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Measurements of magneto-Rayleigh–Taylor instability growth during the implosion of initially solid metal liners a)
a)Paper UI3 3, Bull. Am. Phys. Soc. 55, 332 (2010).
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View: Figures


Image of FIG. 1.

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FIG. 1.

(Color) Color-coded density contours from a 2D simulation of a beryllium liner near the start of the current pulse (t1), midway (t2), and close to stagnation on axis (t3). The liner has an initial outer radius to thickness ratio of 6 and a 60 nm surface roughness amplitude. Though prominent bubble-spike structures develop due to the magneto-Rayleigh–Taylor instability, the inside liner surface remains intact enough to compress fusion fuel to obtain about 86% of the 1D simulated yield (Ref. 6).

Image of FIG. 2.

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FIG. 2.

(Color) Description of the hardware used during the experiments. (a) Half-section diagram of the power-feed hardware surrounding the load. (b) Photograph of the return-current can and liner as installed in the Z facility. (c) Schematic of the two-frame backlighter illustrating the 3∘ angle above/below horizontal. In the one-frame system only a single laser target and crystal are used, which are all positioned to lie in the horizontal plane passing through the midheight of the target.

Image of FIG. 3.

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FIG. 3.

(Color) Measured load currents from the Al target experiments. The radiograph times are overlaid as vertical bars. Slightly different machine configurations were used during the two experimental series, resulting in a slightly higher peak current and larger foot during series 2.

Image of FIG. 4.

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FIG. 4.

(Color) Analysis of a preshot radiograph from z1965 demonstrating the spatial resolution of the two-frame 6.151 keV backlighter. (a) Radially stretched radiograph image of the edge of the liner showing the machined sinusoidal perturbations. (b) Lineout through the radiograph image at the position indicated by the red bars demonstrating a 10%–90% edge-spread width of about 15 μm.

Image of FIG. 5.

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FIG. 5.

Example x-ray characterization radiographs of Al and Be targets. (a) Whole body 85 keV Al target radiograph (series 1) showing the 2 mm diameter W rod on axis. (b) High-magnification view of the liner wall showing the machined perturbations. (c) Magnified 65 keV image of a uniform-thickness section of a Be target. (d) Magnified view of the same Be target in a region with thickness variations.

Image of FIG. 6.

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FIG. 6.

(Color) Example surface profile data from Al and Be targets. (a) Contour plot of Al surface profile. (b) 3D version of the same data. (c) Higher-resolution image of Al surface profile (from a test piece), in which the expected 1.25 μm machining grooves are visible. (d) Contour plot of Be surface profile. (e) Higher-resolution image of Be surface profile. (f) 3D version of the same data. Note the change in contour plot amplitude units from nanometers to micrometers in going from Al to Be.

Image of FIG. 7.

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FIG. 7.

(Color) Al liner data obtained during series 1. (a) Optical photo of the liner target installed in Z. (b) 6.151 keV radiograph of the central 4 mm height of the liner target. Six λ =400 μm perturbations range from 1.6 to 4 mm axially and six λ =200 μm perturbations range from 0.4 to 1.6 mm axially. The axial region from 0 to 0.4 mm was unperturbed. (c) Expanded views of the two liner edges from a preshot radiograph and eight frames taken during the current pulse (Fig. 3) at 30.5, 42.7, 45.8, 57.0, 63.6, 67.7, 79.0, and 83.0 ns, respectively. The radiographs have been cropped and rotated so that the z-axis is horizontal.

Image of FIG. 8.

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FIG. 8.

(Color) Al liner data obtained during series 2 using the single-frame 6.151 keV backlighter. The MRT instability was seeded in the upper half of the targets (2–4.2 mm) with various sinusoidal perturbations. The rest of the target was machined as smooth as possible. (a) Full radiograph image from z2102 (t = 47.8 ns), taken when the ablation jets were well-defined. (b) Full radiograph image from z2064 (t = 75.4 ns), taken at a later time in the implosion.

Image of FIG. 9.

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FIG. 9.

(Color) Expanded views of the z2064 radiograph data shown in Fig. 8. The images shown have been cropped and rotated so that the z-axis is horizontal. (a) Diagram illustrating the position and amplitudes of the sinusoidal perturbations applied to the 2–4.2 mm region of the target. Note the distorted vertical scale. (b) Left and right side radiograph images of the perturbed region of the target. A red line shows the initial liner contour from part (a) on the scale of the image. (c) Left and right side radiograph images of the unperturbed region of the target. Note the decreased azimuthal symmetry relative to (b).

Image of FIG. 10.

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FIG. 10.

(Color) Beryllium liner data obtained during shot z2060 of series 3. (a) Radiograph image taken at t = 90.4 ns. (b) Radiograph image taken at t = 105.4 ns. The initial liner outer and inner radii are indicated by the vertical green and red bars, respectively. (c) Horizontal lineout through the radiographs showing the average transmission as a function of horizontal distance. To indicate the symmetry of the data, the transmission lines were flipped about the zero axis and replotted as dashed lines. Note that the opaque region on the axis of the radiographs is caused by two of the eight return-current posts surrounding the load, not the on-axis tungsten rod.

Image of FIG. 11.

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FIG. 11.

(Color) Analysis of the λ =400 μm data from series 1. The peak-to-valley amplitude vs time measured from the experiments is plotted as black crosses, where the extent of the crosses represents the measurement error. The green squares are the equivalent from LASNEX simulations. The dashed lines are various solutions to Eq. (1) obtained using a growing exponential approximation (red), a cosh function approximation (magenta), or a direct integration of the equation (cyan) as discussed in the text.

Image of FIG. 12.

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FIG. 12.

Comparison of experimental radiographs of Al liners from series 1 (Fig. 7) and simulated radiographs calculated from a 3D GORGON simulation.

Image of FIG. 13.

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FIG. 13.

(Color) Analysis of Be liner radiographs from series 3. The top plot indicates when the radiographs were taken relative to the current. The bottom plot compares the radial density profiles inferred from an Abel inversion of the data in Fig. 10 with profiles from 3D GORGON simulations. The initial density is also shown for comparison.


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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.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Measurements of magneto-Rayleigh–Taylor instability growth during the implosion of initially solid metal liners a)