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ON THE SURFACE TOPOGRAPHY OF LOCAL OVERHEATING AND PLASMA FORMATION DUE TO INITIAL CONDITION PERTURBATIONS SOURCING THE ELECTROTHERMAL INSTABILITY ON HIGH-CURRENT-DENSITY CONDUCTORS
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Study of the electrothermal and MHD instabilities in exploding cylindrical foil liner
Abstract An experimental and numerical study of the plasma instabilities in an electrical exploding cylindrical Al liner is reported. The Al liner 3 mm in diameter and 10 μ m in thickness is exploded at the Qin-1 facility (450 ns, 400 kA). Various diagnostics, such as multi-frame laser shadowgraphy, an x-ray framing camera, and an x-ray backlighting system are developed. The different imaging systems are sensitive to plasma of different areal densities based on the comparison between the experiments and simulation, which reveal the dynamics of the exploding liner in more detail. The laser shadow images show the low-density plasma (∼1–2 × 10 −4 g cm −2 ) at the edge of the liner, and both the amplitude and wavelength of the plasma instabilities increase over time, which are considered to be magnetohydrodynamic (MHD) instabilities rather than electrothermal instabilities. During the ablation of the liner, quasi-periodic azimuthally correlated striations are directly observed in extreme ultraviolet (EUV) self-emission images. Meanwhile, the vertical filaments, which are electrothermal instabilities for plasma under the condition of ∂ η /∂ T < 0, are also observed in EUV self-emission images. The x-ray backlighting images of the exploding liner are obtained by placing an X -pinch load on the current-return path to serve as an x-ray point source (∼1 ns, ∼10 μ m). The x-ray backlighting results show the behavior of the high-density plasma (∼1.89 × 10 −3 g cm −2 ), which includes the transition from electrothermal to MHD instabilities. Finally, we realized a 2D MHD simulation of the exploding liner under experimental conditions, which shows good agreement with the results of the experimental perturbation.
Effect of surface roughness on phase transition timing in megaampere pulsed-power–driven exploding conductors
An understanding of material phase transitions in megaampere pulsed-power–driven exploding conductors is important for predicting the growth of hydrodynamic instabilities in magneto-inertial fusion concepts. Here, this study analyzes phase transitions in electrical conductor explosions using 1D Lagrangian and 2D arbitrary Lagrangian–Eulerian resistive magnetohydrodynamic simulations to show that micrometer-scale surface roughness can lead to the electrothermal instability (ETI), a feedback effect that concentrates resistive heating and leads to early melting and ablation. Simulations of the Mykonos electrothermal instability II (METI-II) experiment show melting begins 19% sooner for machined rods with micrometer-scale surface roughness than for rods without these features. The surface magnetic field is 41 T around the initial region of melt, representing a lower magnitude than both the 86 T from 1D simulations and the 85 T threshold reported elsewhere. In 2D simulations with micrometer-scale surface roughness, temperature measurements indicate the critical point temperature of aluminum is reached 17% faster in comparison with 1D simulations. Values from 2D simulations with surface roughness align with predictions from ETI theory, and the observed temperature redistribution further supports the ETI as an underlying mechanism. Simulation results are validated against experimental photonic Doppler velocimetry data. This study shows 1D simulations are adequate to model conductors with sub-micrometer-scale surface roughness in this high-energy-density regime; however, 2D or 3D simulations are required to capture the full range of physics for accurately describing phase transitions in conductors with micrometer-scale or larger surface roughness.
UNR Grant Proposal Contribution
The work of Carrier et. al. (citation needed for Matt’s effect of surface roughness on phase transitions/ETI paper) demonstrates that 1D and 2D resistive magnetohydrodynamic (MHD) simulations can reliably model exploding aluminum rods driven by megaampere currents. Close agreement between simulation results and photonic Doppler velocimetry data from the Mykonos electrothermal instability (METI-II) campaign builds confidence in predictive modelling capabilities for pulsed-power HED experiments. Furthermore, 2D MHD simulations show how machined features and micro-scale surface roughness can seed the electrothermal instability (ETI). Surface roughness was observed to reduce the time of melt by 19%, with ETI growth driving the enhanced heating of the rod surface.
Controlling morphology and improving reproducibility of magnetized liner inertial fusion experiments
X-ray imaging indicates magnetized liner inertial fusion (MagLIF) stagnation columns have a complicated quasi-helical structure with significant variations in x-ray brightness along the column. In this work, we describe MagLIF experiments aimed at controlling these stagnation structures by varying the initial liner geometry and composition. First, by varying the initial aspect ratio of the liner, we demonstrate a change in the stagnation structures that is consistent with helical magneto Rayleigh–Taylor (MRT) instabilities feedthrough from the outer-to-inner surfaces of the liner. Second, to minimize the seed for such instabilities, we incorporate a dielectric coating on the outer surface of the beryllium liner, which has previously been shown to reduce the growth of the electrothermal instability, a likely seed for MRT growth. Using this coating, we achieve a stagnation column with significantly reduced helical structure and axial variation in x-ray brightness. We discuss how this coating changes the evolution of structures through stagnation along with the spatial uniformity of neutron production. Finally, we show that these more uniform stagnations also result in improved reproducibility in stagnation temperatures and primary DD neutron yield.
Hall instability driven seeding of helical magneto-Rayleigh–Taylor instabilities in axially premagnetized thin-foil liner Z-pinch implosions
Helical magneto-Rayleigh–Taylor instability (MRTI) structures have been observed in z-pinch-driven liner implosion experiments with a pre-imposed axial magnetic field. We show that the formation of these helical structures can be described by a Hall magnetohydrodynamical (HMHD) model. We used the 3D extended magnetohydrodynamics simulation code PERSEUS (which includes Hall physics) [Seyler and Martin, Phys. Plasmas 18, 012703 (2011)] to study these helical instabilities and show that a Hall interchange instability in low-density coronal plasma immediately surrounding the dense liner is responsible for producing helically oriented effects in the magnetic field and current density within the coronal layer. Here, this seeds the helical pitch angle of the MRTI even when other proposed helical seeding mechanisms are either not present in the experiments or not accounted for in the simulations. For example, this mechanism does not require low-density power-feed plasmas to be swept in from large radius or the development of electrothermal instabilities. The Hall Instability is, thus, a new, independent explanation for the origin of the helical instabilities observed in axially premagnetized liner experiments. Simulation results supporting this mechanism are presented.
Three-dimensional feedback processes in current-driven metal
Using three-dimensional (3D) magnetohydrodynamic simulations, we study how a pit on a metal surface evolves when driven by intense electrical current density j. Redistribution of j around the pit initiates a feedback loop: j both reacts to and alters the electrical conductivity σ, through Joule heating and hydrodynamic expansion, so that j and σ are constantly in flux. Thus, the pit transforms into larger striation and filament structures predicted by the electrothermal instability theory. Both structures are important in applications of current-driven metal: Here, the striation constitutes a density perturbation that can seed the magneto-Rayleigh-Taylor instability, while the filament provides a more rapid path to plasma formation, through 3D j redistribution. Simulations predict distinctive self-emission patterns, thus allowing for experimental observation and comparison.
Final Report for Tech-X Corporations’s contribution to Enhancing Understanding of High Energy Density Plasmas from Wire Array and Solid Liner Implosions Using Fluid Modeling with Kinetic Closures
Recent results from experiments and simulation of magnetically driven pulsed power liners have explored the role of the early-time electrothermal instability in the evolution of the magneto-Rayleigh-Taylor instability. Our focus will be on understanding the development of such instabilities and the potential stabilization mechanisms via electron thermal conduction, viscosity, and large magnetic fields which we expect could play a significant role in supporting the success of the MagLIF program. Experiments have shown that studies of high-energy density plasmas from wire-array implosions require physics modeling that goes well beyond simple models such as ideal magnetohydrodynamics. The goal of this work is to provide increased understanding of these experiments by employing simulations with a multi-fluid extended-MHD model which uses kinetic closures for thermal conduction, resistivity and viscosity. We will use codes easily available to the wider research community, including university students, with a secondary goal of providing the community with well-benchmarked tools capable of advanced modeling of high-energy-density plasmas.
The study of local overheating and plasma formation on stainless steel z-pinch targets
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.
Parylene-N Coatings of Thin Foils for the Mitigation of Neutral Contaminant Desorption and Plasma Formation
Previous experiments utilizing the planar MITL foil platform (T.J. Smith et al. RSI 2021) on the 1-MA, 100-ns Mykonos facility have shown neutral atomic and molecular hydrogen in the gap after rapid heating of the foil surfaces before breakdown. Additionally, previous attempts at using parylene-N as a coating for power flow surfaces on the 1-MA, 100-ns Zebra facility have shown tamping of the electrothermal instability at thicknesses of 50-60 μm (T.M. Hutchinson et al. Phys. Rev. E 2018).
MPD work at MIT
MPD work at MIT is presented in the form of the view-graphs. The following subject areas are covered: the MIT program, its goals, achievements, and roadblocks; quasi one-dimensional modeling; two-dimensional modeling - transport effects and Hall effect; microscopic instabilities in MPD flows and modified two stream instability; electrothermal stability theory; separation of onset and anode depletion; exit plane spectroscopic measurements; phenomena of onset as performance limiter; explanations of onset; geometry effects on onset; onset at full ionization and its consequences; relationship to anode depletion; summary on self-field MPD; applied field MPD - the logical growth path; the case for AF; the challenges of AF MPD; and recommendations.
Weibel-like instability in magnetohydrodynamics
In magnetohydrodynamics (MHD), a density perturbation perpendicular to an electron temperature gradient generates a magnetic field around itself that acts to increase the perturbation, which can lead to instability. An MHD dispersion relation is obtained for perturbations perpendicular to a fixed electron temperature gradient with an initial in-plane magnetic field, including resistivity, viscosity, and the electrothermal coefficient. Instability occurs for sufficiently small electron temperature-gradient scale lengths determined by the ion collisionless skin depth. Both viscosity and resistivity are required to prevent growth at arbitrarily small spatial scales and to give a physical result for the fastest growing mode. The perpendicular electrothermal coefficient is only significant for a narrow range of low electron Hall parameters, causing a modest reduction in magnetic field growth and modifying the criteria for instability in the presence of viscosity. If the definition of the Weibel instabilityis extended to include all instabilities due to anisotropy in the electron velocity distribution, then this is a Weibel-like instability because an electron temperature gradient implies an anisotropic electron velocity distribution. Here, the implications for the formation of filaments in laser-produced plasmas and for the verification of MHD codes are considered.
Electrothermally induced eddy currents in segmented electrode MHD channels.
Electrothermally induced instability of plasma moving in infinite segmented electrode MHD channel perpendicular to magnetic field, analyzing current distribution evolution
Imaging of Electrothermal Filament Formation in a Mott Insulator
Resistive switching—the current- and voltage-induced change of electrical resistance—is at the core of memristive devices, which play an essential role in the emerging field of neuromorphic computing. This study is about resistive switching in a Mott insulator, which undergoes a thermally driven metal-to-insulator transition. Two distinct switching mechanisms are reported for such a system: electric-field-driven resistive switching and electrothermal resistive switching. The latter results from an instability caused by Joule heating. Here, we present the visualization of the reversible resistive switching in a planar V 2 O 3 thin-film device using high-resolution wide-field microscopy in combination with electric transport measurements. We investigate the interaction of the electrothermal instability with the strain-induced spontaneous phase separation in the V 2 O 3 thin film at the Mott transition. The photomicrographs show the formation of a narrow metallic filament with a minimum width ≲500 nm. Although the filament formation and the overall shape of the current-voltage characteristics (IVCs) are typical of an electrothermal breakdown, we also observe atypical effects such as oblique filaments, filament splitting, and hysteretic IVCs with sawtoothlike jumps at high currents in the low-resistance regime. We are able to reproduce the experimental results in a numerical model based on a two-dimensional resistor network. This model demonstrates that resistive switching in this case is indeed electrothermal and that the intrinsic heterogeneity is responsible for the atypical effects. This heterogeneity is strongly influenced by strain, thereby establishing a link between switching dynamics and structural properties.
Single Crystals of Vanadium Oxides as a Lens for Understanding Structural and Electronic Phase Transformations, Ion Transport, Chemo-Mechanical Coupling, and Electrothermal Neuronal Emulation
Vanadium oxides cystallize in a diverse array of structures and compositions arising from the redox versatility of vanadium, variable covalency of V−O bonds, and myriad coordination geometries. Their open frameworks present abundant interstitial sites that enable insertion of guest-ions. In such compounds, V3d electron and spin localization and disorder couple strongly to structural preferences. The rich structural diversity manifests as a “rugged” free energy landscape with multiple interconvertible polymorphs. Such a landscape sets up structural, electronic, and magnetic transitions that underpin the promise of these materials as ion-insertion battery electrodes; compact primitives for brain-inspired computing, and heterogeneous catalysts. Here, we examine the structural and compositional diversity, electronic instabilities, defect dynamics, structure transformations, mechanical properties, and surface structure of vanadium oxides using single crystals as a distinctive lens. Single crystals enable the measurement of structure−function correlations without the ensemble and orientational averaging inevitable in polycrystalline materials. Their well-defined surfaces further enable examination of facet-dependent reactivity toward molecular adsorbates, ion fluxes, and lattice (mis)matched solids. We provide a comprehensive account of vanadium-oxide single-crystal studies, from delineation of common structural motifs to single-crystal growth techniques, topochemical modification strategies, mechanisms underpinning electronic instabilities, and implementation as electrothermal neurons and battery electrode materials.
Morphological and nanomechanical changes in tungsten in high heat flux conditions
Abstract Morphological and nanomechanical alteration of tungsten in extreme environments, like those in edge localized modes in nuclear fusion environments, up to 46.3 GWm −2 heat fluxes were experimentally simulated using electrothermal plasma. Surface and subsurface damage to the tungsten is seen mainly in the form of pore formation, cracks, and resolidified melt instabilities. Mirco voids, rosette-type microfeatures, core-shell structure, particle enrichment, and submicron channels all manifest in the damaged subsurface. The formation of voids in the subsurface was determined to originate from the ductile fracture of hot tungsten by plastic flow but not developed to cracking. The voids were preferentially settled in grain boundaries, interfaces. The directionality of elongated voids and grains is biased to the heat flow vector or plasma pathway, which is the likely consequence of the thermally driven grain growth and sliding in the high-temperature conditions. The presence of a border between the transient layer and heat-affected zone is observed and attributed to plasma shock and thermal spallation of fractural tungsten at high temperature. Plasma peening-like hardening effects in tungsten were observed in the range of 22.7–46.3 GWm −2 but least in the case of the lowest heat flux, 12.5 GWm −2 .
Rate effects on instabilities in slightly ionized plasmas
Results are presented of numerical computer calculations of dispersive wave growth rates in slightly ionized plasmas. The effects of employing a plasma model with detailed consideration of rate and radiative processes involving the electron quantum states were studied. Acoustic and electrothermal waves in unseeded argon are found to be frozen with the latter damped. Rate thermal modes can exhibit large growth. Mode mixing and switching in both seeded and unseeded argon are demonstrated.