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Simulations of electrothermal instability growth in solid aluminum rodsa)
a)Paper QI3 2 Bull. Am. Phys. Soc. , 289 (2012).
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View: Figures


Image of FIG. 1.

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FIG. 1.

Log density contours showing electrothermal instability development from a Cu rod simulation that (a) includes radiation losses and one that (b) does not include radiation losses at the same time.

Image of FIG. 2.

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FIG. 2.

Electrical drive current as a function of time used in all of the simulations. This current history is identical to the inferred VISAR load current measurement in previous Al solid rod experiments.

Image of FIG. 3.

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FIG. 3.

Time sequence of log density contours (g/cc) from a 2D Al rod HYDRA simulation which show instability development after perturbations have already grown by more than a factor of 100 and have become visible at this scale (a) (t = 3 ns, 5 MA), (b) (t = 8 ns, 6.5 MA), (c) (t = 13 ns, 8 MA), (d) (t = 18 ns, 9.5 MA).

Image of FIG. 4.

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FIG. 4.

Axially averaged radial profiles of density (blue curve), magnetic pressure (red curve), material pressure (green curve), total effective pressure (black curve), and current density (magenta curve) corresponding to Fig. 3(b) at time t = 8 ns, 6.5 MA.

Image of FIG. 5.

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FIG. 5.

Plot of the density and temperature phase space for Al that is unstable to the striation form of the electrothermal instability. The boundary between the light and dark gray regions is defined by the density and temperature points in the Al conductivity model where the derivative of resistivity with respect to temperature ( ) changes signs. Superimposed on this plot are points representing temperature and density conditions observed in the 2D HYDRA simulations at t = −7 ns (black circle), t = −2 ns (blue circle), t = 3 ns (red circle), t = 8 ns (green circle), t = 18 ns (magenta circle), and t = 23 ns (cyan circle). The highest density points at each time represent material at the front of the magnetic diffusion wave, while lower density points represent the outermost surface conditions of the rod.

Image of FIG. 6.

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FIG. 6.

Plot of the multi-mode instantaneous growth rate of RMS temperature perturbations (solid line) and RMS density perturbations (dashed line) as a function of radial position at time t = 8 ns, 6.5 MA and corresponds to Fig. 3(b) .

Image of FIG. 7.

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FIG. 7.

Estimated characteristic wavelength scale of electrothermal instabilities for a current density of as a function of density for material temperatures of (red line) 0.025 eV, (green line) 0.09 eV, and (blue line) 0.36 eV. These values were calculated using the same Al conductivity tables used in the HYDRA simulations.

Image of FIG. 8.

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FIG. 8.

Multi-mode time history of spatially averaged (where ) RMS temperature perturbations, (eV) (dashed line) and RMS areal density perturbations, (g/cc) (solid line).

Image of FIG. 9.

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FIG. 9.

Instantaneous multimode growth rate of RMS temperature perturbations shown in Fig. 8 (solid line). Also plotted for comparison are theoretical electrothermal instability growth rates, neglecting thermal conduction, calculated using Eq. (1) and simulated values of current density, material density, and heat capacity spatially averaged in regions with .

Image of FIG. 10.

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FIG. 10.

Log density contours from 2D Al liner simulations with initial shell thicknesses of 500 m, 100 m, 50 m, and 25 m at identical times.

Image of FIG. 11.

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FIG. 11.

Log density contours from 2D Al solid rod simulations with initial radii of 2 mm, 3 mm, 4 mm, and 5 mm at identical times.

Image of FIG. 12.

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FIG. 12.

Log density contours from 2D Al solid rod simulations with current rise times of 50 ns, 100 ns, 150 ns, and 200 ns at a time near peak expansion of the rod when electrothermal instabilities are fully developed in each case.

Image of FIG. 13.

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FIG. 13.

Log density contours of the 2D Al solid rod simulations shown in Fig. 12 but 30 ns later in time and well in MRT stage of instability development.

Image of FIG. 14.

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FIG. 14.

Areal density perturbation as function of time for Al rod simulations with various multipliers on the amplitude of the initial surface roughness.


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A recent publication [K. J. Peterson , Phys. Plasmas , 092701 (2012)] describes simulations and experiments of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns rise time current pulse on Sandia National Laboratories Z accelerator. Quantitative analysis of the high precision radiography data obtained in the experiments showed excellent agreement with simulations and demonstrated levels of instability growth in dense matter that could not be explained by magneto-Rayleigh-Taylor instabilities alone. This paper extends the previous one by examining the nature of the instability growth in 2D simulations in much greater detail. The initial instability growth in the simulations is shown via several considerations to be predominantly electrothermal in nature and provides a seed for subsequent magneto-Rayleigh-Taylor growth.


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Scitation: Simulations of electrothermal instability growth in solid aluminum rodsa)