Wire Array Implosions Research Articles

Investigation of Electromagnetic-Flute-Mode Instability in a High-Beta$Z$-Pinch Plasma

Recent experiments (laser multiframe shadowgraphy and Faraday rotation diagnostics) with Al imploding wire arrays in the 1-MA Zebra accelerator at the Nevada Terawatt Facility have demonstrated that a significant amount of current is going through the central region of the high-beta precursor plasma. With time, the perturbations develop both long scale structures and short-wavelength oscillations in the directions perpendicular to the magnetic field. The most likely candidate for the observed phenomena is the flutelike electromagnetic modes. These are excited in the current-carrying high-beta inhomogeneous precursor plasma due to the curvature of the magnetic field produced by the current. These modes may also play a role in the stagnation phase of Z-pinches. In this paper, nonlinear equations describing electromagnetic-flute-type oscillations in the high-beta precursor plasma are derived, and the linear stage of instability of these waves is examined. A comparison with the experimental results is performed as well

Dynamics of Mass Transport and Magnetic Fields in Low-Wire-Number-ArrayZPinches

The dynamics of mass transport were observed in a wire array implosion with multiframe laser probing. Plasma bubbles arise at breaks in the wires. Interferometry shows that the leading edge of the bubbles brings material to the axis of the array. The speed of this material was measured to be > or =3 x 10(7) cm/s during the wire array implosion. A shock was observed during the collision of the bubbles with the precursor. The Faraday effect indicates current flowing in breaks on the wires. The current switches from the imploding mass to the on-axis plasma column at the beginning of the x-ray pulse.

Experiments on the implosion of heterogeneous wire arrays on the S-300 facility

Results are presented from experiments on the implosion of simple and nested wire arrays of different mass and material composition (W and/or Al). The experiments were performed on the S-300 facility (a high-current pulsed power generator with a voltage pulse amplitude of 700 kV, current amplitude of 2.5–3.5 MA, and pulse duration of 100 ns) at the Kurchatov Institute (Moscow). The imploding arrays were recorded using five-frame laser shadowgraphy, three-frame image-tube photography, an optical streak camera, X-ray pinhole cameras with different filters, X-ray polychromator, and X-ray spectrometer on the basis of a convex mica crystal. Laser probing measurements indicate that the current-carrying structure undergoes a fast (over a time shorter than 10 ns) global rearrangement, which manifests itself as the emergence of transparent regions. This effect is presumably related to the grouping of the wires, which carry currents of a few tens of kiloamperes, or to the current filamentation in their common plasma corona. The radiation of liners of different chemical composition in the final compressed state has been investigated. Electric measurements performed in experiments with nested arrays (e.g., with an aluminum outer liner and a tungsten inner liner) indicate that the inner array, which is still at rest, intercepts the electric current from the outer array when the latter penetrates through it. The effect of the “fall” of the outer liner through the inner one in the course of magnetic implosion has been revealed for the first time by analyzing X-ray emission spectra.

Studies of the distribution of the Z-pinch radiance during the implosion of wire arrays in the angara-5-1 facility

Results are presented from time-integrated measurements of soft X-ray emission from Z-pinches during the implosion of simple and nested wire arrays. The blackening density distribution obtained with the help of a pinhole camera is recalculated into the time-integrated Z-pinch radiance. It is found that, in the case of a simple wire array, up to 70% of the total SXR energy emitted during a discharge is radiated from the axial region, the rest of energy being radiated from plasma jets, whereas in the case of a nested wire array, more than 90% of the SXR energy is radiated from the axial region.

A model for ablated-plasma distribution and width for wire-array Z-pinch implosions

A one-dimensional radial magnetohydrodynamic model of the plasma ablated from a multi-MA wire-array Z pinch is developed. The model is used to compute the mass weighted-density width δ of the plasma at the end of the ablation phase. The wire-array cores are represented as a prescribed source of plasma injection. The plasma, beyond a thin boundary layer, is approximated as a perfect conductor experiencing only magnetic forces and negligible pressure gradients. Assuming that the current driving the Z-pinch implosion increases linearly with time t during the ablation phase, and that the mass-ablation rate varies as tν, it is shown that the density width δ is a function of the dimensionless parameter λ=ua(ta)ta∕r0, where ua is the ablation velocity, ta is the total ablation time, and r0 is the initial wire-array radius. The velocity ua is defined such that its product with the mass-ablation rate equals the magnetic force at r0, which is assumed to be the mass injection point. A solution is obtained for the plasma flow in semianalytical form when the current is an exponential function of time, and ua is constant. The ablated plasma density width δ obtained under these two sets of conditions is compared. In addition, assuming that the plasma sheath at stagnation is proportional to the width δ, scaling relationships for the peak x-ray power radiated when the pinch stagnates on axis are suggested.

Measurement and modeling of the implosion of wire arrays with seeded instabilities

In order to study wire array Z-pinch instabilities, perturbations have been seeded by etching 15μm diameter aluminum wires to introduce 20% modulations in radius with a controlled axial wavelength. These perturbations seed additional imploding structures that are studied experimentally on the 1MA, 250ns MAGPIE generator [S. V. Lebedev et al., Plasma Phys. Control. Fusion 47, A91 (2005)] and with three-dimensional magnetohydrodynamic calculations using the ALEGRA-HEDP [A. C. Robinson and C. J. Garasi, Comput. Phys. Commun. 164, 408 (2004)] and GORGON [J. P. Chittenden et al., Plasma Phys. Control. Fusion 46, B457 (2004)] codes. Simulations indicate that current path nonuniformity at discontinuities in the wire radius result in perturbation-induced magnetic bubble formation. Imploding bubbles originating from discontinuities are observed experimentally, and their collision on axis determines the start of the main x-ray pulse rise. These mechanisms likely govern dynamics of standard wire array Z pinches, and tailoring the profile of imploding mass may allow x-ray pulse shaping for inertial confinement fusion applications.

Models of radiation yield from wire array implosion at 1MA Zebra generator

The snowplow and thin shell models that have the analytical solutions in zero dimensions are linked with the ideal magnetohydrodynamic (MHD) and radiation MHD codes to calculate the radiation yield from the imploding wire array loads at 1MA Zebra generator. Radiation MHD simulations show that the strong radiation cooling affects plasma dynamics at all stages of the implosion and drives plasma into the radiative collapse at the final stage of the implosion. Being applied to the implosion of an Al wire array with the mass per unit length 3.82μg∕mm, these simulations show that the thermalization of the kinetic energy can be essentially completed when the radius of the imploding pinch shrinks below ∼10μm. If we assume such a perfect compression, then the plasma energy gain will be 10kJ with total radiation yield of about 5kJ, while the emitted radiation spectrum will be blackbody-like with an equilibrium temperature of 200eV. The only effective mechanism of energy coupling for the imploding plasma, driven by the magnetic piston, is the inductive work of the magnetic field due to the motional impedance. However, the mechanism of anomalous plasma heating, acting in the plasma fraction that was left behind the collapsing current sheath, can couple additional energy into the plasma and can explain the variety of radiation performance features. An adequate model of the radiation yield should consider the stagnating z pinch as an object with strong density and temperature gradients.

Radiation properties and implosion dynamics of planar and cylindrical wire arrays, asymmetric and symmetric, uniform and combined X-pinches on the UNR 1-MA zebra generator

In the following experiments, we studied implosions of different wire arrays and X-pinches produced on the 1-MA Zebra generator at the University of Nevada, Reno. Diagnostics included both spatially-resolved and time-gated X-ray imaging and spectroscopy, and laser probing. In particular, we compared planar wire arrays, to which little energy could be coupled via the conventional magnetic-to-kinetic conversion mechanism, to cylindrical wire arrays of comparable dimensions and mass. The planar wire arrays were shown to radiate much higher peak power and more energy in subkiloelectronvolt and kiloelectronvolt spectral ranges than cylindrical wire arrays. We tested the theoretical conjecture that enhanced resistivity due to the small-scale inhomogeneity of wire-array plasmas has a major effect on dynamics, energy coupling and radiation performance of wire-array Z-pinches. The study of Al, Alumel, and W cylindrical wire arrays shows a wide variety of characteristic behaviors in plasma implosions discussed hereinafter. Additional experimental results for symmetric and asymmetric, uniform stainless steel, Cu, Mo, combined Al/Mo, Mo/Al, Al/W, W/Al, and Mo/W X-pinches are also presented. New data for the total radiation yield are obtained. The planar structures of X-pinch plasma and the corresponding electron beam was observed for most of X-pinches. The generation of hot spots along original wires positions-cooler than those from the cross-wire region-and arc structures with hot spots between wires were found for X-pinches composed from Al, Cu, and W wires.

Monochromatic X-ray self-emission imaging of imploding wire array Z-pinches on the Z accelerator

A monochromatic X-ray self-emission imaging diagnostic has been developed for the Z accelerator, which drives 20 MA in 100 ns to implode wire array Z-pinches, generating up to 250 TW of soft X-ray radiation. This instrument reflects eight pinhole images from a flat Cr/C multilayer mirror (MLM) onto a 1-ns time-resolved microchannel plate detector. The MLM reflects 277-eV photons with /spl sim/5-eV bandwidth and 20% peak reflectivity, and an aluminized parylene filter shields the detector from visible light. High-energy bremsstrahlung X-rays do not follow the reflected beam path, and so the background on the shielded detector is reduced compared to a standard pinhole camera. The MLM-reflected images offer low-photon-energy spectral resolution that filtration alone cannot, yielding high-quality images of the final stages of the Z-pinch implosion. Initial data on Z from a Cu wire array will be presented. Observed phenomena include implosion instabilities, zippered implosion of a piston onto a precursor column during the onset of stagnation, accretion of trailing colder mass during the X-ray pulse, and cathode reemission. The inferred implosion velocity is significantly less than thin-shell implosion model calculations, and well below what is required for efficient Cu K-shell radiation. Instability-dominated, bright-spot Cu K-shell emission is seen on a second adjacent eight-frame filtered pinhole camera that is in the same beamline.

Investigation of regimes of wire array implosion on the 1MA Zebra accelerator

Implosion of wire arrays was investigated at the 1MA Zebra accelerator by multiframe laser probing and gated x-ray self-emission diagnostics. Different regimes of implosion were observed in Al and Cu wire arrays. Implosion of Al loads with masses of 33–37μg∕cm produces a dense pinch 1–1.5mm in diameter. Strong instabilities are observed in the Z pinch at the time of stagnation. Implosion of “overmassed” loads produces a plasma column 3–4mm in diameter with a core. The plasma column does not collapse during the x-ray pulse. The core of the plasma column is not subjected to the kink instability and transforms to a chain of dense spots in the later stage. Different regimes of implosion were observed in Al 8×15μm loads presumably due to variations in the current pulse and load conditions. Observed regimes are compared to three-dimensional hybrid simulation of ideal and nonideal magnetohydrodynamics modes of implosion.

Study of the magnetic fields and soft X-ray emission generated in the implosion of double wire arrays

Results are presented from measurements of the azimuthal magnetic field generated during the implosion of double (nested) tungsten wire arrays in the Angara-5-1 facility at currents of ∼3 MA. It is found that the inner array affects the current distribution in the interarray space and that there is an optimal mass (an optimal number of wires) of the inner array at which the full width at half-maximum of the soft X-ray pulse (in the photon energy range of >100 eV) is minimal. On the average, double wire arrays provide a better reproductibility, higher power, and shorter duration of the soft X-ray pulse in comparison to single arrays.

Hybrid simulation of the Z-pinch instabilities for profiles generated during wire array implosion in the Saturn pulsed power generator

Experimental evidence suggests that the energy balance between processes in play during wire array implosions is not well understood. In fact the radiative yields can exceed by several times the implosion kinetic energy. A possible explanation is that the coupling from magnetic energy to kinetic energy as magnetohydrodynamic plasma instabilities develop provides additional energy. It is thus important to model the instabilities produced in the after implosion stage of the wire array in order to determine how the stored magnetic energy can be connected with the radiative yields. To this aim three-dimensional hybrid simulations have been performed. They are initialized with plasma radial density profiles, deduced in recent experiments [C. Deeney et al., Phys. Plasmas 6, 3576 (1999)] that exhibited large x-ray yields, together with the corresponding magnetic field profiles. Unlike previous work, these profiles do not satisfy pressure balance and differ substantially from those of a Bennett equilibrium. They result in faster growth with an associated transfer of magnetic energy to plasma motion and hence kinetic energy.

K-shell radiation physics in low- to moderate-atomic-number z-pinch plasmas on the Z accelerator

Dense z-pinches produced by 100 ns implosions of wire arrays or gas puffs produce substantial soft X-ray power. One class of z-pinch radiation sources includes low- to moderate-atomic-number K-shell radiators, such as aluminum and iron. These loads are designed for 1–10 keV K-shell X-ray generation, and offer opportunities for crystal spectroscopy that can reveal fundamental properties of the plasma when studied using plasma spectroscopic modeling. Typically these plasmas are characterized by ion densities of ∼ 10 20 cm - 3 , diameters of 1–5 mm, electron temperatures up to several keV, and a range of opacities of the K-shell lines. Measurements from wire arrays on Sandia's 20 MA Z accelerator are presented along with collisional radiative and hydrodynamic simulations. The impact of opacity and 3D structure on non-LTE, non-diffusive radiation transport and X-ray production is discussed.

Pulsed-power-driven high energy density physics and inertial confinement fusion research

The Z accelerator [R. B. Spielman, W. A. Stygar, J. F. Seamen et al., Proceedings of the 11th International Pulsed Power Conference, Baltimore, MD, 1997, edited by G. Cooperstein and I. Vitkovitsky (IEEE, Piscataway, NJ, 1997), Vol. 1, p. 709] at Sandia National Laboratories delivers ∼20MA load currents to create high magnetic fields (>1000T) and high pressures (megabar to gigabar). In a z-pinch configuration, the magnetic pressure (the Lorentz force) supersonically implodes a plasma created from a cylindrical wire array, which at stagnation typically generates a plasma with energy densities of about 10MJ∕cm3 and temperatures >1keV at 0.1% of solid density. These plasmas produce x-ray energies approaching 2MJ at powers >200TW for inertial confinement fusion (ICF) and high energy density physics (HEDP) experiments. In an alternative configuration, the large magnetic pressure directly drives isentropic compression experiments to pressures >3Mbar and accelerates flyer plates to >30km∕s for equation of state (EOS) experiments at pressures up to 10Mbar in aluminum. Development of multidimensional radiation-magnetohydrodynamic codes, coupled with more accurate material models (e.g., quantum molecular dynamics calculations with density functional theory), has produced synergy between validating the simulations and guiding the experiments. Z is now routinely used to drive ICF capsule implosions (focusing on implosion symmetry and neutron production) and to perform HEDP experiments (including radiation-driven hydrodynamic jets, EOS, phase transitions, strength of materials, and detailed behavior of z-pinch wire-array initiation and implosion). This research is performed in collaboration with many other groups from around the world. A five year project to enhance the capability and precision of Z, to be completed in 2007, will result in x-ray energies of nearly 3MJ at x-ray powers >300TW.

Characteristics and scaling of tungsten-wire-arrayz-pinch implosion dynamics at 20 MA

We present observations for 20-MA wire-array z pinches of an extended wire ablation period of 57%+/-3% of the stagnation time of the array and non-thin-shell implosion trajectories. These experiments were performed with 20-mm-diam wire arrays used for the double- z -pinch inertial confinement fusion experiments [M. E. Cuneo, Phys. Rev. Lett. 88, 215004 (2002)] on the Z accelerator [R. B. Spielman, Phys. Plasmas 5, 2105 (1998)]. This array has the smallest wire-wire gaps typically used at 20 MA (209 microm ). The extended ablation period for this array indicates that two-dimensional (r-z) thin-shell implosion models that implicitly assume wire ablation and wire-to-wire merger into a shell on a rapid time scale compared to wire acceleration are fundamentally incorrect or incomplete for high-wire-number, massive (>2 mg/cm) , single, tungsten wire arrays. In contrast to earlier work where the wire array accelerated from its initial position at approximately 80% of the stagnation time, our results show that very late acceleration is not a universal aspect of wire array implosions. We also varied the ablation period between 46%+/-2% and 71%+/-3% of the stagnation time, for the first time, by scaling the array diameter between 40 mm (at a wire-wire gap of 524 mum ) and 12 mm (at a wire-wire gap of 209 microm ), at a constant stagnation time of 100+/-6 ns . The deviation of the wire-array trajectory from that of a thin shell scales inversely with the ablation rate per unit mass: f(m) proportional[dm(ablate)/dt]/m(array). The convergence ratio of the effective position of the current at peak x-ray power is approximately 3.6+/-0.6:1 , much less than the > or = 10:1 typically inferred from x-ray pinhole camera measurements of the brightest emitting regions on axis, at peak x-ray power. The trailing mass at the array edge early in the implosion appears to produce wings on the pinch mass profile at stagnation that reduces the rate of compression of the pinch. The observation of precursor pinch formation, trailing mass, and trailing current indicates that all the mass and current do not assemble simultaneously on axis. Precursor and trailing implosions appear to impact the efficiency of the conversion of current (driver energy) to x rays. An instability with the character of an m = 0 sausage grows rapidly on axis at stagnation, during the rise time of pinch power. Just after peak power, a mild m = 1 kink instability of the pinch occurs which is correlated with the higher compression ratio of the pinch after peak power and the decrease of the power pulse. Understanding these three-dimensional, discrete-wire implosion characteristics is critical in order to efficiently scale wire arrays to higher currents and powers for fusion applications.

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.

Wire-array implosion onto a deuterated fibre at the S-300 facility

The implosion of a wire array z-pinch onto a deuterated fibre was studied on S-300 facility (4 MA, 700 kV and 100 ns; RRC Kurchatov Institute, Moscow). The peak power of soft X-rays exceeded 200 GW and the total emitted energy was 2–8 kJ. The radiation was close to the radiation of a black body with a temperature of 40 eV. The neutron yield from the D–D reaction reached 2 × 108 per shot. The mean energy of neutrons determined from time-of-flight analysis in the axial direction (downstream) was shifted from 2.45 MeV towards higher energies.

Measurements of the Axial Magnetic Field during the Implosion of Wire Arrays in the Angara-5-1 Facility

Results are presented from measurements of the axial magnetic field during the implosion of tungsten wire arrays in the Angara-5-1 facility at currents of 2.5–4.5 MA. The azimuthal structure of the plasma produced from the wires is examined using the effect of the compression of the axial magnetic flux by this plasma. It is shown that the plasma starts to penetrate into the axial region of the wire array at the very beginning of implosion. A mechanism other than the formation of a closed current-carrying shell is proposed for describing the transfer of the external axial magnetic field to the central region of the array.

Comparison of a copper foil to a copper wire-array Z pinch at 18 MA

Results from the first solid foil implosion on the 18-MA Z accelerator are reported. The foil implosion is compared to a 300-wire-array implosion with the same material and the same diameter, height, and total mass. Though both the foil and the array produced comparable x-ray yields, the array’s radiation burst was twice as powerful and half as long as the foil’s. These data along with x-ray backlighting images and inductance measurements suggest that the foil implosion was more unstable than the wire-array implosion.

Hybrid simulations of Z-pinches

Three-dimensional hybrid simulations with kinetic ions and fluid electrons of Z-pinch plasmas are being used to investigate the linear and nonlinear development of sausage and kink instabilities with model profiles in the presence of effects which go beyond ideal magnetohydrodynamics. In addition, the hybrid simulations are also being applied to model start-up plasmas in long pulse Z-pinch implosions with experimental profiles and parameters. The first study demonstrates that the Hall term is destabilizing even in the presence of an otherwise stabilizing axial magnetic field. The second study shows that the non-equilibrium start-up phase of wire array implosions is characterized by rapid distortions of the plasma column.