Publications

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Plasma formation from intensely ohmically heated conductors is known to be highly non-uniform, as local overheating can be driven by micron-scale imperfections. Detailed understanding of plasma formation is required to predict the performance of magnetically driven physics targets and magnetically-insulated transmission lines (MITLs). Previous LDRD-supported work (projects 178661 and 200269) developed the electrothermal instability (ETI) platform, on the Mykonos facility, to gather high-resolution images of the self-emission from the non-uniform ohmic heating of z-pinch rods. Experiments studying highly inhomogeneous alloyed aluminum captured complex heating topography. To enable detailed comparison with magnetohydrodynamic (MHD) simulation, 99.999% pure aluminum rods in a z-pinch configuration were diamond-turned to ~10nm surface roughness and then further machined to include well-characterized micron-scale "engineered" defects (ED) on the rod's surface (T.J. Awe, et al., Phys. Plasmas 28, 072104 (2021)). In this project, the engineered defect hardware and diagnostic platform were used to study ETI evolution and non-uniform plasma formation from stainless steel targets. The experimental objective was to clearly determine what, if any, role manufacturing, preparation, or alloy differences have in encouraging nonuniform heating and plasma formation from high-current density stainless steel. Data may identify improvements that may be implemented in the fabrication/preparation of electrodes used on the Z machine. Preliminary data shows that difference in manufacturer has no observed effect on ETI evolution, stainless alloy 304L heated more uniformly than alloy 310 at similar current densities, and that stainless steel undergoes the same evolutionary ETI stages as ultra-pure aluminum, with increased emission tied to areas of elevated surface roughness.

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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.

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A direct observation of the stratified electrothermal instability on the surface of thick metal is reported. Aluminum rods coated with 70μm Parylene-N were driven to 1 MA in 100ns, with the metal thicker than the skin depth. The dielectric coating suppressed plasma formation, enabling persistent observation of discrete azimuthally correlated stratified thermal perturbations perpendicular to the current whose wave numbers, k, grew exponentially with rate γ(k)=0.06ns-1-(0.4ns-1μm2rad-2)k2 in ∼1g/cm3, ∼7000K aluminum.

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Ultrafast optical microscopy of metal z-pinch rods pulsed with megaampere current is contributing new data and critical insight into what provides the fundamental seed for the magneto-Rayleigh-Taylor (MRT) instability. A two-frame near infrared/visible intensified-charge-coupled device gated imager with 2-ns temporal resolution and 3-μm spatial resolution captured emissions from the nonuniformly Joule heated surfaces of ultrasmooth aluminum (Al) rods. Nonuniform surface emissions are consistently first observed from discrete, 10-μm scale, subelectronvolt spots. Aluminum 6061 alloy, with micrometer-scale nonmetallic resistive inclusions, forms several times more spots than 99.999% pure Al 5N; 5-10 ns later, azimuthally stretched elliptical spots and distinct strata (40-100μm wide by 10μm tall) are observed on Al 6061, but not on Al 5N. Such overheat strata, which are aligned parallel to the magnetic field, are highly effective seeds for MRT instability growth. These data give credence to the hypothesis that early nonuniform Joule heating, such as the electrothermal instability, may provide the dominant seed for MRT.

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Enhanced implosion stability has been experimentally demonstrated for magnetically accelerated liners that are coated with 70 μm of dielectric. The dielectric tamps liner-mass redistribution from electrothermal instabilities and also buffers coupling of the drive magnetic field to the magneto-Rayleigh-Taylor instability. A dielectric-coated and axially premagnetized beryllium liner was radiographed at a convergence ratio [CR=R_in,0/R_in(z,t)] of 20, which is the highest CR ever directly observed for a strengthless magnetically driven liner. Lastly, the inner-wall radius R_in(z,t) displayed unprecedented uniformity, varying from 95 to 130 μm over the 4.0 mm axial height captured by the radiograph.

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Magnetically driven implosions (MDIs) on the Z Facility assemble high-energy-density plasmas for radiation effects and ICF experiments. MDIs are hampered by the Magneto-Rayleigh-Taylor (MRT) instability, which can grow to large amplitude from a small seed perturbation, limiting achievable stagnation pressures and temperatures. The metallic liners used in Magnetized Liner Inertial Fusion (MagLIF) experiments include astonishingly small (-10 nm RMS) initial surface roughness perturbations; nevertheless, unexpectedly large MRT amplitudes are observed in experiments. An electrothermal instability (ETI) may provide a perturbation which exceeds the initial surface roughness. For a condensed metal resistivity increases with temperature. Locations of higher resistivity undergo increased Ohmic heating, resulting in locally higher temperature, and thus still higher resistivity. Such unstable temperature (and pressure) growth produces density perturbations when the locally overheated metal changes phase, providing the seed perturbation for MRT growth. ETI seeding of MRT on thick conductors carrying current in a skin layer has thus far only been inferred by evaluating MRT amplitude late in the experiment. A direct observation of ETI is vital to ensure our simulation tools are accurately representing the seed of the deleterious MRT instability. In this LDRD project, ETI growth was directly observed on the surface of 1.0-mm-diameter solid Al rods which were pulsed with 1 MA of current in 100 ns. Fine structures resulting from ETI-driven temperature variations were observed directly through high resolution gated optical imaging. Data from two Aluminum alloys (6061 and 5N) and a variety fabrication techniques (conventional machining, single-point diamond turned, electropolished) enable evaluation of which imperfections provide a seed for ETI growth and subsequent plasma initiation. Data is relevant to the early stages of MagLIF liner implosions, when the ETI seed of MRT may be initiated, and provides a fundamentally new dataset with which to test our state-of-the-art simulation tools.

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This paper explores the role of electro-thermal instabilities on the dynamics of magnetically accelerated implosion systems. Electro-thermal instabilities result from non-uniform heating due to temperature dependence in the conductivity of a material. Comparatively little is known about these types of instabilities compared to the well known Magneto-Rayleigh-Taylor (MRT) instability. We present simulations that show electrothermal instabilities form immediately after the surface material of a conductor melts and can act as a significant seed to subsequent MRT instability growth. We also present the results of several experiments performed on Sandia National Laboratories Z accelerator to investigate signatures of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns risetime current pulse. These experiments show excellent agreement with electrothermal instability simulations and exhibit larger instability growth than can be explained by MRT theory alone. © 2012 American Institute of Physics.

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Existing monochromatic X-ray backlighting diagnostics at 1.865 and 6.151 keV have been combined to create a two-color monochromatic X-ray backlighting diagnostic. The use of different photon energies can allow a much broader range of areal densities to be observed in a single experiment. Here, we apply the two-color backlighter to the study of instability growth on the outside edge of an initially solid copper rod target driven by a 100-ns rise-time current pulse with a peak value of 20 MA. The different opacity of Cu at these two photon energies allows a dynamic range of ∼1600x to be surveyed instead of ∼60x (assuming a useful transmission range of 5%-95%). © 2006 IEEE.

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Fast z-pinches provide intense 1-10 keV photon energy radiation sources. Here, we analyze time-, space-, and spectrally-resolved {approx}2 keV K-shell emissions from Al (5% Mg) wire array implosions on Sandia's Z machine pulsed power driver. The stagnating plasma is modeled as three separate radial zones, and collisional-radiative modeling with radiation transport calculations are used to constrain the temperatures and densities in these regions, accounting for K-shell line opacity and Doppler effects. We discuss plasma conditions and dynamics at the onset of stagnation, and compare inferences from the atomic modeling to three-dimensional magneto-hydrodynamic simulations.

This final report for Project 117863 summarizes progress made toward understanding how X-pinch load designs scale to high currents. The X-pinch load geometry was conceived in 1982 as a method to study the formation and properties of bright x-ray spots in z-pinch plasmas. X-pinch plasmas driven by 0.2 MA currents were found to have source sizes of 1 micron, temperatures >1 keV, lifetimes of 10-100 ps, and densities >0.1 times solid density. These conditions are believed to result from the direct magnetic compression of matter. Physical models that capture the behavior of 0.2 MA X pinches predict more extreme parameters at currents >1 MA. This project developed load designs for up to 6 MA on the SATURN facility and attempted to measure the resulting plasma parameters. Source sizes of 5-8 microns were observed in some cases along with evidence for high temperatures (several keV) and short time durations (<500 ps).

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The main physical processes responsible for plasma ablation in multiwire Z pinches are considered via eigensolutions to one-dimensional steady state magnetohydrodynamics. A double scale-length structure of the plasma accelerating layer is demonstrated. The width of the resistive scale-length that defines the current layer structure is significantly larger than the thermal scale-length, where transport of energy toward the cores and plasma pressure play important roles. The transport of energy is provided mainly by radiation, though electron thermal conduction is also important very close to the plasma-core interface. Another type of solution of the steady state problem is revealed, when local Ohmic heating is important down to the interface. Selection between these two types of solutions is considered from multiple points of view. Although the one-dimensional problem is mainly considered in this paper, it is shown how the one-dimensional results may help to understand results of two-dimensional models.

This paper presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pi-mode, in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by two vastly different numerical codes which were used to simulate arrays with both high wire numbers (up to 600) and low wire number (8). All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires' radial motion may imply substantial lack of wire currents. While the present theory and simulations have ignored the plasma corona and axial variations, it is argued that their effects, and the complete account of the three-dimensional feature of the pi-mode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedge with a reflection condition imposed on the wedge's boundary. © 2007 American Institute of Physics.

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Over the last several years, rapid progress has been made evaluating the double-z-pinch indirect-drive, inertial confinement fusion (ICF) high-yield target concept (Hammer et al 1999 Phys. Plasmas 6 2129). We have demonstrated efficient coupling of radiation from two wire-array-driven primary hohlraums to a secondary hohlraum that is large enough to drive a high yield ICF capsule. The secondary hohlraum is irradiated from two sides by z-pinches to produce low odd-mode radiation asymmetry. This double-pinch source is driven from a single electrical power feed (Cuneo et al 2002 Phys. Rev. Lett. 88 215004) on the 20 MA Z accelerator. The double z-pinch has imploded ICF capsules with even-mode radiation symmetry of 3.1 {+-} 1.4% and to high capsule radial convergence ratios of 14-21 (Bennett et al 2002 Phys. Rev. Lett. 89 245002; Bennett et al 2003 Phys. Plasmas 10 3717; Vesey et al 2003 Phys. Plasmas 10 1854). Advances in wire-array physics at 20 MA are improving our understanding of z-pinch power scaling with increasing drive current. Techniques for shaping the z-pinch radiation pulse necessary for low adiabat capsule compression have also been demonstrated.

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We present the first comprehensive study of high wire-number, wire-array Z-pinch dynamics at 14-18 MA using x-ray backlighting and optical shadowgraphy diagnostics. The cylindrical arrays retain slowly expanding, dense wire cores at the initial position up to 60% of the total implosion time. Azimuthally correlated instabilities at the array edge appear during this stage which continue to grow in amplitude and wavelength after the start of bulk motion, resulting in measurable trailing mass that does not arrive on axis before peak x-ray emission.

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