Ablation stability of laser-driven implosions Page: 3 of 7
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ABLATION STABILITY OF LASER-DRIVEN IMPLOSIONS
D. B. Henderson, R. L. McCrory and R. L. Morse
We extend the perturbation analysis of laser-driven implosions
showing the positive stability of the ablation surface. (The opposite
conclusion has been reported by others).. We present numerical results
from a more complete class of problem. Our conclusions are supported
by general physical arguments.
Recent interest in laser-driven implosion of
spherical pellets of thermonuclear fuel to high
densities has raised important questions about the
symmetry and stability of such implosions. It has
been observed by Henderson and Morsel that small
departures from spherical symmetry of the coupled
hydrodynamic and heat flow processes involved can
be analyzed by a linear perturbation expansion in
scalar spherical harmonics, (I), and that the
analysis is greatly simplified by a decoupling of
equations for different I's and a degeneracy with
respect to the m'a. This mathematical technique
has been applied to the analysis of implosion
asymmetries caused by nonuniform lasar irradiation
of DT pellets by Henderson and orse.2 They also
stated in Ref. 2, but do not show, that similar
calculations indicate positive stability of the
ablation process by which absorbed energy causss
the implosion. Shiau, Goldman, and Wang, using
the same mathematical technique with a similar but
not identical numerical method, have reached the
opposite conclusion. We present here a complete
calculation of the coupled zero-order (radial) and
first-order (perturbed) problem. Three different
kinds of problems have been done: an initial de-
formation corresponding to bumpy surfaces; an
initial deformation corresponding to granularity
or bubbles (nonuniform density); and boundary con-
ditions corresponding to nonuniform laser
illumination. Examples are shown of the first and
last. All three yield the conclusion that the
ablation surface is stable, as mentioned in Ref. 2.
Physical arguments are presented which support this
The zero-order spherical implosion case chosen
here as our example was taken from a study of im-
plosions of 500 Um radius frozen Dr spheres iso-
tropically irradiated by Gaussian laser pulses
with a wavelength of 1.06 go. The zero-order com-
putations were done by a single temperature La-
grangian hydrodynamics coda with electron thermal
conduction. Figure la is a contour plot of the
maximum central densities achieved as a function
of the total pulse energy, E, and the full width
of the pulse at half maximum. T. Figure lb is a
plot of the corresponding center temperatures at
the times of maximum density. The circled points
indicate the case chosen, E - 50 kJ, t - 5.5 x
10-10 sec. This case, which is on the long pulse
side of that value of T which gives the maximum
density for the chosen value of E, produces a
shock clearly separated from the ablation surface
and a shocked region in between that is much
cooler than the blow-off plasma during most of the
implosion. In Figs. 2a and b the zero-order den-
sity and temperature, P, and To, are plotted at
three different times (t --0.21 x 10-9, + 0.24 x
10-9 and + 0.53 x 10-9 s with respect to the
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Henderson, D.B.; McCrory, R.L. & Morse, R.L. Ablation stability of laser-driven implosions, report, June 1, 1974; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1021748/m1/3/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.