Imploding Liner Research Articles

Implosion of heavy metal liners driven by megaampere current pulses

Implosion of heavy metal liners driven by megaampere current pulses

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.

Shape manipulation of a rotating liquid liner imploded by arrays of pneumatic pistons: Experimental and numerical study

Shaping the inner surface of a rotating, imploding liquid metal liner as it compresses a magnetised plasma target is an important aspect of the Magnetised Target Fusion (MTF) scheme pursued by General Fusion. Reduced-order modelling has shown that the liner's inner surface shape can be manipulated during the implosion by spatially varying the amplitude and timing of pressure applied at the liner's outer surface. A sub-scale apparatus was constructed to investigate this concept, using water as the liner material. A simplified axisymmetric model of this apparatus was also developed using OpenFOAM software. Experimental pressure and rotational speed were used as inputs to numerical simulations. Very good agreement between numerical and experimental liner trajectories was obtained for a wide range of implosion parameters. Data analysis confirmed an initially cylindrical inner liner surface can be shaped and the shaped surface remains symmetrical to radial compression ratios of at least 7:1, despite driving the implosion using pneumatic piston arrays. Furthermore, experiments demonstrated suppression of Rayleigh-Taylor instability for shaped implosions by using liner rotation. This is significant, as literature only confirms this suppression for cylindrical implosions. These results increase confidence in simplified numerical modelling as a predictive tool for designing MTF machines.

Three-dimensional magnetohydrodynamic modeling of auto-magnetizing liner implosions on the Z accelerator

Auto-magnetizing (AutoMag) liners are cylindrical tubes that employ helical current flow to produce strong internal axial magnetic fields prior to radial implosion on ∼100 ns timescales. AutoMag liners have demonstrated strong uncompressed axial magnetic field production (>100 T) and remarkable implosion uniformity during experiments on the 20 MA Z accelerator. However, both axial field production and implosion morphology require further optimization to support the use of AutoMag targets in magnetized liner inertial fusion (MagLIF) experiments. Data from experiments studying the initiation and evolution of dielectric flashover in AutoMag targets on the Mykonos accelerator have enabled the advancement of magnetohydrodynamic (MHD) modeling protocols used to simulate AutoMag liner implosions. Implementing these protocols using ALEGRA has improved the comparison of simulations to radiographic data. Specifically, both the liner in-flight aspect ratio and the observed width of the encapsulant-filled helical gaps during implosion in ALEGRA simulations agree more closely with radiography data compared to previous GORGON simulations. Although simulations fail to precisely reproduce the measured internal axial magnetic field production, improved agreement with radiography data inspired the evaluation of potential design improvements with newly developed modeling protocols. Three-dimensional MHD simulation studies focused on improving AutoMag target designs, specifically seeking to optimize the axial magnetic field production and enhance the cylindrical implosion uniformity for MagLIF. By eliminating the driver current prepulse and reducing the initial inter-helix gap widths in AutoMag liners, simulations indicate that the optimal 30–50 T range of precompressed axial magnetic field for MagLIF on Z can be accomplished concurrently with improved cylindrical implosion uniformity.

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.

Tracking interface position of a high-speed imploding composite liner based on magnetic diffusion difference

A technique for tracking the interface position of non-metal–metal composite liners during high-speed implosion is proposed in this paper. Based on the magnetic diffusion difference between metal and non-metal, the interface position information is obtained by measuring magnetic fields in the cavity of the liner. An efficient magnetic flux estimation algorithm based on iterative magnetic diffusion simulation is also proposed to estimate the magnetic flux loss of the liner. Numerical experiments show that the estimation algorithm can reduce the relative error to less than 0.5%. The composite solid liner experimental results show that the maximum error is about 2% under imperfect experimental conditions. Detailed analysis suggests that this method can be widely applied to non-metallic sample materials (electrical conductivity is less than 103 ∼ 104 S/m). The technique provides a useful supplement to the existing interface diagnosis methods for high-speed implosion liners.

Liner Development and Characterization for the PHELIX Containment System

Recent experiments conducted on hazardous materials using the Precision High Energy-density Liner Implosion eXperiment (PHELIX) required development of a new containment system for the apparatus. Unlike many containment systems, the PHELIX containment system includes a cylindrical imploding aluminum liner, which is driven via magnetic fields to approximate velocities of 1.4 km/s before impacting a target. The complex design attributes and monolithic geometry of the liner have been driven by both simulations and empirical measurements. The contents of this paper cover the design considerations and requirements for the liner, the efforts made in fabricating the component, and steps taken to verify performance both as the dynamic driver of the experiment and as a containment system component.

Exploring the parameter space of MagLIF implosions using similarity scaling. III. Rise-time scaling

Magnetized liner inertial fusion (MagLIF) is a z-pinch magneto-inertial-fusion concept studied at the Z Pulsed Power Facility of Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach the peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. In this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in the performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide scaling prescriptions of experimental input parameters defining a MagLIF load and derive the expected scaling laws for stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code hydra. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage φload near the MagLIF load follows a weak scaling law φload∝tφ−0.12 with respect to the characteristic timescale tφ of the voltage source, instead of the ideal φload∝tφ−1 scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study helps understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.

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.

A compact pulsed power driver with precisely shaped current waveforms for magnetically driven loading experiments.

Magnetically driven loading techniques based on high current pulsed power drivers are very important tools for researching material dynamic behaviors and high-pressure physics. Based on the technologies of a Marx generator energy storage and low impedance coaxial cable energy transmission, a compact high current pulsed power driver CQ-7 was developed and established at the Institute of Fluid Physics, China Academy of Engineering Physics, which can generate precisely shaped current waveforms for magnetically driven loading experiments. CQ-7 is composed of 256 two-stage Marx generators in parallel with low impedance, high voltage coaxial cables for current output. The 256 Marx generators are divided into 16 groups, and each separate group can be individually triggered to discharge and shape currents in sequence by a low jitter, high voltage pulse trigger with 16 output signals. The electrical parameters of CQ-7 are a capacitance of 20.48 µF, an inductance of 4.12 nH, and a resistance of 3.35 mΩ in a short circuit. When working at the charging voltage of ±40-±60kV, CQ-7 can deliver a peak current from 5 to 7 MA to the short-circuit loads with a rising time of 400-700ns at different discharging time sequences. Two different experiments were conducted to test the performance of CQ-7: magnetically driven high velocity flyer plates and solid liner implosion. The results show that CQ-7 can accelerate the aluminum flyer plate with a size of 12 × 8 × 1mm3 to more than 7.5 km/s and uniformly drive the aluminum liner with an inner diameter of 6.2mm and a thickness of 0.4mm to more than 9.5 km/s. Furthermore, these experiments indicate that CQ-7 is a robust platform for material dynamics and high-pressure physics.

Magnetic implosion of thin aluminum foil liners

Metal liner implosions driven by a pulsed current generator are used in research on inertial confinement fusion, generation of soft x-ray pulses and megagauss magnetic fields. The energy density in the plasma column formed during the liner stagnation is largely determined by the initial radius and the radial convergence of the liner. When the liner implosion time is close to the current rise time, the liner initial radius is proportional to the current rise time. The paper presents the results of experiments on the fast implosion of cylindrical liners on the MIG generator (2 MA, 80 ns) at the Institute of High Current Electronics, Tomsk, Russia. Liners 0.7–1.0 mm in diameter were made from a 1.8 to 2.5 μm thick aluminum foil. A low-density plasma was pre-injected into the liner area. As the Lorentz force sweeps away the pre-injected plasma, the current switches to the liner in 1–3 ns. Then the liner is imploded in 3–7 ns by a current close to the peak generator current. The stagnation radius measured via time-integrated pinhole camera images was found to be not more than 25 µm. Such a radius of the stagnated plasma assumes that the plasma mass density is several times higher than the solid aluminum density.

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.

Cylindrical metal liner implosion at extremes of pressure and material velocity on an intense pulsed power facility-FP-2.

Highly precise and controllable liner implosions driven by a pulsed power facility have extensive applications in exploration of advanced hydrodynamics at the extremes of pressure and material velocity. In this paper, we describe a new pulsed power facility developed in China named FP-2 (a series of facilities for Fluid Physics investigations-the second generation) for liner implosions. Benefiting from the reliable and stable operation of 48 rail gap switches, the FP-2 facility can steadily transmit a current of 10.5 MA to a dummy load of 10 nH in the case of a charging voltage of ±40kV. The first quarter cycle is 5.5 µs, and the percentage shot-to-shot deviation of the current history is less than 1%. When the aluminum liners of 60mm in height and 0.6mm in thickness are adopted, the maximum velocity of 4.5 and 7.5 km/s has been achieved with the liner diameter of 90 and 60mm, respectively, at the diameter of 10mm. Experimental results show that the percentage shot-to-shot deviation of the liner velocity history is less than 1%. As impact on the target, the maximum of the impact time deviation measured from four perpendicular fiber pins is less than 20ns. Due to the modular design of FP-2, it is convenient for a future upgrade. The confirmation of high-quality implosion on FP-2, such as high repeatability, high reliability, and high symmetry, makes it a bright prospect to explore the advanced hydrodynamic problems at extremes of pressure and material velocity in the future.

Preliminary experimental investigation on small-aspect-ratio cylindrical solid liner implosion using compact pulsed power generator

Small-aspect-ratio cylindrical liner implosion on timescales of the order of hundreds of nanoseconds is important in the fields of high-energy-density physics, implosion dynamics, and inertial confinement fusion. This paper describes the design and development of a cylindrical liner load that has a low inductance and uniform magnetic field and its application in the CQ7 compact pulsed power generator. The dynamic response properties and implosion symmetry of liners with aspect ratios ranging from 5 to 9 are investigated. The experimental results show that the azimuthal symmetry of the liner remains intact, and that a liner with an inner diameter of 6.2 mm and a thickness of 0.4 mm can be accelerated up to 10 km/s before the reflected beam is lost. The demonstrated high performance of the experimental technique used for imploding the liner could be beneficial for studying the implosion and dynamics of materials on compact pulse power generators in the future.

Visualizing magnetically driven converging radiative shock generated in Z-pinch foil liner implosion

A study of the evolution and structure of magnetically driven converging radiative shock waves generated in Z-pinch foil liner implosion at an 8-MA pulsed-power facility is presented. End-on extreme ultraviolet images show an inward propagating shock that is circular to <±5% as a function of azimuthal angle, with a standard deviation in the emission intensity of <±30%, implying good cylindrical symmetry. The launch time and shock trajectory are determined by linear fitting of the measured data, giving a shock speed of Mach 6. One-dimensional radiation hydrodynamics MULTI-IFE-Z simulations agree with the experimental observations qualitatively and confirm the existence of a radiative precursor. It is demonstrated with experiment and simulation that the radiative shock wave is generated by magnetic piston compression of dense plasma shell. Analytic estimates of the post-shock plasma conditions suggest that these Z-pinch magnetically-driven high-Mach shocks are strongly radiatively cooled. It is applicable to the optically thick downstream, optically thin upstream radiative shock regime; thus, it can be described by three-layer model, which potentially could be applied to scale studies of astrophysical shocks in the laboratory.

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.

Fusion gain from cylindrical liner-driven implosions of field reversed configurations

MagLIF experiments [M.R. Gomez et al., Phys. Plasmas 22, 056306 (2015)] on Z have demonstrated the basic principles of Magneto-Inertial Fusion (MIF) for wall confined plasmas. Other MIF schemes have been proposed based on the liner implosion of closed field magnetically confined plasmas such as Field Reversed Configurations (FRCs) [T. P. Intrator et al., Phys. Plasmas 15, 042505 (2008)]. We present a semi-analytical model of liner driven FRC implosions that predicts the fusion gain of such systems. The model predicts a fusion gain near unity for an FRC imploded by a liner driven by the Z Machine. We show that FRCs could be formed and imploded at the Z facility using the AutoMag liner concept [S. A. Slutz et al., Phys. Plasmas 24, 012704 (2017)]. An initial bias magnetic field can be supplied by the external magnets used in MagLIF experiments. The reverse field is then supplied by an AutoMag liner, which has helical conducting paths imbedded in an insulating substance. Experiments [Shipley et al., Phys. Plasmas 26, 052705 (2019)] have demonstrated that AutoMag can generate magnetic fields greater than 30 Tesla inside of the liner. We have performed 2D Radiation MHD simulations of the formation and implosion of an FRC, which are in good agreement with the analytical model. The FRC formation process could be studied on small pulsed power machines delivering about 1 MA.

Instability of Thin Resistive Liners in the Linear Approximation

Magnetic implosion of liners is usually accompanied by the development of the Rayleigh–Taylor instability, which makes it hard to achieve high energy densities. However, the liners, which are thin compared with their skin layer (let us call them resistive), can also experience a different kind of instability, when parallel currents in different liner parts are attracted and draw these parts together dividing the liner into layers and filaments (filamentation or the tearing instability). We consider the problem of perturbation development in an infinitely thin resistive liner accounting for the distribution of the magnetic field, spread of currents, and flow of matter assuming that the perturbations are linear. Considering potential applications for different liner configurations (Z- and $\Theta $ -pinch liners and flat flyers) and the fact that the most destructive instabilities develop from the shortest wavelengths, we restrict our analysis to a planar case, which ignores the curvature of the liner and magnetic field lines. We find that the instability develops from any perturbation wavelengths, similar to the case of a perfectly conducting liner, with the instability growth rate for all the wavenumbers $k$ being of the order of $\sqrt {kg} $ ( $g$ is the liner acceleration), but always less than $\sqrt {kg} $ , and with the maximum growth rates for any directions of the wave vector k being greater than the growth rates of the perfectly conducting liner. One can often treat wire-array liners as resistive and, hence, use the results obtained for the description of instability development after the phase of merging the plasmas produced by individual wires.

On the hydrodynamic stability of an imploding rotating circular cylindrical liquid liner

The hydrodynamic stability of an imploding cylindrical liquid liner is analytically and numerically investigated. Such dynamic system can be used to compress gas trapped by the liner, as one may seek in a hydrogen fusion reactor. For such system it is vital for the liner to stay intact at least up to the turnaround point, which marks the point of maximum compression of the inner gas. New two-dimensional linear stability of Bell-type equation and Wentzel-Kramers-Brillouin (WKB) approximations are derived to account for the rotation of the liner. Excellent agreement is achieved between computational fluid dynamics (CFD) and 1D analysis for the trajectory of the unperturbed liner. Very good agreement is also achieved between the Bell type linear stability solution and the CFD until non-linear effects take hold near the turnaround point. The WKB approximation also agrees well but only at the early stage of the liner motion. Viscosity, surface tension and inner gas stability waves are found to have a small effect for a liner’s radial compression of up to ten. It is seen that the rotation has little effect on the perturbation amplitude during the accelerating stage of the liner, which is dominated by a slow oscillatory growth of a Bell-Plesset type at the studied conditions. However, at the decelerating stage towards the turnaround point, Rayleigh–Taylor rapid perturbation growth is suppressed at sufficiently large rotation rates. Hence, when coupled with non-linear saturation effects, the liner stays much intact until the turnaround point for radial compression ratios of up to ten. New simple linear stability limits are derived and are analysed.

A novel, magnetically driven convergent Richtmyer–Meshkov platform

In this paper, we introduce a novel experimental platform for the study of the Richtmyer–Meshkov instability in a cylindrically converging geometry using a magnetically driven cylindrical piston. Magnetically driven solid liner implosions are used to launch a shock into a liquid deuterium working fluid and, ultimately, into an on-axis rod with a pre-imposed perturbation. The shock front trajectory is tracked through the working fluid and up to the point of impacting the rod through the use of on axis photonic Doppler velocimetry. This configuration allows for precise characterization of the shock state as it impacts the perturbed rod interface. Monochromatic x-ray radiography is used to measure the post-shock interface evolution and rod density profile. The ALEGRA MHD model is used to simulate the dynamics of the experiment in one dimension. We show that late in time the perturbation growth becomes non-linear as evidenced by the observation of high-order harmonics, up to n = 5. Two dimensional simulations performed using a combination of the GORGON MHD code and the xRAGE radiation hydrodynamics code suggest that the late time non-linear growth is modified by convergence effects as the bubbles and spikes experience differences in the pressure of the background flow.