magneto-Rayleigh-Taylor Instability Research Articles

Magneto-Rayleigh–Taylor Instability Driven by a Rotating Magnetic Field: Cylindrical Liner Configuration

We propose using a directional time-varying (rotating) driving magnetic field to suppress magneto-Rayleigh-Taylor (MRT) instability in dynamic Z-pinches. A rotational drive magnetic field is equivalent to two magnetic-field components, {\Theta} and Z, that alternate in time, referred to as an alternate Theta-Z-pinch configuration. We consider the finitely thick cylindrical liner configuration in this paper. We numerically integrate the perturbation equation to stagnation time based on the optimal background unperturbed trajectories. We assess the cumulative growth of the dominant mode selected by some mechanism at the beginning of an implosion. The maximum e-folding number at stagnation of the dominant mode of an optimized alternate Theta-Z-pinch is significantly lower than that of the standard Theta- or Z-pinch. The directional rotation of the magnetic field contributes to suppress the instabilities, independent of the finite thickness. The finite thickness effect plays a role only when the orientation of the magnetic field varies in time whereas it does not appear in the standard Theta- or Z-pinch. The rotating frequency of the magnetic field and the thickness of liner are both having a monotonic effect on suppression. Their synergistic effect can enhance the suppression on MRT instability. Because the MRT instability can be well suppressed in this way, the alternate Theta-Z-pinch configuration has potential applications in liner inertial fusion. This work is supported by the NSFC (Grant Nos. 11405167, 51407171, 11571293, 11605188, and 11605189) and the Foundation of the China Academy of Engineering Physics (No. 2015B0201023).

Design of dynamic screw pinch experiments for magnetized liner inertial fusion

Magnetic implosion of cylindrical metallic shells (liners) is an effective method for compressing preheated, premagnetized fusion fuel to thermonuclear conditions [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] but suffers from magneto-Rayleigh–Taylor instabilities (MRTI) that limit the attainable fuel pressure, density, and temperature. A novel method proposed by Schmit et al. [Phys. Rev. Lett. 117, 205001 (2016)] uses a helical magnetic drive field with a dynamic polarization at the outer surface of the liner during implosion, reducing (linear) MRTI growth by one to two orders of magnitude via a solid liner dynamic screw pinch (SLDSP) effect. Our work explores the design features necessary for successful experimental implementation of this concept. Whereas typical experiments employ purely azimuthal drive fields to implode initially solid liners, SLDSP experiments establish a helical drive field at the liner outer surface, resulting in enhanced average magnetic pressure per unit drive current, mild spatial nonuniformities in the magnetic drive pressure, and augmented static initial inductance in the pulsed-power drive circuit. Each of these topics has been addressed using transient magnetic and magnetohydrodynamic simulations; the results have led to a credible design space for SLDSP experiments on the Z Facility. We qualitatively assess the stabilizing effects of the SLDSP mechanism by comparing MRTI growth in a liner implosion simulation driven by an azimuthal magnetic field vs one driven with a helical magnetic field; the results indicate an apparent reduction in MRTI growth when a helical drive field is employed.

Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

We present the linear theory of two-dimensional incompressible magneto-Rayleigh–Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the stabilising effects of the elasticity. As a consequence, the layer can become more unstable than when only one of these stabilising mechanisms is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.

A survey of fluid and kinetic instabilities relevant to space and laboratory plasmas

ABSTRACTThis paper presents a brief survey of a variety of plasma modeling techniques applied to several space- and fusion-relevant plasma instabilities that are presently of significant interest. These include simulations of the Weibel instability that occurs in astrophysical and laser plasmas, two-fluid plasma instabilities in fusion concepts such as Z-pinches that occur beyond the well-known magnetohydrodynamic instabilities, the magneto–Rayleigh–Taylor instability that occurs in a range of plasmas from the laboratory to space, the Richtmeyer–Meshkov instability which is an important instability in astrophysical and fusion plasmas, and the gradient-drift instability which is known to occur in ionospheric and magnetospheric plasmas. Recent advances in kinetic and fluid modeling provide the ability to study a wide variety of problems using the model that is best suited for the parameter regimes of interest. Some of the key findings are summarized here.

Time-Resolved Thomson Scattering on Gas-Puff Z-Pinch Plasmas at Pinch Time

The conditions and dynamics of neon gas puff Z-pinch plasmas at pinch time are studied on a pulsed power generator with a current rise time of approximately 200-ns and 0.9-mA peak current. Radial tailoring of the gas puff mass-density profile using a triple-nozzle coaxial valve (two annular gas liners and a central jet) allows production of both more stable and less stable (with regard to the magneto-Rayleigh–Taylor instability) Z-pinch implosions. A 526.5-nm, 10-J Thomson scattering diagnostic laser enables probing of the flow dynamics and plasma conditions of these implosions with both spatial and temporal resolutions. The 2.2-ns laser pulse scatters from the plasma electrons and is carried by one optical fiber to a visible light streak camera, and by a bundle of optical fibers to a time-gated camera, both after spectral dispersion by 750-mm spectrometers. The streak camera, with a 10-ns full streak time, provides subnanosecond resolution of the evolution of the pinch plasma parameters through stagnation. The time-gated camera provides spatially resolved spectra (across a field of view of 6.1 mm) at the same time as the streak. Scattering spectra suggest that temperatures are high at stagnation, with the ion temperature as much as three times higher than the electron temperature. However, we consider the possibility of nonthermal explanations for the broad scattering spectra and high effective ion temperature, including collisionality, implosion velocity distributions (velocity gradients), and small-scale hydrodynamic motion.

Role of electron inertia and electron/ion finite Larmor radius effects in low-beta, magneto-Rayleigh-Taylor instability

The magneto-Rayleigh-Taylor (MRT) instability has been investigated in great detail in previous work using magnetohydrodynamic and kinetic models for low-beta plasmas. The work presented here extends previous studies of this instability to regimes where finite-Larmor-Radius (FLR) effects may be important. Comparisons of the MRT instability are made using a 5-moment and a 10-moment two-fluid model, the two fluids being ions and electrons. The 5-moment model includes Hall stabilization, whereas the 10-moment model includes Hall and FLR stabilization. Results are presented for these two models using different electron mass to understand the role of electron inertia in the late-time nonlinear evolution of the MRT instability. For the 5-moment model, the late-time nonlinear MRT evolution does not significantly depend on the electron inertia. However, when FLR stabilization is important, the 10-moment results show that a lower ion-to-electron mass ratio (i.e., larger electron inertia) under-predicts the energy in high-wavenumber modes due to larger FLR stabilization.

Preconditioned wire array Z-pinches driven by a double pulse current generator

Suppression of the core-corona structure and wire ablation in wire array Z-pinches is investigated using a novel double pulse current generator ‘Qin-1’ facility. The ‘Qin-1’ facility allows coupling a ∼10 kA 20 ns prepulse generator with a ∼0.8 MA 160 ns main current generator. The tailored prepulse current preheats wires to a gaseous state and the time interval between the prepulse and the main current pulse allows formation of a more uniform mass distribution for the implosion. The implosion of a gasified two aluminum-wire array showed no ablation phase and allowed all array mass to participate in the implosion. The initial perturbations formed from the inhomogeneous ablation were suppressed, however, the magneto Rayleigh–Taylor (MRT) instability during the implosion was still significant and further researches on the generation and development of the MRT instabilities of this gasified wire array are needed.

Magneto-Rayleigh–Taylor instability driven by a rotating magnetic field

In this paper, we analyze theoretically the magneto-Rayleigh–Taylor instability driven by a rotating magnetic field. Slab configurations of finite thickness are treated both with and without using the Wenzel–Kramers–Brillouin approximation. Regardless of the slab thickness, the directional rotation of the driving magnetic field contributes to suppressing these instabilities. The two factors of the finite thickness and directional rotation of the magnetic field cooperate to enhance suppression, with the finite thickness playing a role only when the orientation of the magnetic field is time varying. The suppression becomes stronger as the driving magnetic field rotates faster, and all modes are suppressed, in contrast to the case of a non-rotating magnetic field, for which the vertical mode cannot be suppressed. This implies that the dynamically alternate configuration of a Theta-pinch and a Z-pinch may be applicable to the concept of Theta-Z liner inertial fusion.

Investigation of surface evolution for stainless steel electrode under pulsed megagauss magnetic field

Surface evolution for a conductor electrode under pulsed megagauss (MG) magnetic field was investigated. Stainless steel rods with 3 mm diameter were driven by 8 MA, 130 ns (10%–90%) current pulse in a series of shots on the Primary Test Stand. Experimental data from two complementary diagnostic systems and simulation results from one-dimensional magneto-hydrodynamics code reveal a transition phase for instability development. The transition, which begins as the conductor surface starts to expand, lasts about 40 ns in the pulse. It ends after the thermal plasma is formed, and striation electrothermal instability growth stops but magneto-Rayleigh-Taylor instability (MRTI) starts to develop. An expanding velocity which grows to about 2.0 km/s during the transition phase was directly measured for the first time. The threshold magnetic field for thermal plasma formation on the stainless steel surface was inferred to be 3.3 MG under a rising rate of about 66 MG/μs, and after that MRTI becomes predominant for a...

Preliminary investigation on the use of low current pulsed power Z-pinch plasma devices for the study of early stage plasma instabilities

This article addresses key features for the implementation of low current pulsed power plasma devices for the study of matter dynamics from the solid to the plasma phase. The renewed interest in such low current plasma devices lies in the need to investigate methods for the mitigation of prompt seeding mechanisms for the generation of plasma instabilities. The low current when driven into thick wires (skin effect mode) allows for the simultaneous existence of all phases of matter from solid to plasma. Such studies are important for the concept of inertial confinement fusion where the mitigation of the instability seeding mechanisms arising from the very early moments within the target’s heating is of crucial importance. Similarly, in the magnetized liner inertial fusion concept it is an open question as to how much surface non-uniformity correlates with the magneto-Rayleigh–Taylor instability, which develops during the implosion. This study presents experimental and simulation results, which demonstrate that the use of low current pulsed power devices in conjunction with appropriate diagnostics can be important for studying seeding mechanisms for the imminent generation of plasma instabilities in future research.

Mode selection of magneto-Rayleigh-Taylor instability from the point of view of Landau phase transition theory

A theoretical model referring to mode selection of Z-pinch-driven magneto-Rayleigh-Taylor (MRT) instability, which explains the generation of fundamental instability mode and evolution of fundamental wavelength in experiments, is proposed on the basis of the Landau theory of phase transition. The basic idea of this phase transition model lies in that the appearance of MRT instability pattern can be considered as a consequence of the spontaneous generation of interfacial structure like the spontaneous magnetization in a ferromagnetic system. It is demonstrated that the amplitude of instability is responsible for the order parameter in the Landau theory of phase transition and the fundamental wavelength appears to play a role analogous to inverse temperature in thermodynamics. Further analysis indicates that the MRT instability is characterized by first order phase transition and the fundamental wavelength is proportional to the square root of energy entering into the system from the driving source. The theory predicts that the fundamental wavelength grows rapidly and saturates reaching a limiting wavelength of the order of the liner's final outer radius. The results given by this theory show qualitative agreement with the available experimental data of MRT instability of liner implosions conducted on the Sandia Z machine as well as Primary Test Stand facility at the Institute of Fluid Physics.

Magneto-Rayleigh–Taylor instability in compressible Z-pinch liner plasmas**Project supported by the National Natural Science Foundation of China (Grant Nos. 11475027, 11274051, 11105017, and 11275030) and the National Basic Research Program of China (Grants No. 2013CB834100).

In this paper, the characteristics of magneto-Rayleigh–Taylor (MRT) instability of liner plasmas in MagLIF is theoretically investigated. A three-region slab model, based on ideal MHD equations, is used to derive the dispersion relation of MRT instability. The effect of compressibility on the development of MRT instability is specially examined. It is shown that the growth rate of MRT instability in compressible condition is generally lower than that in incompressible condition in the presence of magnetic field. In the case of zero magnetic field, the growth rate in compressible assumption is approximately the same as that in incompressible assumption. Generally, MRT instability in (x, y) plane can be remarkably mitigated due to the presence of magnetic field especially for short-wavelength perturbations. Perturbations may be nearly completely mitigated when the magnetic field is increased to over 1000 T during liner implosions. The feedthrough of MRT instability in liner outer surface on inner surface is also discussed.

Direct measurement of the inertial confinement time in a magnetically driven implosion

We report on direct, radiographic measurement of the stagnation phase of a magnetically driven liner implosion. The liner is filled with liquid deuterium and imploded to a minimum radius of 440 μm (radial convergence ratio of 7.7) over 300 ns, achieving a density of ≈10 g/cm3. The measured confinement time is ≈14 ns, compared to 16 ns from 1D simulations. A comparison of measured density profiles with 1D and 2D simulations shows a deviation in the reflected shock trajectory and the liner areal density. Additionally, the magneto Rayleigh-Taylor instability causes enhanced compression with shorter confinement in the bubble region compared to the spikes. These effects combine to reduce the pressure-confinement time product, Pτ, by 25% compared to the simulations.

On the Evolution From Micrometer-Scale Inhomogeneity to Global Overheated Structure During the Intense Joule Heating of a z-Pinch Rod

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

Seeded and unseeded helical modes in magnetized, non-imploding cylindrical liner-plasmas

In this research, we generated helical instability modes using unseeded and kink-seeded, non-imploding liner-plasmas at the 1 MA Linear Transformer Driver facility at the University of Michigan in order to determine the effects of externally applied, axial magnetic fields. In order to minimize the coupling of sausage and helical modes to the magneto Rayleigh-Taylor instability, the 400 nm-thick aluminum liners were placed directly around straight-cylindrical (unseeded) or threaded-cylindrical (kink-seeded) support structures to prevent implosion. The evolution of the instabilities was imaged using a combination of laser shadowgraphy and visible self-emission, collected by a 12-frame fast intensified CCD camera. With no axial magnetic field, the unseeded liners developed an azimuthally correlated m = 0 sausage instability (m is the azimuthal mode number). Applying a small external axial magnetic field of 1.1 T (compared to peak azimuthal field of 30 T) generated a smaller amplitude, helically oriented instability structure that is interpreted as an m = +2 helical mode. The kink-seeded liners showed highly developed helical structures growing at the seeded wavelength of λ = 1.27 mm. It was found that the direction of the axial magnetic field played an important role in determining the overall stabilization effects; modes with helices spiraling in the opposite direction of the global magnetic field showed the strongest stabilization. Finally, the Weis-Zhang analytic theory [Weis et al., Phys. Plasmas 22, 032706 (2015)] is used to calculate sausage and helical growth rates for experimental parameters in order to study the effects of axial magnetic fields.

Effect of the axial magnetic field on a metallic gas-puff pinch implosion

The effect of an axial magnetic field Bz on an imploding metallic gas-puff Z-pinch was studied using 2D time-gated visible self-emission imaging. Experiments were performed on the IMRI-5 generator (450 kA, 450 ns). The ambient field Bz was varied from 0.15 to 1.35 T. It was found that the initial density profile of a metallic gas-puff Z-pinch can be approximated by a power law. Time-gated images showed that the magneto-Rayleigh–Taylor instabilities were suppressed during the run-in phase both without axial magnetic field and with axial magnetic field. Helical instability structures were detected during the stagnation phase for Bz < 1.1 T. For Bz = 1.35 T, the pinch plasma boundary was observed to be stable in both run-in and stagnation phases. When a magnetic field of 0.3 T was applied to the pinch, the soft x-ray energy was about twice that generated without axial magnetic field, mostly due to longer dwell time at stagnation.

Technique for fabrication of ultrathin foils in cylindrical geometry for liner-plasma implosion experiments with sub-megaampere currents.

In this work, we describe a technique for fabricating ultrathin foils in cylindrical geometry for liner-plasma implosion experiments using sub-MA currents. Liners are formed by wrapping a 400 nm, rectangular strip of aluminum foil around a dumbbell-shaped support structure with a non-conducting center rod, so that the liner dimensions are 1 cm in height, 6.55 mm in diameter, and 400 nm in thickness. The liner-plasmas are imploded by discharging ∼600 kA with ∼200 ns rise time using a 1 MA linear transformer driver, and the resulting implosions are imaged four times per shot using laser-shadowgraphy at 532 nm. This technique enables the study of plasma implosion physics, including the magneto Rayleigh-Taylor, sausage, and kink instabilities on initially solid, imploding metallic liners with university-scale pulsed power machines.

Instability growth for magnetized liner inertial fusion seeded by electro-thermal, electro-choric, and material strength effects

A critical limitation of magnetically imploded systems such as magnetized liner inertial fusion (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010)] is the magneto-Rayleigh-Taylor (MRT) instability which primarily disrupts the outer surface of the liner. MagLIF-relevant experiments have showed large amplitude multi-mode MRT instability growth growing from surface roughness [McBride et al., Phys. Rev. Lett. 109, 135004 (2012)], which is only reproduced by 3D simulations using our MHD code Gorgon when an artificially azimuthally correlated initialisation is added. We have shown that the missing azimuthal correlation could be provided by a combination of the electro-thermal instability (ETI) and an “electro-choric” instability (ECI); describing, respectively, the tendency of current to correlate azimuthally early in time due to temperature dependent Ohmic heating; and an amplification of the ETI driven by density dependent resistivity around vapourisation. We developed and implemented a material strength model in Gorgon to improve simulation of the solid phase of liner implosions which, when applied to simulations exhibiting the ETI and ECI, gave a significant increase in wavelength and amplitude. Full circumference simulations of the MRT instability provided a significant improvement on previous randomly initialised results and approached agreement with experiment.

Numerical studies on the formation process of Z-pinch dynamic hohlruams and key issues of optimizing dynamic hohlraum radiation

Dynamic hohlraum is a possible selection to drive inertial confinement fusion. Currently, the ~8 MA PTS facility in China has been completed, which provides a powerful experimental platform of relatively large drive current for researches of dynamic hohlraums and dynamic hohlraum driven inertial fusion. To understand the formation processes and the main characteristics of the dynamic hohlraum, and explore the most important issues affecting the optimization of hohlraum radiation, is not only fundamental in the research of dynamic hohlraums, especially for the experimental design, but also can provide a physical insight for the experimental diagnosis. In this paper the implosion dynamics of a tungsten wire-array Z-pinch embedded with a CH foam converter, especially the impaction interaction of the wire-array plasma with the converter plasma, is numerically investigated using a one-dimensional non-equilibrium radiation magnetohydrodynamic code. In simulations the tungsten plasma is assumed as a plasma shell with a width of 1 mm, and the CH converter plasma is assumed to be uniform with an initial temperature of 0.1 eV. The overall implosion is driven by an assumed current with a peak value of 8 MA and a rise time of 66.4 ns. It is shown that a local high pressure region, which is generated by the impaction of the tungsten plasma with the converter plasma, is crucial to launch the strongly radiating shock wave and to form the dynamic hohlraum. Due to the supersonic radiation transfer in the low opacity CH converter plasma, which is also produced in the high pressure region, there exists a hohlraum region inside the front of the shock wave, in which the radiation is high. At the same time, the plasma pressure is uniform in this hohlraum region, so the plasma will not be disturbed before the shock arrives. As the shock propagates to the axis, the hohlraum becomes small and the radiation temperature is also increased. Basically, the hohlraum radiation is determined by the detailed profiles of plasma conditions when the wire-array plasma impacts onto the CH converter plasma. And these profiles are determined by many factors, such as the drive current, initial masses and radii of the wire-array and the converter, as well as the material of the converter. When the drive current is fixed, the optimal wire-array can be determined. Firstly, the mass ratio of the wire-array to the CH converter is varied. Numerical calculations show that as this ratio is decreased, the shock velocity is increased and the radiation temperature is increased as well. Additionally, the time duration of the radiation pulse before the shock arrives at the axis is remarkably increased. It is also found that when this mass ratio is slightly lower than unity, for example 0.75, a relative optimal dynamic hohlraum can be produced. Secondly, if the mass ratio is fixed and the initial radius of the converter is decreased, it is found that the shock velocity is just slightly changed. However, the peak hohlraum radiation temperature is increased and the radiation pulse becomes remarkably narrow. A suitable radius ratio of the wire-array to the converter, neither too large to induce strong Magneto-Rayleigh-Taylor (MRT) instability nor too small to gain a small kinetic energy of the wire-array before impacting onto the converter surface, should be selected. In the future we will develop two-dimensional code to investigate the effect of MRT instability on the formation of dynamic hohlraums.

Mitigation of Instabilities in a Z-Pinch Plasma by a Preembedded Axial Magnetic Field

The effects of an axial magnetic field on the development of instabilities during a z-pinch implosion are studied using 2-D images and interferometry. The measurements clearly show mitigation of magneto Rayleigh-Taylor instabilities with increased magnitude of the preembedded axial magnetic field. Introducing the axial magnetic field also gives rise to new structures, indicating an interaction between the azimuthal and axial fields.