magneto-Rayleigh-Taylor Instability Research Articles

Modified helix-like instability structure on imploding z-pinch liners that are pre-imposed with a uniform axial magnetic field

Recent experiments at the Sandia National Laboratories Z Facility have, for the first time, studied the implosion dynamics of magnetized liner inertial fusion (MagLIF) style liners that were pre-imposed with a uniform axial magnetic field. As reported [T. J. Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] when premagnetized with a 7 or 10 T axial field, these liners developed 3D-helix-like hydrodynamic instabilities; such instabilities starkly contrast with the azimuthally correlated magneto-Rayleigh-Taylor (MRT) instabilities that have been consistently observed in many earlier non-premagnetized experiments. The helical structure persisted throughout the implosion, even though the azimuthal drive field greatly exceeded the expected axial field at the liner's outer wall for all but the earliest stages of the experiment. Whether this modified instability structure has practical importance for magneto-inertial fusion concepts depends primarily on whether the modified instability structure is more stable than standard azimuthally correlated MRT instabilities. In this manuscript, we discuss the evolution of the helix-like instability observed on premagnetized liners. While a first principles explanation of this observation remains elusive, recent 3D simulations suggest that if a small amplitude helical perturbation can be seeded on the liner's outer surface, no further influence from the axial field is required for the instability to grow.

Laser shadowgraphy diagnostics for insulated-ordinary mixed planar wire array Z pinches

A laser shadowgraphy system was built based on a Nd:YAG laser backlight with a half width of 9 ns and a wavelength of 532 nm. It has the capacity of time resolution and integration simultaneously during the laser lighting time by utilizing a streak camera and a commercial digital camera as the image recording devices. Experimental study of the insulated-ordinary mixed planar wire array Z pinches was carried out on the Qiangguang-I facility. Experimental results indicate that the expansion of corona plasma of the insulated tungsten wires is slower than that of ordinary wires over the ablation stage. Average velocities of the insulated wire and the ordinary wire located at the array outmost edge are 1.1×104 m·s-1 and 1.7×104 m·s-1 between t=44 ns and t=56 ns respectively. In the fastest implosion stage of 10 ns just before the stagnant time, the average imploding velocities were 5.5×105 m·s-1 and 9.3×105 m·s-1 respectively for the plasma on the insulted wires side and the ordinary wires side. The duration of stagnant stage on the insulated wires side is 5.9 ns, while it is 9.5 ns on the ordinary wires side. The collision boundary is deflected to the insulated wires side. A similar magneto Rayleigh-Taylor Instability structure can be observed on the both sides at the stagnant time.

Simulation and mitigation of the magneto-Rayleigh-Taylor instabilities in Z-pinch gas discharge extreme ultraviolet plasma radiation sources

The development and use of a single-fluid two-temperature approximated 2-D Magneto-Hydrodynamics code is reported. Z-pinch dynamics and the evolution of Magneto-Rayleigh-Taylor (MRT) instabilities in a gas jet type Extreme Ultraviolet (EUV) source are investigated with this code. The implosion and stagnation processes of the Z-pinch dynamics and the influence of initial perturbations (single mode, multi- mode, and random seeds) on MRT instability are discussed in detail. In the case of single mode seeds, the simulation shows that the growth rates for mm-scale wavelengths up to 4 mm are between 0.05 and 0.065 ns−1. For multi-mode seeds, the mode coupling effect leads to a series of other harmonics, and complicates MRT instability evolution. For perturbation by random seeds, the modes evolve to longer wavelengths and finally converge to a mm-scale wavelength approximately 1 mm. MRT instabilities can also alter the pinch stagnation state and lead to temperature and density fluctuations along the Z axis, which eventually affects the homogeneity of the EUV radiation output. Finally, the simulation results are related to experimental results to discuss the mitigations of MRT instability.

Electrothermal instability growth in magnetically driven pulsed power liners

This paper explores the role of electro-thermal instabilities on the dynamics of magnetically accelerated implosion systems. Electro-thermal instabilities result from non-uniform heating due to temperature dependence in the conductivity of a material. Comparatively little is known about these types of instabilities compared to the well known Magneto-Rayleigh-Taylor (MRT) instability. We present simulations that show electrothermal instabilities form immediately after the surface material of a conductor melts and can act as a significant seed to subsequent MRT instability growth. We also present the results of several experiments performed on Sandia National Laboratories Z accelerator to investigate signatures of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns risetime current pulse. These experiments show excellent agreement with electrothermal instability simulations and exhibit larger instability growth than can be explained by MRT theory alone.

Radiation characteristics and implosion dynamics of tungsten wire array Z-pinches on the YANG accelerator

We investigated the radiation characteristics and implosion dynamics of low-wire-number cylindrical tungsten wire array Z-pinches on the YANG accelerator with a peak current 0.8–1.1 MA and a rising time ∼ 90 ns. The arrays are made up of (8–32) × 5 μm wires 6/10 mm in diameter and 15 mm in height. The highest X-ray power obtained in the experiments was about 0.37 TW with the total radiation energy ∼ 13 kJ and the energy conversion efficiency ∼ 9% (24 × 5 μm wires, 6 mm in diameter). Most of the X-ray emissions from tungsten Z-pinch plasmas were distributed in the spectral band of 100–600 eV, peaked at 250 and 375 eV. The dominant wavelengths of the wire ablation and the magneto-Rayleigh—Taylor instability were found and analyzed through measuring the time-gated self-emission and laser interferometric images. Through analyzing the implosion trajectories obtained by an optical streak camera, the run-in velocities of the Z-pinch plasmas at the end of the implosion phase were determined to be about (1.3–2.1) × 107 cm/s.

Influence of induced axial magnetic field on plasma dynamics and radiative characteristics ofZpinches

The influence of an induced axial magnetic field on plasma dynamics and radiative characteristics of Z pinches is investigated. An axial magnetic field was induced in a novel Z-pinch load: a double planar wire array with skewed wires (DPWAsk), which represents a planar wire array in an open magnetic configuration. The induced axial magnetic field suppressed magneto-Rayleigh-Taylor (MRT) instabilities (with m = 0 and m = 1 instability modes) in the Z-pinch plasma. The influence of the initial axial magnetic field on the structure of the plasma column at stagnation was manifested through the formation of a more uniform plasma column compared to a standard double planar wire array (DPWA) load [V. L. Kantsyrev et al., Phys. Plasmas 15, 030704 (2008)]. The DPWAsk load is characterized by suppression of MRT instabilities and by the formation of the sub-keV radiation pulse that occurs before the main x-ray peak. Gradients in plasma parameters along the cathode-anode gap were observed and analyzed for DPWAsk loads made from low atomic number Z (Al) and mid-Z (brass) wires.

Anisotropy and feedthrough in magneto-Rayleigh-Taylor instability

The magneto-Rayleigh-Taylor instability (MRT) of a finite slab is studied analytically using the ideal MHD model. The slab may be accelerated by an arbitrary combination of magnetic pressure and fluid pressure, thus allowing an arbitrary degree of anisotropy intrinsic to the acceleration mechanism. The effect of feedthrough in the finite slab is also analyzed. The classical feedthrough solution obtained by Taylor in the limit of zero magnetic field, the single interface MRT solution of Chandrasekhar in the limit of infinite slab thickness, and Harris' stability condition on purely magnetic driven MRT, are all readily recovered in the analytic theory as limiting cases. In general, we find that MRT retains robust growth if it exists. However, feedthrough may be substantially reduced if there are magnetic fields on both sides of the slab, and if the MRT mode invokes bending of the magnetic field lines.

Measurements of magneto-Rayleigh–Taylor instability growth during the implosion of initially solid metal liners

A recent publication [D. B. Sinars et al., Phys. Rev. Lett. 105, 185001 (2010)] describes the first controlled experiments measuring the growth of the magneto-Rayleigh–Taylor instability in fast (∼100 ns) Z-pinch plasmas formed from initially solid aluminum tubes (liners). Sinusoidal perturbations on the surface of these liners with wavelengths of 25–400 μm were used to seed single-mode instabilities. The evolution of the outer liner surface was captured using multiframe 6.151 keV radiography. The initial paper shows that there is good agreement between the data and 2-D radiation magneto-hydrodynamic simulations down to 50 μm wavelengths. This paper extends the previous one by providing more detailed radiography images, detailed target characterization data, a more accurate comparison to analytic models for the amplitude growth, the first data from a beryllium liner, and comparisons between the data and 3D simulations.

Computational investigation of the magneto-Rayleigh–Taylor instability in Z-pinch implosions

The instability evolvement induced by single mode and random density seeds have been investigated by using the Magnetics Atom Radiation Electron Dynamics (MARED) code, which is a two dimensional, three temperature, radiation magnetohydrodynamic Lagrangian code developed for the Z-pinch implosion simulation. The instability development during each stage (linear, weak nonlinear, and nonlinear) and its corresponding characteristics are studied with single-mode seeds. The evolvement of the dominant mode and its final wavelength are revealed through the development of seeds composed of modes covering the “whole” spectrum or just a “band-type” range of it. In addition, the relationship between the initial perturbation amplitude and the final x-ray output are also discussed. Through these discussions, the MARED code is found able to reproduce the primary dynamic characteristics of the Z-pinch implosions and the development of the instability qualitatively agrees with the theoretical analyses and experimental observations, which shows us a modest expectation of the broad coverage of the future application.

Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field

The radial convergence required to reach fusion conditions is considerably higher for cylindrical than for spherical implosions since the volume is proportional to r2 versus r3, respectively. Fuel magnetization and preheat significantly lowers the required radial convergence enabling cylindrical implosions to become an attractive path toward generating fusion conditions. Numerical simulations are presented indicating that significant fusion yields may be obtained by pulsed-power-driven implosions of cylindrical metal liners onto magnetized (>10 T) and preheated (100–500 eV) deuterium-tritium (DT) fuel. Yields exceeding 100 kJ could be possible on Z at 25 MA, while yields exceeding 50 MJ could be possible with a more advanced pulsed power machine delivering 60 MA. These implosions occur on a much shorter time scale than previously proposed implosions, about 100 ns as compared to about 10 μs for magnetic target fusion (MTF) [I. R. Lindemuth and R. C. Kirkpatrick, Nucl. Fusion 23, 263 (1983)]. Consequently the optimal initial fuel density (1–5 mg/cc) is considerably higher than for MTF (∼1 μg/cc). Thus the final fuel density is high enough to axially trap most of the α-particles for cylinders of approximately 1 cm in length with a purely axial magnetic field, i.e., no closed field configuration is required for ignition. According to the simulations, an initial axial magnetic field is partially frozen into the highly conducting preheated fuel and is compressed to more than 100 MG. This final field is strong enough to inhibit both electron thermal conduction and the escape of α-particles in the radial direction. Analytical and numerical calculations indicate that the DT can be heated to 200–500 eV with 5–10 kJ of green laser light, which could be provided by the Z-Beamlet laser. The magneto-Rayleigh-Taylor (MRT) instability poses the greatest threat to this approach to fusion. Two-dimensional Lasnex simulations indicate that the liner walls must have a substantial initial thickness (10–20% of the radius) so that they maintain integrity throughout the implosion. The Z and Z-Beamlet experiments are now being planned to test the various components of this concept, e.g., the laser heating of the fuel and the robustness of liner implosions to the MRT instability.

Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows

A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the compressible Z-pinch plasma with axial flow is presented. Comparing with results of incompressible models, compressibility can reduce the growth rate of the magneto-Rayleigh-Taylor (MRT)/Kelvin-Helmholtz (KH) instability and allow sheared axial flows to mitigate the MRT instability far more effectively. The effect of magnetic field, which cannot be detected in an incompressible model, is also investigated. The result indicates that the mitigation effect of magnetic field on the MRT instability becomes significant as the perturbation wave-number increases. Therefore, with the cooperation of sheared axial flow, magnetic field, and plasma compressibility, the stability of the Z-pinch plasma is improved remarkably. In addition, the analysis also suggests that in an early stage of the implosion, because the plasma temperature is relatively low, the compressible model is much more suitable than the incompressible one based on the framework of MHD theory.

Measurements of the mass distribution and instability growth for wire-array Z-pinch implosions driven by 14–20 MA

The mass distribution and axial instability growth of wire-array Z-pinch implosions driven by 14–20 MA has been studied using high-resolution, monochromatic x-ray backlighting diagnostics. A delayed implosion is consistently observed in which persistent, dense wire cores continuously ablate plasma until they dissipate and the main implosion begins. In arrays with small interwire gaps, azimuthally correlated axial instabilities appear during the wire ablation stage and subsequently seed the early growth of magneto-Rayleigh–Taylor instabilities. The instabilities create a distributed implosion front with trailing mass that may limit the peak radiation power.

Experimental studies of Z-pinches of mixed wire array with aluminum and tungsten

In the form of joint experiment between China and Russia, the experimental studies of Zpinches of mixed wire array of aluminum (A1) and tungsten (W) were carried out on S-300 generator,which was located on Kurchatov Institute of Russia. The experimental results were compared with those of single A1 array and single W array, respectively. There are obvious difference between mixed one and single one in their photon spectral distributions. The intensity of K-series emission lines from the mixed wire array Z-pinch is lower than that from single A1 array. The radiated lines with wavelengths less than 1.6nm were not found in single W array Z-pinches. In the Z-pinch processes, the area radiating x-arys in mixed wire array is smaller than that of single A1 array, but is larger than that of single W array. The radiated energy from mixed wire array Z-pinch is higher than that from single A1 array, but is slightly lower than that from single W array. The FWHM of x-ray pulse with a maximal power 0.3—0.5TW and total energy 10—20kJ is about 25ns, which radiated from Z-pinches with a radial convergence of 4—5 on S-300 generator. The shadow photograph of the mixed wire-array Z-pinch plasma by laser probe shows that the core-corona configuration was formed and the corona was moving toward the center axis during the wire-array plasma formation, that the interface of the plasma is not clear, and that therer are a number of structures inside. They also suggests that there was an obvious development of Magneto Rayleigh-Taylor instability in the Z-pinch process as well.

The magneto-Rayleigh–Taylor instability in dynamic z pinches

The magneto-Rayleigh–Taylor (MRT) instability limits the performance of dynamic z pinches. This instability develops at the plasma-vacuum/field interface, growing in amplitude throughout the implosion, thereby reducing the peak plasma velocity and spatial uniformity at stagnation. MRT instabilities are believed to play a dominant role in the case of high wire number arrays, gas puffs and foils. In this article, the MRT instability is discussed in terms of initial seeding, linear and nonlinear growth, experimental evidence, radiation magnetohydrodynamic simulations, and mitigating schemes. A number of experimental results are presented, where the mitigating schemes have been realized. In general, the problem is inherently three dimensional, but two-dimensional simulations together with theory and experiment enhance our physical understanding and provide insight into future load design.

Dynamics and stability of twisted-wire arrays

A multiwire screw pinch, a variant of a z -pinch load, is proposed as a means for further improvement of load performance for high-current 100-ns pulsed-power generators used for terawatt X-ray radiation. Wires twisted along a curved load surface are suggested to be an effective way to create an axial magnetic field and to generate and to maintain rotation of the subsequently formed plasma shell due to conservation of angular momentum. A multiwire screw pinch is predicted to mitigate the growth of the magneto-Rayleigh–Taylor instabilities, to provide a higher pinch compression ratio and more effective X-ray generation compared to classical z -pinch loads. A model based on the self-consistent simulation of the dynamics of a twisted plasma shell and the development of Rayleigh–Taylor (R-T) perturbations on a plasma surface is proposed to quantitatively study the effect of various physical factors on the generation of X rays. The model provides us with a tool for the analysis of processes that occur during the implosion of the plasma-shell–wire-core system. We plan for the R-T perturbations to break through the plasma shell at the moment when the internal radius of a shell becomes zero, where the greatest possible values of kinetic energy and X-ray radiation power ought to be obtained. The results of numerical simulations for the Sandia National Laboratories' Z generator are presented and discussed.

The dynamics of wire array Z-pinch implosions

Wire array Z-pinch dynamics are studied in experiments with 16-mm diameter arrays of between 8 and 64, 15-μm diameter aluminum wires, imploded in 200–260 ns by a 1.4-MA current pulse. Side-on laser probing shows early development of noncorrelated m=0-like instabilities with an axial wavelength ∼0.5 mm in individual wires. End-on interferometry (r-θ plane) shows azimuthal merging of the plasma with a density of 1017 cm−3 in 90–65 ns for 8–64 wires, respectively. At the same time low-density plasma reaches the array axis and forms a precursor pinch by 120–140 ns. At 0.7–0.85 of the implosion time a global m=0 instability with a wavelength of 1.7–2.3 mm was detected in soft x-ray gated images, laser probing, and optical streaks. The time when the instability reaches the observable level corresponds to the number of e-foldings for the growth of the classical Rayleigh–Taylor instability of ∫γ dt∼5.6–7. The scaling of this number with the number of wires is consistent with the instability growth from the seed level determined by the averaging of uncorrelated density perturbations in individual wires. Preliminary results from a 4×4 array permit the simultaneous observation by laser probing of the characteristic bubble and spike structure of the magneto Rayleigh–Taylor instability.

High yield inertial confinement fusion target design for a z-pinch-driven hohlraum

Calculations are presented for a high yield inertial fusion design, employing indirect drive with a double-ended z-pinch-driven hohlraum radiation source. A high current (∼60 MA) accelerator implodes z pinches within an enclosing hohlraum. Radial spoke arrays and shine shields isolate the capsule from the pinch plasma, magnetic field, and direct x-ray shine. Our approach places minimal requirements on z-pinch uniformity and stability, usually problematic due to magneto-Rayleigh–Taylor instability. Large inhomogeneities of the pinch and spoke array may be present, but the hohlraum adequately smooths the radiation field at the capsule. Simultaneity and reproducibility of the pinch x-ray output to better than 7% are required, however, for good symmetry. Recent experiments suggest a pulse shaping technique, through implosion of a multishell z pinch. X-ray bursts are calculated and observed to occur at each shell collision. A capsule absorbing 1 MJ of x rays at a peak drive temperature of 210 eV is found to have adequate stability and to produce 400 MJ of yield. A larger capsule absorbs 2 MJ with a yield of 1200 MJ.

Two-dimensional radiation-magnetohydrodynamic simulations of SATURN imploding Z pinches

Z-pinch implosions driven by the SATURN device [D. D. Bloomquist et al., Proceedings of the 6th Institute of Electrical and Electronics Engineers (IEEE) Pulsed Power Conference, Arlington, VA, edited by P. J. Turchi and B. H. Bernstein (IEEE, New York, 1987), p. 310] at Sandia National Laboratory are modeled with a two-dimensional radiation magnetohydrodynamic (MHD) code, showing strong growth of the magneto-Rayleigh–Taylor (MRT) instability. Modeling of the linear and nonlinear development of MRT modes predicts growth of bubble-spike structures that increase the time span of stagnation and the resulting x-ray pulse width. Radiation is important in the pinch dynamics, keeping the sheath relatively cool during the run-in and releasing most of the stagnation energy. The calculations give x-ray pulse widths and magnitudes in reasonable agreement with experiments, but predict a radiating region that is too dense and radially localized at stagnation. We also consider peaked initial density profiles with constant imploding sheath velocity that should reduce MRT instability and improve performance. Krypton simulations show an output x-ray power ≳80 TW for the peaked profile.