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Two-photon polymerization printed lattices as support structures in multi-shell ICF targets: Platform development and initial assessment

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Recent interest in fielding direct drive multi-shell targets on the NIF [Kim Molvig et al. Phys. Rev. Lett. 116, 255003 (2016), S. X. Hu et al. Phys. Rev. E 100, 063204 (2019)] has highlighted the need for a low density structure to support the inner shell(s) and to avoid energy loss in the acceleration and collision process. We have developed a two-shell platform to evaluate the use of low density two-photon polymerization (2PP) printed lattices as a support structure between the shells. 2PP structures are an attractive option for the inner shell support because they can be produced at densities as low as 5 mg/cc and their 3D structure can be exactly tailored to the user's needs. However, idealized 1D simulations of lattice strut surrogate thin shells indicate that the lattice will only isotropize before the shells collide if the strut thickness is sufficiently fine. This platform makes use of high resolution Fresnel zone plate images to evaluate the uniformity of the post-collision inner shell and provide information on how efficiently the lattice structure isotropizes. As a proof of principle, initial experiment contrast the case of 5µm lattice struts that cause significant disfiguration of the inner shell with the uniform post-collision inner shell in the absence of this material. Finer lattice structures on future experiments will evaluate post-collision inner shell uniformity. This new platform and accompanying diagnostic technique can also be used to evaluate both asymmetry in capsule drive and target non-uniformities with resolution up to mode 40.
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Two-photon polymerization printed lattices as support structures in
multi-shell ICF targets: Platform development and initial assessment
Brett Scheiner,1, a) Mark J. Schmitt,1Derek Schmidt,1Lynne Goodwin,1and Frederic J. Marshall2
1)Los Alamos National Laboratory, Los Alamos NM, 87545
2)Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14636
(Dated: 31 August 2020)
Recent interest in fielding direct drive multi-shell targets on the NIF [Kim Molvig et al. Phys. Rev. Lett. 116,
255003 (2016), S. X. Hu et al. Phys. Rev. E 100, 063204 (2019)] has highlighted the need for a low density
structure to support the inner shell(s) and to avoid energy loss in the acceleration and collision process. We
have developed a two-shell platform to evaluate the use of low density two-photon polymerization (2PP)
printed lattices as a support structure between the shells. 2PP structures are an attractive option for the
inner shell support because they can be produced at densities as low as 5 mg/cc and their 3D structure can
be exactly tailored to the user’s needs. However, idealized 1D simulations of lattice strut surrogate thin shells
indicate that the lattice will only isotropize before the shells collide if the strut thickness is sufficiently fine.
This platform makes use of high resolution Fresnel zone plate images to evaluate the uniformity of the post-
collision inner shell and provide information on how efficiently the lattice structure isotropizes. As a proof
of principle, initial experiment contrast the case of 5µm lattice struts that cause significant disfiguration
of the inner shell with the uniform post-collision inner shell in the absence of this material. Finer lattice
structures on future experiments will evaluate post-collision inner shell uniformity. This new platform and
accompanying diagnostic technique can also be used to evaluate both asymmetry in capsule drive and target
non-uniformities with resolution up to mode 40.
I. INTRODUCTION
Direct drive multi-shell targets such as the triple shell
Revolver1–3 and the Direct Drive Double Shell4designs
are currently under development and may provide an
alternative pathway to achieving higher yields on the
National Ignition Facility. These targets aim to burn
a liquid fuel volume at low inner shell convergence(
10) using a volume-like ignition scheme utilizing a high-
Z pusher1,5–7. Among the benefits of such multi-shell
schemes is the reduction in magnification of asymmetries
compared to conventional hot-spot ignition which usually
undergo a single-shell convergence of 30 or more. This re-
duction comes at the cost of adding additional shells, and
hence more Rayleigh-Taylor-unstable interfaces, to pro-
vide the pressure needed to drive the inner pusher shell.
One advantage of directly driven multi-shell targets is
that they take advantage of a larger hydro-efficiency (de-
fined here as the ratio of shell payload kinetic energy to
laser energy) than what is available for indirectly driven
double shell targets3. These designs rely on the availabil-
ity of a low density support structure to support the inner
shell(s) and avoid energy loss during the acceleration and
convergence of the ablator. In fact, the difference in en-
ergy transferred to the second shell can be decreased by
more than 50% when using 40mg/cc foam in place of a
low density 5mg/cc material. However, the demonstra-
tion of a low density support has not yet been reported.
This paper presents a two-shell platform for the eval-
uation of the effect of low density inter-shell supports on
a)Electronic mail: bss@lanl.gov
the drive of the inner shell. The support tested here is a
two-photon polymerization (2PP) 3D printed8stochas-
tic lattice, such as those shown in Fig. 1(a)-(d). The
effect of the 2PP support on the inner shell is evaluated
via backlit x-ray radiography using Fresnel zone plates9
to produce high resolution images of the outer surface
of the mid-Z inner shell. This surface presents a sharp
jump in x-ray absorption and allows for decomposition to
Legendre modes from `= 0 to `&40. Differences in the
uniformity of the outer surface caused by the 2PP lattice
are evaluated by comparison with cone-in double shell
targets that have no material between the shells. This
method of comparison is also applicable to other sup-
port structures such as inter-shell tents, similar to what
is used to support a target in a hohlraum10, as well as
other sources of non-uniformity such as that transferred
from the ablator due to asymmetry in the laser drive.
This paper also presents an initial assessment of the
lattice design requirements. Experiments of double shell
targets with 141 and 44 mg/cc lattices show significant
disfiguration of the outer surface, suggesting that these
lattice structures may persist to some extent through the
shell collision. A dimensional analysis based model is for-
mulated to predict the scaling of the lattice density with
time, radiation irradiance, opacity, and initial mass. This
model compares well with 1D simulations of surrogate
thin plastic shells, with thickness matched to that of the
lattice struts, that are used to evaluate the ability of the
lattice structure to disassemble and isotropize under the
radiation preheat from the hot coronal plasma of the ab-
lator. It is found that for NIF scale targets, sufficient
time (&10 ns) is available for this to occur with 5µm
thick struts. For Omega scale targets, thinner lattice
struts are needed to achieve the same effect due to the
2
FIG. 1. Two-photon polymerization printed structures of
varying density used to support the inner shell of a double
shell target. (a) A hemispherical shell with an average density
of 7.2 mg/cc supporting an inner 400µm diameter chromium
shell. (b) A hemispherical shell with an average density of
21.3 mg/cc. (c) A hemispherical shell with an average den-
sity of 44 mg/cc. (d) A hemispherical shell with an average
density of 141 mg/cc and an integral solid-density tamper
layer.
compressed time scale ( a few nanoseconds) of these im-
plosions. Future experiments will evaluate this behavior
experimentally as the 2PP printing capability improves.
A successful demonstration of a uniformly driven inner
shell when using 2PP lattices will allow for greatly im-
proved collision efficiency in direct drive multi-shell tar-
gets.
This paper is organized as follows: Section II A de-
scribes the target design and experiment goals and
Sec. II B overviews the diagnostics used. Section II C
gives an overview of the processing of the images from
these experiments for the purpose of determining non-
unifomity, Sec. II D presents the results for initial exper-
iments without the 2PP lattice, and Sec. II E presents
the results of the first experiments with the 2PP lat-
tice. Section IIIA presents a dimensional analysis based
model of the lattice density and Sec. IIIB shows 1D sim-
ulations of a surrogate lattice structure and discusses the
requirements for disassembly of the lattice structure due
to coronal radiation. Section IV discusses the results and
future prospects. Concluding remarks are made in Sec.
V.
II. EXPERIMENTS
A major source of non-uniformity of the inner shells
of multi-shell targets is that which is seeded by varia-
tions in the pressure drive that it encounters during the
shell collision process. These pressure variations can take
the form of density, temperature, or charge state varia-
tions in the material mediating the collision, which can
include inter-shell material or the surface layers of the
shells themselves. The pressure variations encountered
in the targets presented here primarily take the form of
mass density variations caused by the lattice structure
that persists through the collision process. This section
describes the targets (Sec. II A), diagnostics (Sec. II B),
and image processing methods (Sec. II C) used to diag-
nose the non-uniformity transferred to the inner shell of
a direct drive double shell target during the shell collision
(Sec. II D and Sec. II E).
A. Targets
Figure 2 shows the two types of targets that were
fielded during the Revolver-19B (Shots 94955-94971)
and Revolver-20A (Shots 96145-96158) shot days on the
Omega laser. These experiments served two goals. The
first was to assess the collision efficiency (see Ref. 2) and
uniformity in the absence of 2PP material using the Re-
volver 19B target (hereafter 19B). In this case, the inner
shell was supported using a gold cone. No inter-shell ma-
terial was present, besides a thin GDP tamping layer on
the molybdenum inner shell; See Table I for design pa-
rameters. Revolver-20A (hereafter 20A) was designed to
contrast the uniformity of the lattice-held inner shell to
the case of 19B where no inter-shell material was present.
The 20A targets were fielded with a 2PP stochastic
lattice with nominal densities of 44 and 141 mg/cc. The
lattice was designed by using the nTopology software to
set up a stochastic tetrahedral mesh by varying the num-
ber of points in the 3D structure. For a given lattice
strut diameter, the in-between spacing is kept constant at
roughly 100 microns with the number of interconnecting
points adjusted to slightly vary the density to exactly the
volume fraction required to achieve the desired volume-
averaged density. Future experiments with variations of
the 2PP lattice, such as those in Fig. 1(a) and (b), will be
fielded in the 20A target design to provide information on
the requirements for minimizing the effect of the lattice
on the inner shell. These requirements will be elaborated
further in Sec. III.
B. Diagnostics
Backlit X-ray radiography was the main form of di-
agnostic for these experiments. On each shot, radio-
graphs were obtained via two backlighters and images
were formed at the image plane of each of two framing
cameras using either a Fresnel zone plate9or pinhole as
the main optic. In all instances of use, the pinhole camera
images utilized 6.701 keV Heαemission from an Fe foil
laser-illuminated with an irradiance of 8×1014W/cm2
over a 500µm diameter spot. This camera used a 4 by 4
array of 10 micron pinholes at 4x magnification. The im-
3
GDP Ablator
Mo Shell
GDP
Tampe r
Au Cone
Printed Skin
2PP Stochastic
Lattice
Cr Shell
GDP Tamper
Empty Void
Revolver 19B
Revolver 20A
FIG. 2. A schematic of the Revolver 19B (top) and 20A (bot-
tom) targets.
Type 19B 20A
Ablator Material GDP CH
OD & thickness 1233µm ×29µm 1200µm ×25µm
Inner Material Mo Cr
OD & thickness 393µm ×13µm 395µm ×17µm
Inner Support Au cone 2PP lattice
44 mg/cc
or 141 mg/cc
Tamper 21µm GDP 20µm printed skin
Optional 20µm GDP
Phase Plate SG5-860 SG5-650
Beams 39 symmetric 40 polar drive
excluding cone
Energy 8.8 kJ 11.5 kJ
Pulse 1 ns square 1 ns square
Irradiance 2.8×1014 W/cm22.5×1014 W/cm2
TABLE I. Target design and drive characteristics
age integration time was 50ps. These images were used
as a baseline with which to compare the FZP images.
On each shot, the FZP imager9was used to produced
a single image of the inner shell. The selected time for
each images was chosen to either capture the pre- or post-
collision shell. A time series of the inner shell evolution
was constructed by obtaining images on subsequent near-
identical shots at different times. The target was backlit
via a laser-illuminated Ti foil for 19B and Fe foil for 20A
targets, each illuminated with a 1ns square pulse and an
irradiance of 810 ×1014W/cm2.
As described in Ref. 9, the FZP was composed of N
= 512 zones with an outermost zone width of ∆r= 140
nm. The focal length of this lens, f= 4N(∆r)2, is set
by the X-ray wavelength λand is related to the object-
FZP and FZP-image distances pand qby the thin lens
formula 1/p + 1/q = 1/f. Here, the total length between
the image plane and object is fixed as L=p+q. For the
Ti backlighter, f= 151.86 mm, p= 158.78 mm, and q=
3487.82 mm, giving a magnification of M=q/p = 21.97
at the image plane. For the Fe backlighter energy p and
q are varied, giving M=14.95.
Since the FZP is a diffractive lens, 0th order un-
diffracted light can fall on the image formed by the 1st
order diffracted component, and registers as an unfocused
contribution to the measured intensity. This can be seen
as a bright region on the surface of the opaque inner shell
in the images shown in Fig. 3. The ratio of the zeroth
and first order light for these zone plates are reported
in Ref. 9 and depend on backlighter energy. For the Ti
backlit images, the 0th and 1st order components were
similar, and for Fe energies, the 1st order component was
several times larger than the 0th. The improvement in
contrast can be seen by comparing the image of the 20A
target in Fig. 4 to the t= 1.9 ns panel in Fig. 3.
The resolution of the image formed by the FZP for
monoenergetic emission is given by the diffraction limit
1.22∆r= 170nm. However, the presence of emission at
other energies degrades the resolution. For example, the
presence of two nearby lines for Ti at 4.750 and 4.727
keV reduces the resolution to 1.4µm9. The ability to
record fine details also requires sufficient resolution at
the detector. This limits the resolution of the current
system. For Ti and Fe images, the resolution was ap-
proximately 2.5µm and 3.7µm, respectively, with the dif-
ferences primarily stemming from the different magni-
fication for each energy. The images were recorded on
film using the four photocathode strips of X-ray Framing
Camera 1. The film was digitized at 20 and 10 micron
resolution, for Ti and Fe backlit images, respectively, so
that each pixel was significantly less than the system res-
olution. For reference, 5.6 mm wide film at a magnifi-
cation of M=14.95 scanned at 10µm resolution results
in a physical target plane distance of 0.67µm/pixel. For
the 20µm scan with M=21.97 the physical target plane
distance per pixel is 0.91µm.
4
t=1.9 ns 94960
400 µm
t=3.3 ns 94962
94967
t=3.6 ns
94966
t=3.8 ns
94969
t=4.3 ns
Pre-collision
Post-collision
Implosion Time
FIG. 3. Titanium backlit FZP images of the 19B target ob-
tained at successively later times during the implosion. One
pre-collision and four post-collision images are shown. The
purple arrow indicates the location of the compressed tamp-
ing layer and ablator material.
100 300 500
100
300
500
100 300 500
100
300
500
FIG. 4. (a) An iron backlit FZP image of the post-collision
20A target. (b) The same image after 30 iterations of the
anisotropic diffusion filter.
C. Image Processing
The uniformity of the shell was analyzed by the detec-
tion of the sharp absorption feature (discussed in detail
in Sec. II D) by using image segmentation techniques. In
noisy images, such as those commonly encountered in x-
ray radiography of ICF targets, the reduction of noise is
required to avoid spurious detection of false boundaries
between image regions. This well known necessity is per-
haps most visible in the widely used Canny edge detec-
tion algorithm11 which optimally detects edges with low
error rate and good localization, i.e. accuracy of position.
However, each of these are not independent. In this algo-
5
rithm, one pays a price in edge localization for a low error
rate and vice versa. Often, one will increase the gaussian
smoothing parameter in this method at the expense of
image resolution12. Likewise, the accurate localization
of boundaries in graph-based and other image segmen-
tation methods can be hindered by low image quality,
including noise and background intensity gradients. In
our particular application, we aim to provide high spa-
tial resolution data. Therefore, the reduction in accurate
localization incurred in exchange for a low error rate in
edge detection or segmentation is not desirable. Instead,
we make use of the edge-preserving anisotropic diffusion
filter12 prior to segmentation.
The anisotropic diffusion filter evolves the anisotropic
diffusion equation
∂I
∂t =∇ · c(||∇I||)I(1)
a fixed number of iterations using the image as the ini-
tial condition, I(x, y, t = 0), for the 2D domain. Here,
c(||∇I||) is a diffusion coefficient, often called the con-
ductance in this application, which depends on the local
estimate of the image gradient. The denoised image is
obtained by iteration until the desired level of smoothing
is obtained. Evolution of Eq. 1 results in diffusion, i.e.
smoothing of pixel intensity values, preferentially along
the contours of intensity, instead of along the direction
of the gradient. This preserves features of the image that
involve sharp changes in intensity. This method is readily
available in a variety of software packages and can be eas-
ily applied. Here, we use the implementation in Matlab
which estimates the image gradient using the 8 nearest
neighbor pixels and uses an exponential conductance to
preserve high contrast edges13. The filter was iterated 30
times to obtain the desired denoised image. The effect
of anisotropic diffusion filter iteration on the reconstruc-
tion of a edge of known Legendre polynomial spectra is
explored in the Appendix using constructed test images.
In general, features of width either near the resolution
limit or pixel size of the image are degraded with suc-
cessive iteration, while larger features are preserved. A
comparison of the original and filtered image is shown in
Fig. 4.
After denoising, the high contrast edge of the tar-
get is detected via segmentation by using the Matlab
implementation13 of the lazy snapping technique14. This
method computes the graph cut along the boundaries
of an over-segmented image, updating with the selection
of several foreground (points on the opaque target) and
background (points on the rest of the image) pixels. An
example of the boundary between the foreground and
background is shown in Fig. 5 for the 20A targets. This
boundary is used for the Legendre mode decomposition.
The edge location R(θ) as a function of polar coordinate
θis then decomposed into a series of Legendre polyno-
mials
R(cos θ) =
N
X
0
a`P`(cos θ),(2)
100 300 500
100
300
500
100 300 500
100
300
500
100 300 500
100
300
500
0 20 40
10-2
10-1
100
0 20 40
10-2
10-1
100
0 20 40
10-2
10-1
100
FIG. 5. The high contrast edge of the inner shell detected
through image segmentation and the corresponding Legendre
decomposition for three 2PP lattice targets.
where the coefficient a`is given by
a`=2`+ 1
2Zπ
0
R(cos θ)P`(cos θ) sin θdθ, (3)
and P`is the `th Legendre polynomial. In regions where
data is missing, such as the case with the black bar in
Fig. 3 between the micro channel plate strips, the values
are filled in with the average radius so that a0returns
the target radius. Data for the entire 2πis considered by
fitting a`from each half target, divided along the target
axis (aligned with the PDD drive axis), and then av-
eraging the values. To compare the spectra for images
with large chunks of missing data, the reported values
for components with ` > 0 are amplified to give a a full
πequivalent amplitude (assuming that the spectrum of
Legendre modes in the missing section is the same).
D. No-lattice experiments
Initial FZP images shown in Fig. 3 were obtained dur-
ing 5 separate implosions of nearly identical 19B targets.
One image was obtained for each shot at successively
later times during the inner shell implosion, including
6
one pre-collision image. As stated in Sec. II A, the goal
was to evaluate the uniformity of the outer surface of the
inner shell and measure the effects of the shell collision
on this uniformity in the absence of the 2PP lattice, pro-
viding a baseline for the comparison of experiments with
the lattice present.
The method of evaluation is though the extraction and
Legendre mode decomposition of the outer surface of the
inner shell from the FZP images. This is discussed in de-
tail in Sec. II C. Ideally, the backlighter energy is chosen
so that the propagation path-length through the abla-
tor adds little to the optical depth along the line of sight.
Additionally, the opacity of the inner shell material needs
to be high enough that the path length just inward of the
limb contributes a majority of the optical depth along the
line of sight so that high contrast of the inner shell outer
shell surface can be achieved. For inner shell materials
such as Cr or Mo, this is easily satisfied within less than
the 2.5µm resolution of the FZP imager. The length of
a chord a distance h= 2.5µm inward from the edge of a
circle of radius R= 200µm is L= 2ph(2Rh) = 63µm.
This path-length result in near-complete attenuation of
the Ti and Fe X-rays. Therefore the detected edge at the
outer surface is an excellent approximation to the outer
surface of the target’s inner shell.
However, the approximation that the ablator adds lit-
tle to the optical depth is not always satisfied. This is
particularly true with the use of the lower energy tita-
nium backlighter. While this backlighter was of sufficient
energy to produce x-rays to which the ablator shell and
tamper remain transparent early in time, the convergence
of the ablator material onto the inner shell after the col-
lision resulted in a more opaque layer of material near
the interface. This effect is visible in the FZP images for
shots 94966, 94967, and 94969 as a dim edge, distinct
from that of the inner shell, in front of the bright back-
lighter spot. For these images, the location of the outer
ablator shell is indicated by the violet arrow shown in
Fig. 3 . The same features are not seen in Fe backlit pin-
hole images (not shown) obtained at the same time. This
indicates that the converged ablator and tamper material
remains transparent for the higher Fe backliter energy.
This hypothesis is confirmed by inspecting synthetic
radiographs generated from post-shot simulations using
the radiation hydrodynamics code HYDRA15. Figure
6(a) shows the Lagrangian plot from these simulations.
The color coding of the figure indicates the different ma-
terial layers, with the ablator shown in purple, the pary-
lene tamper layer in green, and the molybdenum shell in
red. The figure indicates that the parylene tamper and
ablator shell continue to converge post collision, which
is expected to increase the optical depth through the
material. This can be seen directly in Fig. 6(b) which
shows lineouts along the center of the synthetic radio-
graphs generated from this simulation. The time of these
lineouts is shown by the red arrows in Fig. 6(a), and can
be compared with the time of the experimental images
indicated by the five yellow arrows. The lineouts ini-
0 200 400 600 800 1000
0
0.2
0.4
0.6
0.8
1
Radius (cm)
Time (ns)
(A)
(B)
FIG. 6. (a) A Lagrangian plot from post-shot simulations of
the 19B target. The yellow arrows indicate the time of each
FZP radiograph shown in Fig. 3. (b) Synthetic radiograph
lineouts at the times indicated by the red arrows in part (a).
tially show a sharp absorption edge before and just after
the collision, with the sharpness of the edge degrading
in time, and significantly reducing the contrast between
the shell, tamper, and ablator. This degradation can be
seen in the FZP images of shots 94967, 94966, and 94969
in Fig. 3. This is compounded by the fact that the FZP
undiffracted zeroth order component is large for the ti-
tanium backlighter energy, further reducing the contrast.
As a result, only the first two images were analyzed for
uniformity.
The first two radiographs from the time series in Fig. 3
were processed and decomposed into their Legendre spec-
tra using the methods outlined in Sec. II C. The ini-
tial decomposition for the post-collision image from shot
94960 shows very little power due to low mode asym-
metry (` < 10). The post collision image from shot
94962 demonstrates an increase in low mode asymme-
try after the shell collision, which is also visible in the
image as well. An important feature to note is that the
pre- and post-collision shell show very little asymmetry
at all modes in comparison to those shown on the same
y-axis scale in Fig. 5(to be discussed in Sec. II E). This
clearly demonstrates the ability of the FZP x-ray imaging
7
Shot 94962
0 1020304050
Legendre mode
10-2
100
Shot 94960
0 1020304050
Legendre mode
10-2
100
FIG. 7. The Legendre decomposition of the pre-collision and
post-collision shells from shots 94960 and 94962, respectively.
technique to detect asymmetry of the inner shell induced
by the inter-shell material.
E. 2PP lattice experiments
Images of the post-collision inner shell were obtained
for the 20A targets with two different variations in 2PP
lattice density. These images are shown in Fig. 5 along
with the Legendre decomposition of the detected inner
shell outer surface obtained using the method outlined
in Sec. II C. These images show large amounts of non-
uniformity seeded by the 44 mg/cc (shot 96154) and 200
mg/cc (shots 96155 and 96156) 2PP lattices. Images
prior to shell collision at t= 1.9 ns were also obtained
(not shown) and the initial uniformity is similar to that
shown at the same time in Fig. 3. This indicates that
the non-uniformity is due to the persistence of the lattice
structure through the shell collision. These experiments
demonstrate the ability to diagnose the persistence of the
2PP lattice structure at the time of collision and demon-
strate that it is a viable platform for studying the effects
of variations in this structure on inner-shell density per-
turbations.
III. LATTICE STRUCTURE DISSASSEMBLY
One of the central questions in the use of a 2PP lattice
in the construction of multi-shell ICF targets is whether
or not the material can be designed to isotropize suffi-
ciently to act as a uniform material in the hydrodynam-
ics of the shell collision. If the material retains signifi-
cant density perturbations at the time of collision it is
not a viable option as a low density support. Answering
this question requires the proper simulation of the 2PP
printed lattice that is inherently three-dimensional. Such
simulations are beyond the scope of this work. In this sec-
tion, we formulate a simple dimensional analysis model
for the expansion of the 2PP lattice (Sec. III A) and com-
pare it with simulations of surrogate structures in a one-
dimensional geometry (Sec. III B). These simulations il-
lustrate qualitative features of the behavior of the lat-
tice during an implosion and illustrate how the lattice
structure begins to isotropize under the radiation-driven
heating from the direct drive ablation region. These re-
sults illustrate some of the issues that must be considered
when scaling designs between Omega and the NIF.
A. Dimensional analysis based model
During the ablation of a direct drive ablator, the
heated corona is in local thermodynamic equilibrium
and emits radiation with a Plankian spectrum Bν(Te) =
23/c/[exp( /kBTe)1], where h is Plank’s constant,
νthe radiation frequency, Tethe electron temperature,
and kBBoltzmann’s constant. Some radiation, particu-
larly at higher energy but also depending on the ablator
material, penetrates the shell and heats the lattice struc-
ture. For a CH ablator, the mass attenuation coefficient
is such that radiation below 1keV is effectively blocked.
The radiation that makes it through the ablator tends to
be of high enough energy that the printed lattice struc-
ture is optically thin to it. As a result, the lattice ini-
tially absorbs energy uniformly with a rate determined
by the lattice opacity: R
0Iνκν. As it heats, the lat-
tice expands and decreases in density, disassembling and
producing a more isotropic plasma as time progresses.
The extent to which this occurs depends on the target
and lattice design parameters, as well as the timescales
available for disassembly.
To formulate a model based on this scenario, we as-
sume that the flux density from the ablation region is
absorbed by the lattice which has an opacity κν. The rel-
evant quantities for the model are time t,Iν,ρ, and κν.
A linear system relating these quantities to the base units
of mass (M), length (L), and time (t) can be constructed.
The Buckingham Π theorem relates the basis of the null
space of this linear system to the powers of the quan-
tities from which the linear system was constructed16.
The resulting model relates the input quantities and is
zero-dimensional. The linear system is
t Iνρ κν
[M] 0 1 1 1
[L] 0 0 3 2
[t] 1 3 0 0
,(4)
which has a null space of dimension 1 with the basis
vector (3,1,2,3). Therefore, the constant Π is related to
8
the model quantities via
Π = t3λIλ
νρ2λκ3λ
ν.(5)
With the choice of λ= 1/2, the density of the lattice
structure scales as
ρ= Πt3/2I1/2
νκ3/2
ν.(6)
This relation gives the scaling of the density of a lattice
strut with the irradiance from the corona, opacity, and
time. As will be seen in the next section, the time is
particularly important when scaling between Omega and
NIF scales for fixed lattice strut thickness.
We also argue on physical grounds that the constant
Π is an increasing function of the lattice strut thickness
x. Consider the struts in two separate lattices with
similar values of Iν,κν, but different thicknesses so that
one is twice the initial mass (M0) and volume (V0) of the
other. The initial density in each case is the same: ρ0=
M0/V0= 2M0/2V0. Assuming the mass ablation rate
is fixed by the values of Iνand κν, and that the ablated
material’s velocity is also set by these quantities, it would
take twice as long for the thicker strut to reach the same
density. Stated in another way, in a fixed amount of
time, ρ(t)M0. Therefore, the constant Π is expected
to increase with the thickness of the initial lattice strut
and the density can be written as
ρM0t3/2I1/2
νκ3/2
ν.(7)
This relation is shown to be in good agreement with sim-
ulations in the next section.
B. Simulations
Several simulations were carried out using the 1-D La-
grangian radiation hydrodynamics code Helios17. The
first set of simulations consider a single, thin, 1 5µm
shell, placed midway between the ablator and inner shell.
The thin shell was meant to represent a single strut of the
2PP lattice. Since the 2PP lattice is optically thin to the
radiation from the ablator, it is expected that the simu-
lation of a single strut is characteristic of multiple struts
up until the point in time where the inter-shell pressure
begins to achieve equalization. However, the expansion
of the single thin shell only occurs in the radial direc-
tion. In 3D, the expansion and disassembly of a strut
is more efficient. As a result, these simulations are only
qualitative in nature.
Figure 8 shows the region averaged density for the sin-
gle thin shell for initial shell thicknesses of 1µm, 2µm,
3µm, and 5µm placed midway through a 20A target (See
Table I for specifications). The time of the laser shutoff
is marked in the figure by the vertical gray line and the
material that comprises the thin shell is seen to decrease
in density until this time. The figure indicates that the
density after laser shutoff is smaller for thinner initial
10-1 100
Time (ns)
10-1
100
Density (g/cc)
1 m
2 m
3 m
5 m
Laser Off
t-3/2
123456
Initial Mass (M0)
0
0.1
0.2
0.3
Density (g/cc)
(t=1ns)
M0
(A)
(B)
FIG. 8. (A) The time dependence of the density of lattice-
surrogate thin shells placed inside of a 20A target. The end
of the 1ns square laser pulse is indicated by the vertical line.
(B) The density at the end of the laser pulse as a function of
the initial strut mass.
shells, indicating more complete disassembly. For 1µm
the density is approximately 5% of the initial value while
for 5µm it is 20%. The subsequent increase in density at
1.5 ns is due to the compression by the incoming ablator.
In 3D, recompression in this manner would not occur.
Two trends demonstrated in Figure 8 are in good
agreement with the model from Sec. III A. The first,
shown in Figure 8(A) is the predicted ρt3/2scaling
of the density with time, shown as the dashed black line
in the figure. The density is in good agreement after an
initial period of coronal heating in the ablation region
and energy absorption by the thin shell. Inspection of
the energy bins at the outer boundary of the thin shell
in Fig. 9 show that a fixed illuminance develops for the
energy range E > 1keV by 0.2ns. This portion of the
spectrum is that produced by the ablation region. By
0.6 ns, additional radiation at E500eV is produced from
the shock heated interior of the ablator shell since the
ablator is optically thick to radiation at these energies.
The thin shell is also opaque at this energy and there-
fore this does not contribute significantly to the uniform
heating. The scaling of the density with time does not
change after the appearance of the 500eV peak. These re-
sults justify the assumption of a constant Iνin the model
from Sec. III A.
The second trend in agreement with the model shown
in Figure 8(B) is the scaling of density with initial strut
9
012345
Energy (keV)
10-6
10-5
10-4
10-3
I (TW/cm2/eV)
0.1 ns
0.2 ns
0.6 ns
0.8 ns
FIG. 9. The irradiance of the outer surface of the thin shell
in each energy bin at t = 0.1, 0.2, 0.6, and 0.8 ns.
mass ρM0. The figure shows that this relation is
in excellent agreement with the simulation results. This
indicates that finer lattice structures are better suited
to achieving a more uniform inter-shell medium prior to
shell collision.
A second set of simulations were carried using the pulse
and target specifications for NIF scale Revolver experi-
ments. These simulations are meant to illustrate some
qualitative features of the lattice in the intended applica-
tion. The first of these was to demonstrate the expansion
of the material to a nearly uniform density in the inter-
shell region. The second was to demonstrate differences
in the behavior of the 2PP lattice upon scaling up to the
NIF. The simulations use a 80µm thick 5mm OD CH ab-
lator and inner 65µm thick 1700 µm OD Cr inner shell
coated with 60µm of CH, similar in scale to experiments
currently being planned and carried out on the NIF. The
target was driven by a 6.5 ns laser pulse with a 2 ns ramp
leading up to a flat top delivering a maximum irradiance
of 2.5×1014W/cm2at the capsule surface. The simula-
tions approximate the lattice through the use of 14 thin
shells, of either 1µm or 2µm thickness, placed at even
intervals between the ablator and inner shell.
Figure 10 shows the mass density of the target as a
function of time for the 6.5ns duration of the laser pulse.
The initial position of the 14 thin shells are visible be-
tween the ablator and inner shell. The shells expand
in time until about 4.5ns when the inter-shell volume
reaches a uniform density of approximately 13mg/cc. At
its fully expanded extent the boundaries between the
shells are still visible. This is an artifact of simulation
resulting from the inability of zones to mix with one an-
other. The figure illustrates that with sufficient time, the
thin shells can achieve a density that is a factor of 34
lower than that which is possible on Omega time scales.
Figure 11(A) and (B) shows the region averaged den-
sity for each thin shell for initial 1µm and 2µm lattices.
The corresponding laser pulse is shown in Fig. 11(C).
During the initial laser pulse, each thin shell begins to
compress and then disassemble during the first nanosec-
ond. After the onset of disassembly at t1 ns, the
density decreases with a power law exponent less than
FIG. 10. The mass density of a NIF scale Revolver target
with several 1µm shells as a surrogate for the 2PP lattice.
2. This faster rate of disassembly is expected during
the ramp of the laser pulse since the irradiance from the
corona is increasing with the increasing coronal tempera-
ture. Between 2 and 4ns the density decreases as ρt2.
Once again, a rate faster than ρt3/2is expected since
the thin shell has acquired some initial kinetic energy
due to the pulse ramp. In both cases for 1µm and 2µm
lattices, a constant density is achieved at t4.5. For
the 1µm lattice in Fig. 11(A) this is 13mg/cc, while for
the 2µm lattice in Fig. 11(B), this is approximately 25
mg/cc. These values are in agreement with the ρM0
scaling of Sec. III A. Like the Omega scale 1D thin shell
simulations, these simulations also feature unphysical re-
compression of each shell by the ablator. This can be
seen in Fig. 11(A) and (B) as the upswing in density of
each shell near the time of its collision with the ablator.
The simulations of this section present several impor-
tant qualitative features by using simple 1D surrogate
structures. However, proper multidimensional modeling
of the lattice will be important for understanding the role
of the material in the seeding of perturbations on the in-
ner shell and ablator. Acceleration of the ablator against
a non-uniform structure can lead to non-uniformity that
seeds Ralyeigh-Taylor growth upon deceleration on the
inner shell. Furthermore, if significant variations in den-
sity persist at the end of the acceleration of the ablator,
these variations can lead to different rates of Ralyeigh-
Taylor growth due to Atwood number variations trans-
verse to the interface. Without 2D simulations, it is un-
10
100101
10-2
100
Density (g/cc)
1 Micron Shells - 13 mg/cc
100101
10-2
100
Density (g/cc)
2 Micron Shells - 25 mg/cc
100101
Time (ns)
0
0.5
1
Relative Power
Laser Pulse
(C)
(B)
(A)
FIG. 11. (A) The region averaged density for each of the 14
surrogate 1µm thin shells as a function of time. (B) The re-
gion averaged density for each of the 14 surrogate 2µm thin
shells. (C) The corresponding laser pulse for (A) and (B).
Note that the individual shell densities begin to deviate from
their average as the outer imploding shell sequentially im-
pinges upon them (starting around 2.5 ns).
clear if the perturbations to the inner shell seen in Fig. 4
are primarily due to direct imprint of the lattice struc-
ture or to seeded growth during the deceleration of the
ablator. These questions will be the subject of future
studies.
IV. DISCUSSION
The experiments presented in this paper demonstrate
an ability to diagnose fine features (up to `40) on
the inner shell of multi-shell targets resulting from the
inter-shell lattice support structure. Comparison of tar-
gets with and without this structure demonstrates that
differences in the design can be distinguished by high res-
olution FZP images. While the present lattice structures
result in a large perturbation on the inner shell, these
results are somewhat expected in light of the analysis
of Sec. III. This section discusses the 20A lattice struc-
tures using these results and discusses future prospects,
including lower-density experiments currently under de-
velopment.
As discussed in Sec. II E, images of 20A inner shells
in Figs. 4 and 5 show large amounts of non-uniformity
on the inner shell. Two possibilities were proposed for
the seeding of this non-uniformity: direct imprint of the
lattice structure due to persistence of density variations
at the time of collision, or (2) ablator mediated imprint.
In the latter case, the lattice seeds non-uniformity in the
ablator during the acceleration phase that subsequently
grow during deceleration and transfer to the inner shell
during the collision. The simulations shown in Fig. 8(B)
predict that a 5µm lattice strut would only be 20% of
its initial density at the end of the laser pulse. It is
unclear if this density is sufficient for the primary imprint
mechanism to be direct imprint. Although inconclusive,
it is interesting to note that no high-mode non-uniformity
was present in self emission images of the ablator at the
end of the laser pulse.
Future 2PP lattice designs will attempt to mitigate the
non-uniformity seeded by the lattice. On Omega, where
the implosion timescale is short, thicker lattice struts are
unfavorable because there is insufficient time for their dis-
assembly during the laser pulse. The model of Sec. III A
suggests three main pathways to decrease the density of
the lattice after a given time duration: increasing the ra-
diation irradiance, increasing the opacity, or decreasing
the strut thickness. Since the irradiance is fixed by the
properties of the ablator, which are set by other target
design parameters such as the laser pulse, intensity, and
desired payload mass and in-flight aspect ratio, we focus
on the latter two possibilities.
Upcoming experiments on Omega will specifically fo-
cus on the effect of finer lattice structures on inner shell
uniformity. A hemispherical shell of thin 1µm struts,
shown in Fig. 12, has been constructed for this purpose.
By the estimation in Sec. III B, in 1D this would result
in a factor of 5 reduction in lattice density at the time of
collision. This reduction is expected to be helpful in the
reduction of non-uniformity imprinted on the inner shell.
Another possibility to aid the disassembly of the lattice
structure is to increase the lattice opacity. Addition of
high-z material to the lattice may be a viable pathway
to reducing the lattice density since the lattice density
decreases faster with opacity than in increases with mass.
Possible routes to achieve this range from applying an
atomic layer deposition coating to the addition of high-z
impurities to the printing resin. The necessity of such
modifications to the lattice will be determined in future
experiments.
V. CONCLUSION
In this paper, we have presented an initial analysis of
the use of 2PP printed lattices in multi-shell ICF targets.
11
FIG. 12. A hemispherical support structure with 1µm lattice
struts.
An ability to measure lattice-induced non-uniformity on
the post collision inner shell was demonstrated using a
newly developed platform that takes advantage of the
large opacity of the inner shell and the development of
new high resolution x-ray imaging techniques. The plat-
form has been used to demonstrate the measurement of
Legendre modes `&40 on the 400µm diameter inner
shell. Initial experiments highlight the need for the dis-
assembly of the lattice to prevent lattice-induced non-
uniformity on the inner shell. To aid in this effort, a sim-
ple model was constructed to provide the scaling of the
disassembly with x-ray irradiance, lattice strut thickness,
opacity, and time. This model was found to be in good
agreement with 1D simulations of thin shells designed to
act as a surrogate for a single lattice strut. These results
provide the groundwork for future experimental investi-
gations of 2PP lattices, which will play a vital role in
achieving efficient and symmetric energy transfer to the
inner shells in direct drive multi-shell targets.
ACKNOWLEDGMENTS
We thank the LLE staff for their support during the
shot day. This work was supported by the Labora-
tory Directed Research and Development program of
Los Alamos National Laboratory under project number
20180051DR.
DATA AVAILIBILITY
The data that support the findings of this study are
available from the corresponding author upon reasonable
request and approval for public release by Los Alamos
National Laboratory.
APPENDIX: ERROR CHARACTERIZATION
A major concern of the image analysis is how the sam-
pling and processing of the image affect the measured
Legendre mode spectrum. In this Appendix, the affect
of image resolution and iteration of the anisotropic diffu-
sion filter is explored through the use of a series of test
images with a known Legendre mode spectrum imposed
on the inner shell.
Each simulated Legendre spectrum was constructed
using the following process:
(1) An interface with known amplitude spectrum a`
was used to construct a binary image using Eq. 2. A
specified pixel size of ∆xres /2 was selected, where ∆xres
is the approximate resolution of the imaging system. For
the purpose of this study, the amplitudes of the interface
were a0= 200µm and a50 = 20µm or a50 = 10µm.
(2) The image was convolved with a gaussian of width
xas a crude simulation of the resolution of the imaging
system. This has the effect of blurring the boundary
between foreground and background.
(3) The mean pixel value and gaussian noise level of
the FZP image from shot 94962 in Fig. 3 was sampled in
the image foreground and background. The mean values
were then used to rescale the pixel values of the test image
foreground and background and to add the appropriate
amount of Gaussian noise. For the boundary pixels on
the interface, the mean values and noise level were inter-
polated between the foreground and background values.
(4) The image was filtered using a set number of iter-
ations of the anisotropic diffusion filter. In this section,
variations in the number of iterations were used to un-
derstand the effect on the measured Legendre spectrum.
(5) Canny edge detection with minimal 1 pixel wide
gaussian smoothing was used to obtain the measured in-
terface and the interface was projected onto the Legendre
polynomials to obtain a`. Greater amounts of gaussian
smoothing were not necessary due to the iteration of the
anisotropic diffusion filter.
The above process was used first to explore the effect of
resolution and iteration for the case of a50 = 10µm. For
features of size `= 50, the ∆xres = 2µm resolution of
the test image and the spatial scale of noise fluctuations
(∆xres/2) are no longer much smaller than the scale cor-
responding to the amplitude and azimuthal fluctuations
in the interface. When this occurs, one expects that it-
eration of the anisotropic diffusion filter to degrade the
original amplitude. This can be seen in Fig. 13A where
the measured over exact amplitude decreases from 75% at
10 iterations to just under 50% for 50 iterations. As the
image (and pixel) resolution increase relative to the size
of the interface features, the degradation of the original
signal becomes insignificant, with little difference in the
measured amplitude with iteration number. The same
is true when increasing the feature size relative to the
system resolution. This effect can be seen upon increas-
ing the amplitude to a50 = 20µm. At a fixed number of
iterations (iter. = 30 in Fig. 13A), the fraction of the
12
measured over exact amplitude increases. This behavior
can be understood by evaluating the size of the `= 50
mode.
0.5 1 1.5 2
0.5
1
40 45 50 55 60
10-2
10-1
40 45 50 55 60
10-2
10-1
40 45 50 55 60
10-2
10-1
(C)
(B)
(A)
(D)
FIG. 13. (A) Trends for the ratio of measured to exact Leg-
endre amplitudes with image resolution and anisotropic diffu-
sion filter iteration. (B) Simulated Legendre spectrum around
`= 50 for a50 = 20µm at different resolutions for 30 itera-
tions of the anisotropic diffusion filter. (C) Simulated Legen-
dre spectrum around `= 50 at 2µm resolution for 10, 30, and
50 iterations of the anisotropic diffusion filter. (D) Same as
(C), but with a50 = 10µm.
The Legendre mode induced by a feature of size ∆x
can be estimated by considering the angle it subtends,
θx= arctan(∆x/R), given a target of radius R. Since
there are 2`internodal regions in an angular extent 2π,
the approximation
θ2π
2`(8)
can be used in combination with the angle θxto give an
estimate of the Legendre mode of the value a`induced
by the feature.
For a feature at `= 50, the tangential extent of the
feature is ∆x(`= 50) 12µm. At a resolution of
xres = 2µm, there are roughly 6 independent pixels
per internodal variation, while for ∆xres = 1µm and
xres = 0.66µm, there are 12 and 18, respectively. Since
the test image is formed by recording pixel values at twice
the resolution, the ∆xres = 2µm case would have 12
pixels per internodal variation, which is not significantly
larger than the single pixel scale of the gaussian noise
(noise is added on a pixel by pixel basis). As a result,
the amplitude of the feature is degraded as the filter is it-
erated because intensity values are smoothed across near
by pixels if their intensity values vary significantly. Like-
wise, when the feature size is close to the resolution of
the camera, this is a combined effect of the reduction of
edge sharpness due to blurring, reducing the gradients
in the image, and the degradation due to noise if the
noise level is significant. An increase in ∆x(`)/xres de-
creases the effect of anisotropic diffusion filter iteration
on the measured amplitude, as seen in Fig. 13(A). Like-
wise, Fig. 13(A) also shows that the increase in mode
amplitude from 10 to 20µm results in a larger ratio of
measured to exact amplitude. This decrease in measured
degradation of mode amplitude results from its greater
radial extent of the original `= 50 feature. Summarizing,
the metric for the characterization of the feature degra-
dation are the ratios of ∆x/xres, or ∆x/xpixel, when
xxpixel.
Simulated Legendre spectra in Fig. 13(B)-(D) shows
how iteration and resolution qualitatively change the
measured mode amplitudes. Figure 13(B) shows that as
the image resolution increases, the measured amplitude
of the a50 = 20µm feature is more accurately captured
compared to the initial mode amplitude indicated by the
dashed black line. At lower resolution the degradation
of the `= 50 mode results in increased power in nearby
modes. This is expected because diffusion changes the
intensity values of nearby pixels. Figure 13(C) shows a
similar effect with increased iteration for the 2µm resolu-
tion image. Since the scale length of the noise is compara-
ble to that of the `= 50 mode, increased iteration of the
anisotropic diffusion filter results in degradation and an
increase in amplitude of nearby modes. Figure 13D shows
similar effects for an initial amplitude of a50 = 10µm.
These features are consistent with those discussed in the
previous paragraph.
For the purposes of estimating the error for the cur-
rent experimental data, the evaluation of the inner shell
just after collision at R185µm with 3.7µm resolution,
would result in roughly 5 independent measurement val-
ues at `= 30. The film images are digitized at 1µm
resolution so this scale of features are reproduced over
approximately a 15 pixel wide region in the digitized im-
age. A few of the larger Legendre amplitudes in the spec-
trum near `= 30 are of order 5µm, naively suggesting
that these amplitudes may be significantly degraded by
the iteration process since this is near the resolution and
noise scales. However, these are not single mode varia-
tions, and many of the features leading to this amplitude
are in excess of 20µm, e.g. the visible structure in the
green line overlaid on the images of Fig. 5. Therefore, we
estimate, in comparison with the similar case of `= 50
and a50 = 20µm with 6 independent measurement points
13
per internodal variation in Fig. 13(a), that the measured
amplitudes up to `= 30 are no less than 60% of the ac-
tual value. The values at lower Legendre modes will be
more accurate than those at `= 30.
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Article
Full-text available
Simulations predict that directly driven multi-shell targets can provide a robust alternative to conventional high-convergence implosion concepts by coupling two to three times more energy into the final igniting thermonuclear fuel assembly than indirect-drive concepts. The three-shell directly driven Revolver concept [K. Molvig, M. J. Schmitt, B. J. Albright, E. S. Dodd, N. M. Hoffman, G. H. McCall, and S. D. Ramsey, Phys. Rev. Lett. 116, 255003 (2016)] utilizes a design that maximizes laser energy conversion into inward kinetic energy of the outermost ablator shell (∼9%) while minimizing the DT fuel convergence (∼9) to reduce the mixing of material from the innermost shell into the fuel. Inherent in this design concept is the use of 192 narrow beams (with a 1/e laser beam-to-capsule diameter ratio of 0.33) from the National Ignition Facility laser pointed in a polar direct drive laser configuration. In this paper, we demonstrate that low average laser intensity at the capsule surface (≤300 TW/cm²) limits the measured laser backscatter, indicating that a greater amount of laser energy is coupled into the target. Omega experiments have been performed to determine the coupling of laser energy to the outermost shell of a scaled Revolver target (i.e., the ablator shell) by measuring capsule implosion trajectories and scattered-light fractions for two different drive configurations. Comparisons of simulated shell trajectory and velocity profiles with experimental data obtained from self-emission images show good agreement and are consistent with measured scattered light data. Moreover, the low levels of scattered light measured are consistent with post-shot simulation results that show high hydro-coupling efficiency. These results strengthen the case for using narrow beams at low intensity to drive large ablator capsules for future direct-drive, multi-shell ignition concepts.
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Double shell capsules are predicted to ignite and burn at relatively low temperature (∼3 keV) via volume ignition and are a potential low-convergence path to substantial α-heating and possibly ignition at the National Ignition Facility. Double shells consist of a dense, high-Z pusher, which first shock heats and then performs work due to changes in pressure and volume (PdV work) on deuterium-tritium gas, bringing the entire fuel volume to high pressure thermonuclear conditions near implosion stagnation. The high-Z pusher is accelerated via a shock and subsequent compression of an intervening foam cushion by an ablatively driven low-Z outer shell. A broad capsule design parameter space exists due to the inherent flexibility of potential materials for the outer and inner shells and foam cushion. This is narrowed down by design physics choices and the ability to fabricate and assemble the separate pieces forming a double shell capsule. We describe the key physics for good double shell performance, the trade-offs in various design choices, and the challenges for capsule fabrication. Both 1D and 2D calculations from radiation-hydrodynamic simulations are presented.
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