Determining the Self-Similar Stage of the Rayleigh-Taylor Instability via LLNLs NIF Discovery Science Experiments A. Shimony12 C.M. Huntington3 K.A. Flippo4 Y. Elbaz5 S.A. MacLaren3 D. Shvarts16and G. Malamud12

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Determining the Self-Similar Stage of the Rayleigh-Taylor Instability via LLNL’s NIF

Discovery Science Experiments

A. Shimony1,2, C.M. Huntington3, K.A. Flippo4, Y. Elbaz5, S.A. MacLaren3, D. Shvarts1,6and G. Malamud1,2

1Nuclear Research Center Negev, Beer Sheva 84190, Israel

2University of Michigan, Ann Arbor, MI 48109, USA

3Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

4Los Alamos National Laboratory, Los Alamos, NM 87545, USA

5Israel Atomic Energy Commission, Tel Aviv 61070, Israel

6Ben Gurion University of the Negev, Beer Sheva 84105, Israel

We report a novel measurement of the late time self-similar growth constant αBof the Rayleigh-

Taylor instability (RTI) from controlled initial perturbations. To this end, we have developed a

laser-driven experiment, ﬁelded on the National Ignition Facility (NIF), to explore deeply non-linear,

multimode hydrodynamic growth of a planar interface. The measured value is αB= 0.038 ±0.008,

which is consistent with previously reported 2D simulations and closer to previously reported 3D

simulations. This resolved the known discrepancy between experiments and simulations of RTI.

The Rayleigh-Taylor instability (RTI) evolves when a

light ﬂuid pushes a heavy ﬂuid [1,2] and ubiquitous in

physical systems of substantial diﬀerent length scales like

Inertial Conﬁnement Fusion (ICF) capsules [3] and super-

novae [4]. In the case of a narrowband multimode initial

perturbation, the RTI reaches the regime of self-similar

evolution after G≈3 [5], where Gis the number of bub-

ble merger generations. At this stage, the magnitudes of

the spike and bubble (hSand hB, respectively) are given

by hS/B =αS/BAgt2, where gis a constant acceleration

at the unstable interface, A=ρ2−ρ1

ρ1+ρ2is the Atwood num-

ber ( ρ1and ρ2are the densities of the lighter ﬂuid and

the density of the heavier ﬂuid, respectively), tis the

evolution time, and αis a constant that describes the

growth, which may be diﬀerent for the spike and bubble.

The value of αBgoverns the mixing process and has been

a topic of research for decades.

Despite active research, signiﬁcant discrepancies re-

main between theoretical, computational, and experi-

mental calculations of αB. Recent theoretical model re-

sults suggest a value of ∼0.05 for 3D immiscible ﬂu-

ids [5]. This result is consistent with LEM experiments

[6] and bubble-merger models [7,8], but a factor of ∼2

higher than the results of full numerical 3D simulations

[9,10]. This last result is claimed to be attributed to the

entrainment of the two ﬂuids in the bubble caused by a

3D small scale turbulent ﬂow, which reduces the eﬀec-

tive Atwood number by ∼2 for miscible ﬂuids, as shown

in full numerical simulations [11].

To resolve the discrepancy, introduced above, between

experiments and simulations, a precise comparison be-

tween them should be made. The initial perturbations

in most of the past simulations were of a narrowband, so

that long wavelengths were absent in the initial growth

and the resulted evolution of the mixing zone was of bub-

ble merger dynamics. However, in past experiments, the

control over the initial perturbations was limited and ini-

tial long wavelengths could aﬀect growth and increase the

measured value of αB, as demonstrated by simulations

[12]. In this work, we present a novel experiment, with

a controlled narrowband initial perturbation [13], which

was performed on the National Ignition Facility (NIF).

The experimental results were compared to a model and

to a hydrodynamic simulation.

Several aspects of the present experimental conﬁgura-

tion were adapted from similar hydrodynamics studies on

the National Ignition Facility (NIF), including the laser

drive, structure of the ablator [14,15], low-density foam

conﬁguration [15,16], and x-ray source [15,17]. Essen-

tial elements are described below; further details can be

found in the relevant publications.

The unstable interface under investigation consisted of

a plastic disk at a density of 1.43 g/cm3, mated to a foam

cylinder. As shown in Fig. 1, the portion of the plastic

facing the hohlraum and served as the “ablator” was plas-

tic doped with a fraction of iodine (C50H47I3, “CHI”),

which served to stop moderate-energy x-rays (Au M-

band >2 keV) from reaching the interface. Following

the CHI ablator, a layer of polyamide-imide plastic (PAI,

C22H14N2O3) formed the bulk of the dense interface, ex-

cept for a 300 µm wide strip of the CHI that spanned

half of the target width at the interface with the foam.

While the PAI was largely transparent to the diagnostic

x-rays, the purpose of this tracer strip was to absorb the

x-rays and provide contrast in the image, highlighting

the region location of the dense layer as it mixed into the

low-density foam.

The same x-ray opaque tracer-layer concept that was

used in the plastic was employed in the foam. Most of the

foam cylinder was machined from carbon resorcinol foam

(CRF) at an initial density of approximately 0.08 g/cm3.

In a groove machined half-way through the cylinder, a

300 µm wide strip of carbon foam with a nickel dopant

(C88Ni12) [18], also nominally 0.08 g/cm3, was inserted.

The nickel K-edge at 8.3 keV strongly absorbed the 9

keV diagnostic x-ray signal, providing a contrasting dark

layer where the doped foam was mated to the PAI plastic.

arXiv:2210.06631v1 [physics.flu-dyn] 12 Oct 2022

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DeterminingtheSelf-SimilarStageoftheRayleigh-TaylorInstabilityviaLLNL'sNIFDiscoveryScienceExperimentsA.Shimony1;2,C.M.Huntington3,K.A.Flippo4,Y.Elbaz5,S.A.MacLaren3,D.Shvarts1;6andG.Malamud1;21NuclearResearchCenterNegev,BeerSheva84190,Israel2UniversityofMichigan,AnnArbor,MI48109,USA3LawrenceLivermor...

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Determining the Self-Similar Stage of the Rayleigh-Taylor Instability via LLNLs NIF Discovery Science Experiments A. Shimony12 C.M. Huntington3 K.A. Flippo4 Y. Elbaz5 S.A. MacLaren3 D. Shvarts16and G. Malamud12

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