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DOE OSTI2020

Caltech Lab Experiments and the Insights They Provide Into Solar Corona Phenomena

A comprehensive overview of two decades of Caltech experiments relevant to solar corona physics is presented. The extent to which the experiments scale to the solar corona, the basic configurations and operation, and the importance of the magnetic force J × B common to all the experiments is discussed. Summaries are given of the various configurations used, the main observations, and interpretations of these observations, including new models developed to provide these interpretations. Topics include observations and explanations for flux rope self-collimation, axial flows along flux ropes, eruption of arched flux ropes, strapping magnetic fields that inhibit eruption, the torus instability, and effects such as X-ray emission of a kink-driven secondary Rayleigh-Taylor instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Kelvin-Helmholtz instability as one of the key features for fast and efficient emulsification by hydrodynamic cavitation

The paper investigates the oil–water emulsification process inside a micro-venturi channel. More specifically, the possible influence of Kelvin-Helmholtz instability on the emulsification process. High-speed visualizations were conducted inside a square venturi constriction with throat dimensions of 450 µm by 450 µm, both under visible light and X-Rays. We show that cavity shedding caused by the instability results in the formation of several cavity vortices. Their rotation causes the deformation of the oil stream into a distinct wave-like shape, combined with fragmentation into larger drops due to cavitation bubble collapse. Later on, the cavity collapse further disperses the larger drops into a finer emulsion. Thus, it turns out that the Kelvin-Helmholtz instability is similarly characteristic for hydrodynamic cavitation emulsification inside a microchannel as is the Rayleigh-Taylor instability for acoustically driven emulsion formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Numerical study of implosion instability mitigation in magnetically driven solid liner dynamic screw pinches

Magnetized liner inertial fusion experiments on the Z accelerator suffer from magneto-Rayleigh–Taylor instabilities (MRTI) that compromise integrity of the imploding cylindrical liner, limiting achievable fusion fuel conditions and ultimately reducing magneto-inertial fusion target performance. Dynamic screw pinches (DSP) provide a method to reduce MRTI in-flight via application of magnetic field line tension to the imploding liner outer surface. In contrast with z-pinches that drive implosions with an azimuthal magnetic field, dynamic screw pinches enforce an additional axial drive magnetic field component, making the overall drive magnetic field helical. As the liner implodes, cumulative MRTI development is reduced by dynamically shifting the orientation of the fastest growing instability modes. Three-dimensional magnetohydrodynamic simulations show that the DSP mechanism effectively stabilizes initially solid cylindrical liner implosions driven by Z-scale current pulses, indicating that MRTI mitigation increases with the ratio of axial to azimuthal drive magnetic field components (i.e., the drive field ratio). We also performed a spectral analysis of the simulated imploding density distributions, extracting wavelength and pitch angle of the simulated MRTI structures to study their dynamics during the implosion. Simulations of liners initially perturbed with drive-field-aligned sinusoidal structures indicate that MRTI mitigation in DSP implosions decreases with perturbation wavelength, once again suggestive of magnetic field line tension effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Code-to-code comparison between FLASH and HYDRA in gas-puff Z-pinch modeling

The numerical modeling of gas-puff Z pinches involves the nonlinear coupling of a broad range of complex, multi-physics phenomena that makes such simulations challenging. The challenge is further compounded by nonlinear instabilities that can impact the dynamics of imploding gas-puff Z pinches, such as the magneto Rayleigh–Taylor instability (MRTI). If the growth rate and amplitude of the latter is comparable to the relevant timescales and properties of the imploding plasma, the MRTI can dramatically alter implosion dynamics, dictate pinch stability, and govern the plasma properties achievable in pulsed-power-driven laboratory experiments. National Laboratories and academic teams have developed numerical tools that can accurately model Z-pinch configurations and provide reliable design capabilities that can guide experimental choices and assist in interpreting experimental results. Most such tools, however, are not broadly available. Here, we present newly developed Z-pinch simulation capabilities of the publicly available FLASH code, applied in the study of MRTI growth and dynamical effects in gas-puff implosions. To verify the new implementations, we perform a comparison of FLASH gas-puff implosion simulations with previously published calculations with the HYDRA code from Lawrence Livermore National Laboratory, which have been validated with experimental data from the CESZAR pulsed-power driver at the University of California, San Diego. The experiments involved double- and triple-nozzle configurations, in an experimental attempt to stabilize the pinch to the MRTI. The code-to-code comparison shows similar results between the FLASH and HYDRA simulations, supporting the use of FLASH in the modeling of future gas-puff Z-pinch experiments at CESZAR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Seeding the Electrothermal Instability through a Three-Dimensional, Nonlinear Perturbation

Electrothermal instability plays an important role in applications of current-driven metal, creating striations (which seed the magneto–Rayleigh-Taylor instability) and filaments (which provide a more rapid path to plasma formation). However, the initial formation of both structures is not well understood. Here, simulations show for the first time how a commonly occurring isolated defect transforms into the larger striation and filament, through a feedback loop connecting current and electrical conductivity. Simulations have been experimentally validated using defect-driven self-emission patterns.

42 ENGINEERING↗

NASA NTRS1993

The early ultraviolet spectral evolution of Nova Cygni 1992

We report on the high resolution ultraviolet line profile evolution of Nova Cygni 1992 using the International Ultraviolet Explorer (IUE) satellite and the Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope (HST). Our observations cover the period from discovery in 1992 February through 1993 April. The initial expansion velocity, derived from P Cyg profiles on Mg II and other resonance lines, was about 4500 km/s. All resonance transitions displayed P Cyg profiles around the time of UV maximum. We first discuss the spectral development as the initially optically thick atomic absorption curtain became optically thin. We then present the interpretation of the nebular spectral stage. The high resolution line profiles show that the shell rapidly developed nearly symmetric knots, or filaments, of emission. The optically thin transitions show an emission weighted expansion velocity of about 1800 km/s, consistent with the velocity inferred from the radio and infrared data. The emission lines display a symmetric set of filaments that appeared as soon as the line profiles became optically thin. The GHRS observations demonstrate that the filaments were located in the inner, slower moving parts of the ejecta. These probably record an initial low wave number instability imposed on the ejecta at the time of outburst. We suggest that the likely cause is a Rayleigh-Taylor instability. The emission at later stages is dominated by the filaments and, since this phenomenon is seen in virtually all novae, nebular line formation codes will have to account for the density inhomgeneities in order to adequately determine abundances for nove ejecta.

Shore, Steven N.↗

NASA NTRS2002

An Experimental Investigation of Incompressible Richtmyer-Meshkov Instability

Richtmyer-Meshkov (RM) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and eventually become a turbulent flow. It is closely related to Rayleigh-Taylor instability, which is the instability of a planar interface undergoing constant acceleration, such as caused by the suspension of a heavy fluid over a lighter one in the earth's gravitational field. Like the well-known Kelvin-Helmholtz instability, RM instability is a fundamental hydrodynamic instability which exhibits many of the nonlinear complexities that transform simple initial conditions into a complex turbulent flow. Furthermore, the simplicity of RM instability (in that it requires very few defining parameters), and the fact that it can be generated in a closed container, makes it an excellent test bed to study nonlinear stability theory as well as turbulent transport in a heterogeneous system. However, the fact that RM instability involves fluids of unequal densities which experience negligible gravitational force, except during the impulsive acceleration, requires RM instability experiments to be carried out under conditions of microgravity. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. The impulsive acceleration is generated by bouncing a rectangular tank containing two different density liquids off a retractable vertical spring. The initial perturbation is produced prior to release by oscillating the tank in the horizontal direction to produce a standing wave. The instability evolves in microgravity as the tank travels up and then down the vertical rails of a drop tower until hitting a shock absorber at the bottom. Planar Laser Induced Fluorescence (PLIF) is employed to visualize the flow. PLIF images are captured by a video camera that travels with the tank. Figure 1 is as sequence of images showing the development of the instability from the initial sinusoidal disturbance far into the nonlinear regime which is characterized by the appearance of mushroom structures resulting from the coalescence of baroclinic vorticity produced by the impulsive acceleration. At later times in this sequence the vortex cores are observed to become unstable showing the beginnings of the transition to turbulence in this flow. The amplitude of the growing disturbance after the impulsive acceleration is measured and found to agree well with theoretical predictions. The effects of Reynolds number (based on circulation) on the development of the vortices and the transition to turbulence are also determined.

Jacobs, J. W.↗

DOE OSTI2022

Instability seeding mechanisms due to internal defects in inertial confinement fusion targets

Performance degradation in laser-driven inertial confinement fusion (ICF) implosions is caused by several effects, one of which is Rayleigh–Taylor instability growth. Defects in ICF targets, such as internal voids and surface roughness, create instability seeds in the shell as shocks propagate through the target. A comprehensive understanding of seeding mechanisms is essential to characterize the impact of target defects on inflight shell integrity and mass injection into the central, lower-density vapor region. An analysis of early-time behavior of both single-mode shell mass modulations and isolated voids is performed by examining the evolution of the acoustic waves launched by these target imperfections. A systematic study of localized perturbation growth as a function of defect placement and size is presented. Furthermore, the use of low-density ablator materials (such as foams) is suggested as a potential mitigation strategy to improve target robustness against the impact of defect-initiated growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

On the study of hydrodynamic instabilities in the presence of background magnetic fields in high-energy-density plasmas

Blast-wave-driven hydrodynamic instabilities are studied in the presence of a background B-field through experiments and simulations in the high-energy-density (HED) physics regime. In experiments conducted at the Laboratoire pour l’utilisation des lasers intenses (LULI), a laser-driven shock-tube platform was used to generate a hydrodynamically unstable interface with a prescribed sinusoidal surface perturbation, and short-pulse x-ray radiography was used to characterize the instability growth with and without a 10-T B-field. The LULI experiments were modeled in FLASH using resistive and ideal magnetohydrodynamics (MHD), and comparing the experiments and simulations suggests that the Spitzer model implemented in FLASH is necessary and sufficient for modeling these planar systems. These results suggest insufficient amplification of the seed B-field, due to resistive diffusion, to alter the hydrodynamic behavior. Although the ideal-MHD simulations did not represent the experiments accurately, they suggest that similar HED systems with dynamic plasma-β (=2μ0ρv2/B2) values of less than ∼100 can reduce the growth of blast-wave-driven Rayleigh–Taylor instabilities. These findings validate the resistive-MHD FLASH modeling that is being used to design future experiments for studying B-field effects in HED plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

On the interpretation of the beta(sub p) relation in interstellar clouds

Troland and Heiles (1986) have recently presented an updated compilation of observational data concerning the relationship between the interstellar magnetic field strength B and the gas density rho (or, equivalently, the particle density n). One of the main findings of their survey was that B remains constant over the density range 0.1 - approx. 100 cu. cm and shows evidence for increase only a higher densities. They compared this result with theoretical predictions based on the Parker-instability scenario for the formation and evolution of interstellar clouds in the presence of the galactic magnetic field. In this picture, low-density gas is driven by the magnetic Rayleigh-Taylor instability into magnetic valleys, where it accumulates into denser concentrations. The gas initially flows along the magnetic field lines and there is little increase of the field strength with density; B only starts to rise when n becomes large enough for self-gravity to begin competing with the magnetic stresses. For a cloud mass of approx. 1,000 sub M and the measured background field strength, the critical density for contraction in approx. 75 cu. cm. Troland and Heiles therefore concluded that this scenario is basically consistent with the observations. This conclusion is debated.

Koenigl, A.↗

DOE OSTI2021

A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

In this work, a model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V 0 ∝ kh(k, 0) that eventually decays in time as 1/kV 0 t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude h rms (k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of kh rms for the initial spectrum is used to calculate a nonlinear factor F NL that reduces V 0 , as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝t θ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

42 ENGINEERING↗

NASA NTRS1978

On the role of steepened structures and drift waves in equatorial spread F

A description is presented of a unified model of equatorial spread F which organizes much of the observational data and theoretical results in a self-consistent way. It is suggested that an initial bottomside instability nonlinearly evolves to the point that very steep gradients develop and that these steepened structures are responsible for the power spectra observed by probe experiments. This primary process is very likely the Rayleigh-Taylor instability. Observations indicate that some of the bottomside structures rise into the topside. It is shown that the observed gradients on the edges of these rising bubbles should be unstable to drift waves with a linear growth rate of about 1 per second and a perpendicular wavelength, for maximum growth, near the ion gyroradius.

Costa, E.↗

NASA NTRS1979

The instability of a horizontal magnetic field in an atmosphere stable against convection

The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3 of a solar radius beneath the surface of the sun, a field of 100 G develops ripples over a scale of 1000 km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10 billion years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether, the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.

Parker, E. N.↗

NASA NTRS1994

The delayed-detonation model of a type Ia supernovae. 1: The deflagration phase

The nature of the 'delayed detonation' mechanism of Khokhlov for the explosion of Type Ia supernovae is investigated by using two-dimensional numerical hydrodynamics simulations. A new algorithm is used to treat the deflagration front. Assuming that it propagates locally at the laminar flame speed, the deflagration is insufficient to unbind the star. Expansion shuts of the flame; much of this small production of iron group nuclei occurs at lower densities, which reduces the electron-capture problem. The burning front does become wrinkled, but the wavelength of the instability is much larger than the computational grid size and is resolved; this is consistent with previous analysis. Because the degenerate star has an adiabatic exponent only slightly above 4/3, the energy released by deflagration drives a pulsation of large amplitude. During the first expansion phase, adiabatic cooling shuts off the burning, and a Rayleigh-Taylor instability then gives mixing of high-entropy ashes with low-entropy fuel. During the first contraction phase, compressional heating reignites the material. This paper deals with the deflagration phase, from the onset of burning, through expansion and quenching of the flame, to the first contraction.

Arnett, David↗

NASA NTRS2022

Hybrid Kinetic Model of the Interaction Between the Dense Plasma Clouds and Magnetospheric Plasma on Large Time and Spatial Scales, and Comparison With MMS Observations

We present a new simulation results of the cloud dynamics in the ambient magnetospheric plasma on the large time and spatial scales. It was assumed that these impulsive structures observed by the MMS spacecraft originally were created because of the reconnection at the magnetopause. Our new 3-D hybrid kinetic modeling on the large time and spatial scales captures several of these processes: an excitation of the electromagnetic waves (whistler and shear-Alfvén waves) and plasma instabilities (mirror and flute); a formation of shock waves, and collapsing diamagnetic cavity; particle acceleration. A strong overshoot in plasma density profile was observed in the modeling and MMS observation at the interface between the cloud and magnetospheric plasma. The cloud expansion into ambient magnetospheric plasma causes the flute waves connected with excitation of the Rayleigh-Taylor instability observed at the overshoot in plasma density profile across the external magnetic field. The modeling demonstrates a formation of the whistler waves at the initial stage which propagate in the external magnetic field direction. At the later stage, a formation of shear-Alfvén waves was observed

A. S. Lipatov↗

DOE OSTI2022

Design of high-pressure iron Rayleigh–Taylor strength experiments for the National Ignition Facility

Iron is an important metal, scientifically and technologically. It is a common metal on Earth, forming the main constituent of the planet's inner core, where it is believed to be in solid state at high pressure and high temperature. It is also the main component of many important structural materials used in quasistatic and dynamic conditions. Laser-driven Rayleigh–Taylor instability provides a means of probing material strength at high pressure and high temperature. The unavoidable phase transition in iron at relatively low pressure induces microstructural changes that ultimately affect its strength in this extreme regime. This inevitable progression can make it difficult to design experiments and understand their results. Here, we address this challenge with the introduction of a new approach: a direct-drive design for Rayleigh–Taylor strength experiments capable of reaching up to 400 GPa over a broad range of temperatures. We use 1D and 2D hydrodynamic simulations to optimize target components and laser pulse shape to induce the phase transition and compress the iron to high pressure and high temperature. At the simulated pressure–temperature state of 350 GPa and 4000 K, we predict a ripple growth factor of 3–10 depending on the strength with minimal sensitivity to the equation of state model used. The growth factor is the primary observable, and the measured value will be compared to simulations to enable the extraction of the strength under these conditions. These experiments conducted at high-energy laser facilities will provide a unique way to study an important metal.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales

Hydrodynamic instabilities such as Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities usually appear in conjunction with the Kelvin–Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. Here in this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.

42 ENGINEERING↗