magneto-Rayleigh-Taylor Instability Research Articles

Magneto-Rayleigh–Taylor instability and feedthrough in a resistive liquid-metal liner of finite thickness

Magneto-Rayleigh–Taylor instability and feedthrough in a resistive liquid-metal liner of finite thickness

Observation of a magneto-Rayleigh-Taylor instability in magnetically collimated plasma jets

We present the direct experimental observation of the formation of a diamagnetic cavity and magneto-Rayleigh-Taylor (MRT) instability in a β≈1 high energy density plasma. Proton radiography is used to measure the two dimensional path-integrated magnetic field in a laser-produced plasma propagating parallel to a preimposed magnetic field. Flutelike structures, associated with the MRT instability, are observed to grow at the surface of the cavity, with a measured wavelength of 1.2 mm and growth time of 4 ns. These measurements are in good agreement with predictions of three dimensional magnetohydrodynamic simulations using the GORGON code. Published by the American Physical Society 2024

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.

Investigation on the scaling of magneto-Rayleigh–Taylor instability to the current rise time of Z-pinch plasmas

Understanding how the magneto-Rayleigh–Taylor instability (MRTI) scales to the current rise time is vital for Z-pinch dynamic hohlraum driven inertial confinement fusion. Wang et al discovered in prior theoretical work that the perturbation amplitude of MRTI before stagnation increases linearly with the current rise time when the implosion velocity of Z-pinch plasma is held constant. In the present work, three types of wire-array experiments with similar implosion dynamics and constant implosion velocity are performed on an 8 MA pulse power generator to investigate the scaling of MRTI to the rise time. It is successfully accomplished for the first time to obtain the similar wire-array Z-pinch implosions in which the current rise time is scaled up to three times on the generator by controlling the trigger time of its 24 modules. Both the experimental results, which include x-ray radiation pulses and x-ray images of imploding plasmas, and the related numerical analysis have shown that the MRTI before stagnation grows linearly with the rise time, as predicted by the theoretical model.

Hall interchange instability as a seed for helical magneto-Rayleigh–Taylor instabilities in magnetized liner inertial fusion Z-Pinches scaled from Z-Machine parameters to a next generation pulsed power facility

Magnetized liner inertial fusion (MagLIF) is a magneto-inertial-fusion concept that is studied on the 20-MA, 100-ns rise time Z Pulsed Power Facility at Sandia National Laboratories. Given the relative success of the platform, there is a wide interest in studying the scaled performance of this concept at a next-generation pulsed-power facility that may produce peak currents upward of 60 MA. An important aspect that requires more research is the instability dynamics of the imploding MagLIF liner, specifically how instabilities are initially seeded. It has been shown in magnetized 1-MA thin-foil liner Z-pinch implosion simulations that a Hall interchange instability (HII) effect [J. M. Woolstrum et al., Phys. Plasmas 29, 122701 (2022)] can provide an independent seeding mechanism for helical magneto-Rayleigh–Taylor instabilities. In this paper, we explore this instability at higher peak currents for MagLIF using 2D discontinuous Galerkin PERSEUS simulations, an extended magneto-hydrodynamics code [C. E. Seyler and M. R. Martin, Phys. Plasmas 18, 012703 (2011)], which includes Hall physics. Our simulations of scaled MagLIF loads show that the growth rate of the HII is invariant to the peak current, suggesting that studies at 20-MA are directly relevant to 60-MA class machines.

Impact of the radial density profile on the Z-pinch stability at a microsecond rise time of the driving current

This paper considers the instabilities of imploding aluminum metal-puff Z-pinches with an outer plasma shell. An experiment was performed on the GIT-12 generator (3.2–3.6 MA, ∼1 μs implosion times, and ∼15 cm initial Z-pinch radius). It was shown that the density profile of the Z-pinch material had the dominant effect on the growth and suppression of instabilities. Two Z-pinch load configurations were used. The first configuration provided a tailored density profile (TDP) [A. L. Velikovich et al., Phys. Rev. Lett. 77, 853 (1996)], which ensured the suppression of the magneto-Rayleigh–Taylor (MRT) instability in the Z-pinch. For the second configuration, the density profile was changed in such a way that a density notch from 10 to 0.5 μg/cm3 occurred at a radius of about 3 cm from the Z-pinch axis. The notch in the density profile and the nonmonotonic increase in density resulted in a completely unstable compression of the Z-pinch. This gave rise to large-scale instabilities, which were detected by optical diagnostics. The instabilities grew and were not suppressed even in the stagnation phase, despite a sharp increase in the density of the Z-pinch material near the axis. The results were interpreted using the model proposed by Curzon et al. [Proc. R. Soc. London A 257, 386 (1960)]. The total instability amplitude is the sum of the amplitudes of MRT and magneto-hydrodynamic (MHD) instabilities. The growth of the total instability in the density notch region is due to the development of MRT instability. Thus, if the density profile has a notch, the Z-pinch compression in the stagnation phase occurs under strong perturbations at the magnetic field/plasma interface. This results in a dramatic growth of MHD instabilities. Hence, a stable implosion of a Z-pinch with TDP is possible only if the density increases monotonically toward the axis.

Linear analytical model for magneto-Rayleigh–Taylor and sausage instabilities in a cylindrical liner

Recent experimental and numerical results demonstrates that the interfacial motion of a liner Z-pinch during the early stage of implosion may be controlled by the coupled effects of magneto-Rayleigh–Taylor (MRT), sausage, and kink instabilities. However, previous treatments of sausage instability have not considered the mechanical properties of the liner material. In this paper, we present an analytical model that allows us to study the effects of liner viscosity and elasticity on the coupling effects of MRT and sausage instabilities, and we further assume that the wavelengths are much smaller than the liner thickness by neglecting the feedthrough effect. The dispersion relations are analyzed. It is found that viscosity suppresses short-wavelength perturbations, and longer wavelengths are needed to achieve the fastest growing mode as the viscosity grows. Elasticity also strongly suppresses short-wavelength perturbations and eventually leads to the appearance of a cutoff wavenumber beyond which the interface always remains stable. In particular, the present approach provides the basis for the development of a more general theory that would also include magnetohydrodynamic instabilities and would allow a more accurate description of liner motion.

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. 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.

Rayleigh–Taylor and Richtmyer–Meshkov instabilities in the presence of an inclined magnetic field

A unified and analytical model is developed to study the effects of an inclined magnetic field on magneto-Rayleigh–Taylor (MRT) and magneto-Richtmyer–Meshkov (MRM) instabilities in ideal magnetohydrodynamics. Unlike either a horizontal or a vertical magnetic field is present, the decay modes possess decaying and oscillation behaviors together. The vorticity transportation is analyzed. The dispersion relations are derived, and some interesting phenomena are observed. For a small R that represents the ratio of the magnetic field strength, or equivalently, the inclination θ, the growth rate of MRT instabilities resembles the case when a vertical magnetic field is present. For a large R, the growth rate resembles to the case when a horizontal magnetic field exists. The maximum growth rate becomes strongly dependent on At instead of on R. Furthermore, analytical expression is obtained for the MRM instability by using the impulsive accelerated model. The decaying and oscillating rates of the perturbed amplitude are explicitly related to θ. For two limiting cases, with either the vertical or the horizontal magnetic field existing, our results retrieve previous one of the theoretical analyses and numerical simulations. Generally, the asymptotic amplitude becomes independent of the wave number of the initial perturbation in the MRM instability. These findings regarding magneto-hydrodynamic interfacial instabilities in an inclined magnetic field could provide physical insights for magnetically driven targets and astrophysical observations. This analytical model is easily expanded to investigate the effects of finite thickness of magnetic slab and sheared magnetic field in relevant to high-energy-density physics and to astrophysics.

Harmonic Generation and Inverse Cascade in the z-Pinch Driven, Preseeded Multimode, Magneto-Rayleigh-Taylor Instability.

The magneto-Rayleigh-Taylor instability (MRTI) plays an essential role in astrophysical systems and in magneto-inertial fusion, where it is known to be an important degradation mechanism of confinement and target performance. In this Letter, we show for the first time experimental evidence of mode mixing and the onset of an inverse-cascade process resulting from the nonlinear coupling of two discrete preseeded axial modes (400- and 550-μm wavelengths) on an Al liner that is magnetically imploded using the 20-MA, 100-ns rise-time Z Machine at Sandia National Laboratories. Four radiographs captured the temporal evolution of the MRTI. We introduce a novel unfold technique to analyze the experimental radiographs and compare the results to simulations and to a weakly nonlinear model. We find good quantitative agreement with simulations using the radiation magnetohydrodynamics code hydra. Spectral analysis of the MRTI time evolution obtained from the simulations shows evidence of harmonic generation, mode coupling, and the onset of an inverse-cascade process. The experiments provide a benchmark for future work on the MRTI and motivate the development of new analytical theories to better understand this instability.

Measurements of the imploding plasma sheath in triple-nozzle gas-puff z pinches

Gas-puff z-pinch implosions are characterized by the formation of a dense annular plasma shell, the sheath, that is driven to the axis by magnetic forces and therefore subject to the magneto-Rayleigh–Taylor instability. Here, the conditions within these sheaths are measured on the 1-MA COBRA generator at Cornell University [Greenly et al., Rev. Sci. Instrum. 79, 073501 (2008)] for various gas species and initial fill densities. The gas-puff loads are initialized by a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet. Thomson scattering and laser interferometry provide spatially resolved flow, temperature, and electron density profiles midway through the implosion, while extreme ultraviolet pinhole cameras record the evolution of the plasma column and photoconducting diodes measure x-ray emission. Analysis of the scattering spectra includes a means of discriminating between thermal and non-thermal broadening to test for the presence of hydrodynamic turbulence. Two types of sheath profiles are observed, those with sharp discontinuities at the leading edge and those with smooth gradients. In both cases, non-thermal broadening is generally peaked at the front of the sheath and exhibits a characteristic decay length that roughly scales with the sheath ion mean free path. We demonstrate that this non-thermal broadening term is inconsistent with laminar velocity gradients and is more consistent with dissipative turbulence driven by unstable plasma waves in a collisionless shock. The resulting differences in sheath profile are then set by the sheath ion collisionality in a manner consistent with recent 1D kinetic simulations [Angus et al., Phys. Plasmas 28, 010701 (2021)].

Study on the magneto-Rayleigh–Taylor instability of inverse exploding planar foils

Experiments of the explosion of thin planar foils have been carried on the QiangGuang-I facility (∼1.4 MA peak current, ∼110 ns rise time) to study the evolution of the plasma instability. An inverse-field configuration was utilized with the current return post placed in the center and two parallel planar aluminum foils of 20 μm thickness, 1 cm width built on each side. The foil was ablated into a plasma slab with a particular width, and the inner surface and outer surface expanded in opposite directions and suffered from unequal magnetic pressure, resulting in divergent instability evolution. To alter plasma acceleration, multiple load configurations, including symmetric and asymmetric cases, were used to change the distance between the foil and back-post. The diagnostic system was fielded to provide a side-on view of exploding foils, including laser shadowgraphy, laser interferometry, and an optical framing camera. The characteristic structure, wavelength spectrum, and growth rate of the instability were compared for both sides. During the early magnetohydrodynamics instability developing stage, the inner side had a similar feature to the outer side surface, but with a larger ratio of the long wavelength in the spectrum. The anti-correlated relationship between the correlation coefficients of two surfaces appeared to be a kink instability mode. When the interface was subjected to deceleration, a transition from an early instability mode to a Magneto-Rayleigh–Taylor (MRT) instability mode was observed in studies, with the growth rate and characteristic wavelength growing fast. Because of the higher magnetic pressure and earlier retardation, the inner edge was more severely affected by MRT instability than the outer edge. A theoretical model was developed to interpret the experimental data.

Studying the Richtmyer–Meshkov instability in convergent geometry under high energy density conditions using the Decel platform

The “Decel” platform at Sandia National Laboratories investigates the Richtmyer–Meshkov instability (RMI) in converging geometry under high energy density conditions [Knapp et al., Phys. Plasmas 27, 092707 (2020)]. In Decel, the Z machine magnetically implodes a cylindrical beryllium liner filled with liquid deuterium, launching a converging shock toward an on-axis beryllium rod machined with sinusoidal perturbations. The passage of the shock deposits vorticity along the Be/D2 interface, causing the perturbations to grow. In this paper, we present platform improvements along with recent experimental results. To improve the stability of the imploding liner to the magneto Rayleigh–Taylor instability, we modified its acceleration history by shortening the Z electrical current pulse. Next, we introduce a “split rod” configuration that allows two axial modes to be fielded simultaneously in different axial locations along the rod, doubling our data per experiment. We then demonstrate that asymmetric slots in the return current structure modify the magnetic drive pressure on the surface of the liner, advancing the evolution on one side of the rod by multiple ns compared to its 180° counterpart. This effectively enables two snapshots of the instability at different stages of evolution per radiograph with small deviations of the cross-sectional profile of the rod from the circular. Using this platform, we acquired RMI data at 272 and 157 μm wavelengths during the single shock stage. Finally, we demonstrate the utility of these data for benchmarking simulations by comparing calculations using ALEGRA MHD and RageRunner.

Effect of tailored density profiles on the stability of imploding Z-pinches at microsecond rise time megaampere currents

To study the effect of the radial density profile of the material of a metal-plasma Z-pinch load on the development of magneto-Rayleigh–Taylor (MRT) instabilities, experiments have been performed at the Institute of High Current Electronics with the GIT-12 generator which produces microsecond rise time megaampere currents. The Z-pinch load was an aluminum plasma jet (PJ) with an outer plasma shell. This configuration leads to the formation of a uniform current sheath in a Z-pinch load upon application of a high-voltage pulse. It was successfully used in experiments with hybrid deuterium gas-puffs (Klir et al 2020 New J. Phys. 22 103036). The initial density profiles of the Z-pinch loads were estimated from the pinch current and voltage waveforms using the zero-dimensional ‘snowplow’ model, and they were verified by simulating the expansion of the PJ formed by a vacuum arc using a two-dimensional quasi-neutral hybrid model (Shmelev et al 2020 Phys. Plasmas 27 092708). Two Z-pinch load configurations were used in the experiments. The first configuration provided tailored load density profiles, which could be described as ρ(r) ≈ 1/r^s for s > 2. In this case, MRT instabilities were suppressed and thus a K-shell radiation yield of 11 kJ cm−1 and a peak power of 0.67 TW cm−1 could be attained at a current of about 3 MA. For the second configuration, the radial density profiles were intentionally changed using a reflector. This led to the appearance of a notch in the density profiles at radii of 1–3 cm from the pinch axis and to magnetohydrodynamic instabilities at the final implosion stage. As a result, the K-shell radiation yield more than halved and the power decreased to 0.15 TW cm−1 at a current of about 3.5 MA.

The effect of anomalous resistivity on fast electrothermal instability

This manuscript presents a new theoretical contribution toward the growth rate of the “fast” form of electrothermal instability (ETI) in the presence of anomalous resistivity (AR). Current-driven ETI is present in all pulsed-power platforms, and has been shown to seed the disruptive magneto Rayleigh–Taylor instability. Fluid simulations of low-density, current-carrying plasmas are often subject to nonphysical runaway Ohmic heating due to an under predicted resistivity when using purely collisional resistivity models. AR models provide mechanisms to increase the resistivity as the drift speed increases through increased current density. The derivation of a new, generalized growth rate is presented for the ETI, which includes a resistivity that is dependent on current density, and marks the key contributions of this work. This new growth rate is then compared to the growth rate without AR. Although the striation form of the ETI growth rate is unaffected by the inclusion of AR, the filamentation form of the ETI growth rate depends on the AR. Hence, the new growth rate is verified through 1D simulations of the filamentation form of ETI. The impact of AR can be significant: up to twelve orders of magnitude on the temporally varying local growth rate for a certain choice of parameters. For experimentally relevant conditions based on kinetic simulations, the growth rate can be increased by up to four orders of magnitude if the AR is dominated by the lower-hybrid drift instability.

Mitigation of magneto-Rayleigh-Taylor instability growth in a triple-nozzle, neutron-producing gas-puff Z pinch

The gas-puff Z-pinch is a well-known source of x-rays and/or neutrons, but it is highly susceptible to the magneto-Rayleigh-Taylor instability (MRTI). Approaches to MRTI mitigation include density profile tailoring, in which nozzles are added or modified to alter the acceleration trajectory, and axial pre-magnetization, in which perturbations are smoothed out via magnetic field line tension. Here, we present two-dimensional magnetohydrodynamic simulations of loads driven by an 850 kA, 160ns driver that suggest these mitigation strategies can be additive. The initial axial magnetic field, B_{z0}, to stabilize a 2.5-cm-radius Ne gas liner imploding onto an on-axis deuterium target can be reduced from 0.7T to 0.3T by adding a second liner with a radius of 1.25cm. Because MRTI mitigation tends to increasingly lower yield with higher B_{z0}, the use of a lower field is advantageous. Here, we predict a reduction in yield penalty from >100× with the single liner to <10× with a double liner. A premagnetized, triple nozzle gas puff could therefore be an attractive source for intense neutrons or other fusion applications.

Liner implosion experiments driven by a dynamic screw pinch

This paper expands upon recent experimental results [Campbell et al., Phys. Rev. Lett. 125, 035001 (2020)], where thin-foil liner implosions were driven by a dynamic screw pinch (DSP) and found to have magneto-Rayleigh–Taylor instability (MRTI) amplitudes up to three times smaller than in implosions driven by a standard z-pinch (SZP). The expanded discussion presented herein includes: (1) a detailed comparison of the MRTI growth measured in the experiment with that calculated from theory; (2) measurements of axial magnetic field injection into the liner interior prior to the implosion, as well as the subsequent compression of this field during the implosion; (3) an in-depth description of how the helical geometry of the DSP can result in earlier implosion and stagnation times relative to the SZP; and (4) particle-in-cell simulations showing different electron drift behavior in the anode–cathode gap of the DSP relative to the SZP, and how this difference may be related to the different current waveforms recorded during the experiments.

Azimuthal magnetic field distribution in gas-puff Z-pinch implosions with and without external magnetic stabilization.

An experimental study of the magnetic field distribution in gas-puff Z pinches with and without a preembedded axial magnetic field (B_{z0}) is presented. Spatially resolved, time-gated spectroscopic measurements were made at the Weizmann Institute of Science on a 300 kA, 1.6 μs rise time pulsed-power driver. The radial distribution of the azimuthal magnetic field, B_{θ}, during the implosion, with and without a preembedded axial magnetic field of B_{z0}=0.26T, was measured using Zeeman polarization spectroscopy. The spectroscopic measurements of B_{θ} were consistent with the corresponding values of B_{θ} inferred from current measurements made with a B-dot probe. One-dimensional magnetohydrodynamic simulations, performed with the code trac-ii, showed agreement with the experimentally measured implosion trajectory, and qualitatively reproduced the experimentally measured radial B_{θ} profiles during the implosion when B_{z0}=0.26T was applied. Simulation results of the radial profile of B_{θ} without a preembedded axial magnetic field did not qualitatively match experimental results due to magneto-Rayleigh-Taylor (MRT) instabilities. Our analysis emphasizes the importance of MRT instability mitigation when studying the magnetic field and current distributions in Z pinches. Discrepancies of the simulation results with experiment are discussed.

Studies on the implosion of pinches with tailored density profiles

This paper presents the results of experimental and theoretical studies of imploding metal-puff Z-pinches. The experiments were carried out on the MIG high-current pulse generator at a current level of about 2 MA and a current rise time of about 100 ns. A plasma gun was used to produce a plasma column with a tailored density profile through which the main electromagnetic pulse of the MIG generator was passed. The experiments have shown that pinches of this type, being compressed, are resistant to dynamic magneto-Rayleigh–Taylor (MRT) instabilities. The experimental results were analyzed using one-dimensional radiation magnetohydrodynamic simulations. It has been shown that in a pinch with a tailored density profile, the formation of a high-temperature plasma at the pinch axis and the generation of x-rays occur at the stagnation stage, i.e. under conditions close to Bennett equilibrium. At this stage, flute-like MRT instabilities develop, causing the pinch to decay.

Implosion dynamics of triple-nozzle gas-puff z pinches on COBRA

Experiments on the 1-MA, 220-ns COBRA generator at Cornell University [J. B. Greenly et al., Rev. Sci. Instrum. 79, 073501 (2008)] were conducted to provide detailed measurements of structured cylindrical gas-puff z pinches. In the experiments, a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet initialize the z-pinch load with various working gases, radial density profiles, and externally applied axial magnetic fields. Planar laser-induced fluorescence provides a measure of the initial neutral gas density of the load, while three-frame laser shearing interferometry and multi-frame extreme ultraviolet (XUV) cameras reveal the formation and propagation of a magneto-Rayleigh–Taylor (MRT) unstable shock layer. Implosion trajectories are compared to simple, experimentally informed models and found to be in good agreement. Differences in the structure of the accelerating plasma sheath and evolution of the MRT instability are observed for different gas species and axial magnetic field strengths, correlating with differences in pinch uniformity and x-ray emission. The average instability growth is compared to linear MRT theory predictions using the instantaneous acceleration of the best-fit implosion models and characteristic instability wavelength, with the effective Atwood number and seed perturbation size as fit parameters. For high density argon center jets, ionization prior to the arrival of the imploding plasma sheath suggests a heating mechanism consistent with photoionization by XUV self-emission.