High Energy Density Physics
Volume 4, Issues 1-2, April 2008, Pages 1-17
Core temperature and density profile measurements in inertial
confinement fusion implosions
J.A. Kocha, , , N. Izumia, L.A. Welserb, R.C. Mancinib, S.W. Haana,
R.W. Leea, P.A. Amendta, T.W. Barbee Jr.a, S. Dalheda, K. Fujitac,
I.E. Golovkind, L. Kleine, O.L. Landena, F.J. Marshallf, D.D.
Meyerhoferf, H. Nishimurac, Y. Ochic, S. Reganf, T.C. Sangsterf, V.
Smalyukf and R. Tommasinia
aUniversity of California, Lawrence Livermore National Laboratory,
P.O. Box 808, L-481, Livermore, CA 94551, USA
bDepartment of Physics, University of Nevada, Reno, NV, USA
cInstitute of Laser Engineering, Osaka University, Japan
dPrism Computational Sciences, Madison, WI, USA
eDepartment of Physics and Astronomy, Howard University, Washington,
DC, USA
fLaboratory for Laser Energetics, University of Rochester, Rochester,
NY, USA
Received 29 June 2007; revised 11 September 2007; accepted 17
September 2007. Available online 16 October 2007.
Abstract
We have measured time-integrated and time-gated electron temperature
(Te) and density (Ne) spatial profiles from indirect-drive implosions.
In our experiments, we used a multiple-pinhole two-dimensional imaging
spectrometer to obtain multispectral X-ray images of the imploded
core. Quantitative comparisons between quasi-monochromatic images in
different energy bands allowed Te and Ne spatial profiles to be
determined using two independent and validated techniques: a multi-
objective search and reconstruction analysis, and an analytical
analysis. We then compared the results to a simple one-dimensional
(1D) mix-free hydrodynamics simulation in order to evaluate the
ability of such a model to predict our experiments. Our data show
spatial Te profiles that are qualitatively consistent with the
predictions of our 1D simulations, but we observe central cores that
are 10-25% cooler and emit X-rays as late as 200 ps after peak
compression. We infer time-gated spatial Ne profiles that are
consistent with our 1D simulations near the times of peak compression,
but we find significant disagreement between time-integrated data and
1D simulation predictions at large radii. Careful analysis of the time-
gated and time-integrated Te and Ne spatial profiles, together with
streaked X-ray emission spectra from core and shell dopants, suggests
mixing of shell material into the core is an important process that
our 1D hydrodynamics simulations fail to capture, and comparison
between image data and a simple analytical model suggests that 2-5
Γ蓋嗣m
of the initial inner shell thickness mixes into the core during the
time period of significant X-ray emission. This mix width is
consistent with the predictions of a growth-factor analysis that
treats instability growth seeded by capsule surface roughness, and
points to the need to consider time-dependent mixing effects when
interpreting Te and Ne spatial profiles derived from multispectral X-
ray image data, particularly at large radii where mixing effects will
be most significant.
Introduction
In inertial confinement fusion (ICF) experiments, high-power pulsed
laser beams directly or indirectly ablate the outer surface of a
spherical capsule containing hydrogen-isotope fuel, typically
deuterium or a mixture of deuterium and tritium [1]. The rocket effect
compresses the capsule to a nearly isobaric final state, with maximum
temperature and local-minimum density at the central core of the
plasma. Time-dependent temperature and density spatial profiles are
determined by many factors, including laser drive symmetry, target
symmetry, mixing of shell material into the fuel, and energy transport
by electron and radiation conduction. Future ICF experiments exploring
thermonuclear ignition will require precise tailoring of these
profiles, and such tailoring requires a detailed understanding of how
the profiles are formed.
X-ray imaging and spectroscopy have long been used to diagnose ICF
plasmas, but these techniques have only recently been used to measure
electron temperature (Te) and density (Ne) spatial profiles [2]. These
earlier experiments were low-convergence (8×) direct-drive
implosions
of plastic capsules containing deuterium gas doped with a trace of
argon for spectroscopic diagnosis. Monochromatic X-ray images at
energies corresponding to the Ar He-Γ蓋斬 (1s3p-1s2) transition were
obtained with a toroidally bent crystal imager [3] coupled to a time-
gated X-ray detector [4], and space-integrated time-resolved X-ray
spectra were obtained with a streaked crystal spectrometer. A two-
objective niched Pareto genetic algorithm (NPGA) based search and
reconstruction (SR) technique was then used to find the Te and Ne
profiles that yielded the best self-consistent fits to the angle-
averaged Abel-inverted He-Γ蓋斬 image intensity profiles and the space-
integrated X-ray spectra, and the time-resolved Te and Ne profile
histories were compared against hydrodynamics simulation predictions
[5].
Reconsideration of this previous work shows several areas of
experiment and analysis that can be improved upon. Since only a single
monochromatic imaging band was available owing to the relatively low
core temperatures, reconstructed Te and Ne profiles relied on limited
space-resolved data and were susceptible to errors because the second
fit objective (the space-integrated X-ray spectra) encoded spatial
variations as subtle variations in spectral line shapes. The single
monochromatic X-ray imaging approach also precluded the subtraction of
background continuum emission images, which are necessarily
superimposed on line-emission images and may have different spatial
profiles. The overall approach to determining Te and Ne profiles was
uncorroborated by comparison to independent approaches. Finally,
spherical symmetry was assumed in the reconstruction process, and this
can introduce errors in the Te and Ne profiles unless the cores are in
fact highly spherical.
We have extended the application of monochromatic imaging for Te and
Ne profile determinations to indirect-drive implosion experiments at
the Omega laser facility [6]. These implosions provided sufficiently
high electron temperatures to produce bright images in Ar He-Γ蓋斬, Ar
Ly-
Γ蓋斬 (3p-1s), and nearby continuum energy bands, allowing a number of
significant qualitative and quantitative improvements to be made over
previous work. These include the following.
(1) Use of a powerful X-ray imaging technique based on an array of
pinholes and a flat Bragg mirror [7] and [8]. This technique provides
a large number of individual X-ray images spread across a wide
spectral range that includes multiple emission lines and background
continuum, allowing images to be numerically added to improve signal-
to-noise (S/N) ratio and allowing comparisons to be made between
multiple line-emission and continuum images. The instrument also
naturally provides space-integrated X-ray spectra when the image data
are integrated perpendicular to the dispersion axis.
(2) Development of a generalized Abel inversion process to allow quasi-
three-dimensional (3D) emissivity unfolds, removing the spherical
symmetry assumption used in previous analysis.
(3) Application of a new three-objective SR technique that finds Te
and Ne profiles that yield the best self-consistent fits to Abel-
inverted He-Γ蓋斬 and Ly-Γ蓋斬 image intensity profiles together
with the
space-integrated X-ray spectra. This process adds an important
spatially resolved constraint (the Ly-Γ蓋斬 image intensity profile) to
the SR technique that was not applicable to earlier experimental data.
(4) Development of a new analytical technique, ratio analysis (RA), to
provide an independent measurement of Te and scaled (dimensionless) Ne
profiles from line-emission images alone. This approach has been
tested and validated with synthetic data, providing a benchmark
against which SR approaches can be compared.
In Section 2 we describe the experiments and instrumentation in
detail. Section 3 describes the image data reduction and analysis, and
Section 4 discusses one-dimensional (1D) hydrodynamics simulations we
performed to compare against the experimental data. Finally, Section 5
discusses the effects of material mixing on the experimental data, and
Section 6 summarizes the results and conclusions and discusses avenues
for further research.
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