cause of turbulent transport in astrophysical Keplerian disks. Our two-dimensional simulations using Athena code demonstrated that in the imploding rotating z-pinch plasmas, in addition to classical Magneto-Rayleigh-Taylor instability, there is also MRI. We use our exact Mag Noh shocked rotating solutions³ as a convenient vehicle for studying MRI in the imploding plasma flow and apply various perturbations to study the instabilities numerically, including following them to the nonlinear regime. The nonlinear development of instabilities results in turbulence, enhanced mixing, and other transport.

(Supported by the DOE/NNSA)

References

¹M. Cvejić, M. et. al., Phys. Rev. Lett. 128, 015001 (2022).

²S. A. Balbus and J. F. Hawley, Ap. J. 376, 214 (1991).

³A. Beresnyak et. al., J. Fluid Mech. 936, A35 (2021).