INERTIAL CONFINEMENT · NIF Targets Validating DT Ice- ... nal location of the beams (small...

INERTIAL CONFINEMENTINERTIAL CONFINEMENT LawrenceLivermoreNationalLaboratory

LawrenceLivermoreNationalLaboratory

October 1999—March 2000, Volume 1, Number 1ICF Semiannual Report

UCRL-LR-105821-00-1

The Development of Plastic Mandrels for NIF Targets

Validating DT Ice-Surface Roughness Diagnostics for NIF �Inertial Confinement Fusion

Exploring the Limits of the National Ignition Facility’s Capsule Coupling

On the Accuracy of X-Ray Spectra Modeling of Dense Inertial Confinement Fusion Plasmas

Demonstration of Time-Dependent Symmetry Control in Hohlraums by Drive-Beam Staggering

Intense High-Energy Proton Beams from Petawatt Laser Irradiation of Solids

On the Web:http://www.llnl.gov/nif/icf.html

This document was prepared as an account of work sponsored byan agency of the United States Government. Neither the UnitedStates Government nor the University of California nor any of theiremployees makes any warranty, express or implied, or assumes anylegal liability or responsibility for the accuracy, completeness, orusefulness of any information, apparatus, product, or process dis-closed, or represents that its use would not infringe privately ownedrights. Reference herein to any specific commercial product, pro-cess, or service by trade name, trademark, manufacturer, or other-wise, does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Government orthe University of California. The views and opinions of authorsexpressed herein do not necessarily state or reflect those of theUnited States Government or the University of California and shallnot be used for advertising or product endorsement purposes.

UCRL-LR-105821-00-1October 1999–March 2000

Printed in the United States of AmericaAvailable from

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Price codes: printed copy A03, microfiche A01.

This work was performed under the auspices of the U.S. Departmentof Energy by University of California Lawrence Livermore NationalLaboratory under Contract No. W–7405–Eng–48.

The ICF Semiannual Report ispublished by the Inertial Confinement Fusion (ICF)Program at the Lawrence Livermore NationalLaboratory. The journal reports selected currentresearch within the ICF Program. Major areas of inves-tigation include fusion target theory and design, targetfabrication, target experiments, and laser and opticalscience and technology. In addition, the Laser Scienceand Technology program element of LLNL’s NIFPrograms serves as a source of expertise in developinglaser and electro-optics capabilities in support of theICF mission and goals and also develops new lasers forgovernment and commercial applications. To keep ourreaders informed of these new capabilities, the ICFSemiannual Report, which replaces the ICF QuarterlyReport, covers additional non-ICF funded, but related,laser research and development and associated appli-cations. Succeeding issues of this journal will not be inprint but will be posted on the ICF Program website.Questions and comments relating to the technical con-tent of the journal should be addressed to ICF/NIF andHEDES Program, Lawrence Livermore NationalLaboratory, P.O. Box 808, L-475, Livermore, CA 94551.

The Cover: The two top figures (see p. 20) showthe comparison between using a Gaussian-fit andedge-fit (bright thin lines) to map the location of thebright band (bright diffuse region) obtained in a simu-lated shadowgraph image from DT ice in a target cap-sule. Shadowgraphy is the primary technique currentlyin use to determine the roughness of the fuel ice layerin transparent shells. The edge-fit (upper figure) intro-duces significantly more noise into the modal analysisof the bright band as compared to the Gaussian-fit andtherefore does not give an accurate representation ofthe ice roughness. The lower-right figure shows a Novagasbag target (p. 36) that was used to produce a long-scalelength, high-density, and high-temperature plas-ma. This type of target provided a vast range ofimportant atomic physics and plasma physics informa-tion. The lower-left figures (p. 44) show gated x-rayimages (5 keV) at 0.8 ns (1.2 ns) of where the early(late) OMEGA laser beams are interacting with the wallplasma. The deviation of the x-ray spots from the origi-nal location of the beams (small circles) is due to wallmotion. The rippling, satin-like background (p. 24) is asimulated transmission interferogram of a two-dimen-sionally rough fuel ice surface.

iUCRL-LR-105821-00-1

Scientific EditorJohn Moody

Publication EditorAl Miguel

DesignerStacy Bookless

Technical EditorsJason CarpenterCindy CassadyAl Miguel

Classification EditorRoy Johnson

Art StaffClayton DahlenStacy BooklessPam DavisAmy Henke

Cover DesignStacy Bookless

ICF Quarterly Report

INERTIAL CONFINEMENTINERTIAL CONFINEMENT

ICF Semiannual Report October 1999–March 2000, Volume 1, Number 1

In this issue:

Foreword iii

The Development of Plastic Mandrels for NIF Targets (R. Cook) 1All NIF capsule options except machined Be require a mandrel upon which the ablatoris deposited. This mandrel, a thin-walled plastic shell, sets the baseline sphericity of thefinal capsule, especially over the low modes. In this report we detail the processes andrelated science that have allowed us to meet target specifications.

Validating DT Ice-Surface Roughness Diagnostics for NIF Inertial Confinement Fusion (J. A. Koch) 13This work describes recent progress in quantifying our capability to measure DT ice-surface roughness in NIF ignition targets. The conclusion is that current diagnostics are accurate and reliable when the proper data analysis procedure is used.

Exploring the Limits of the National Ignition Facility’s Capsule Coupling (L. Suter) 25We find that 3–4¥ increases in absorbed capsule energy appear possible, providing apotentially more robust target and ~10¥ increase in capsule yield.

On the Accuracy of X-Ray Spectra Modeling of Dense Inertial Confinement Fusion Plasmas (S. H. Glenzer) 35This article reports on a test of non-local thermodynamic equilibrium modeling of x-rayemission spectra in dense plasmas. The authors used ultraviolet Thomson scattering toindependently measure the electron temperature of the plasma. Their findings demon-strate that the fully kinetic atomic physics code HULLAC agrees on average to within 6%with the experiment while simplified calculations show discrepancies of order 20%.

Demonstration of Time-Dependent Symmetry Controlin Hohlraums by Drive-Beam Staggering (R. E. Turner) 43ICF targets require a high degree of spatial symmetry in the x-rays that drive theirimplosion. Within a hohlraum, plasma formation changes the laser absorption loca-tions, resulting in time-dependent symmetry shifts. This article reports an experimentthat demonstrates how such shifts can be minimized by firing different beams with different pulse shapes, a process known as beam phasing.

ii

IN THIS ISSUE

UCRL-LR-105821-00-1

Intense High-Energy Proton Beams from Petawatt Laser Irradiation of Solids (R. A. Snavely) 51A significant discovery made with the petawatt laser at LLNL was the efficient genera-tion of well-collimated high-energy proton beams from the rear surface of thin targets.The experimental evidence for the discovery is presented and the acceleration mecha-nism is discussed. There is now widespread interest in the phenomenon motivated bythe potential for a range of novel applications.

Publications and Presentations A-1

iii

FOREWORD

UCRL-LR-105821-00-1

FOREWORDThis first issue of the ICF Semiannual Report contains articles whose diverse subjects

attest to the broad technical and scientific challenges that are at the forefront of the ICFprogram at LLNL.

The first article describes the progress being made at solving the surface roughnessproblem on capsule mandrels. All NIF capsule options, except machined beryllium,require a mandrel upon which the ablator is deposited. This mandrel sets the baselinesphericity of the final capsule. Problems involving defects in the mandrel have been over-come using various techniques so that 2-mm-size mandrels can now be made that meetthe NIF design specification.

The second article validates and provides a detailed numerical investigation of theshadowgraph technique currently used to diagnose the surface roughness of a fuel icelayer inside of a transparent capsule. It is crucial for the success of the indirect-drive igni-tion targets that the techniques used to characterize ice-surface roughness be well under-stood. This study identifies methods for analyzing the bright band that give an accuratemeasure of the ice-surface roughness.

The third article describes a series of realistic laser and target modifications that canlead to 3–4 times more energy coupling and 10 times greater yield from a NIF indirect-drive ignition target. Target modifications include using various mixtures of rare-earthand other high-Z metals as hohlraum wall material and adjusting the laser-entrance-holesize and the case-to-capsule size ratio. Each option is numerically examined separatelyand together.

The fourth article reviews how detailed x-ray and Thomson scattering measurementsfrom a high-density and high-temperature gasbag plasma are used to test spectroscopicmodeling techniques. There is good agreement between the model and experimentaldielectronic capture satellite intensities. However, improvements are required in themodeling of inner shell collisionally populated satellite states. These improvements canhave important implications for the interpretation of inertial confinement fusion capsuleimplosions.

The fifth article reports on experiments using the OMEGA laser that investigate sym-metry control in hohlraums. The experiments explore a control method where differentpointings are used for different groups of beams and the beams are staggered in time.This gives a dynamic beam pointing adjustment during the laser pulse. Measurements ofthe capsule symmetry show agreement with simulations and show the ability to controllow-mode drive asymmetries.

The sixth article reports on the observation of an intense high-energy proton beamproduced by irradiating a thin-foil target with the petawatt laser. This experiment isimportant for understanding new mechanisms of ion acceleration using high-intensityshort-pulse lasers. Proton beams of the type observed here could be of interest for appli-cations ranging from medicine to fast ignition.

John MoodyTarget Ignition Physics ProgramScientific Editor

1UCRL-LR-105821-00-1

All National Ignition Facility (NIF)capsule options except machined Berequire a mandrel upon which the ablatoris deposited. This mandrel, a thin-walledplastic shell, sets the baseline sphericity ofthe final capsule, especially over the lowmodes. Subsequent ablator coating opera-tions may degrade the capsule surface finish and are unlikely to improve it. ForNova capsules, the mandrels were histori-cally ~0.5-mm-diam polystyrene thin-walled microshells produced by solutiondroptower methods.1 However, thesemethods are limited to shell sizes of lessthan 1-mm diameter. In 1997, LawrenceLivermore National Laboratory andGeneral Atomics began to explore the useof microencapsulation techniques to pro-

duce NIF-scale capsule mandrels. Thesetechniques had been largely developed forinertial confinement fusion (ICF) capsulefabrication by researchers at OsakaUniversity for small polystyrene shells;2however, the techniques were easilyextended to produce shells with 2-mmdiameters needed for the NIF. At issue waswhether the required symmetry andsphericity could be achieved. The NIF cap-sule design sphericity specifications areessentially taken from the best sphericitiesachieved for Nova capsules.3 Not only arethe techniques to be used different, but thecapsules are to be four times larger.

The basic microencapsulation process(see Figure 1) involves encapsulating awater droplet with a nonaqueous polymer

THE DEVELOPMENT OF PLASTIC MANDRELSFOR NIF TARGETS

Robert Cook Masaru Takagi

Barry McQuillan* Richard Stephens*

Dropletgeneration

Aqueousphase Solid

shell

Nonaqueouspolymersolution

Loss oforganicsolvent

aq

aq aq Airdry

FIGURE 1. Cartoon ofmicroencapsulation process.(NIF-0401-02076pb01)

*General Atomics

2

THE DEVELOPMENT OF PLASTIC MANDRELS FOR NIF TARGETS

UCRL-LR-105821-00-1

subsequent fabrication steps, as well as alarge mode-2 out-of-round. These lowest-mode asymmetries were thought to origi-nate in the basic hydrodynamics of thecuring process, coupled with density dif-ferences between the bath, oil phase, andinner water phase. Second, the mandrelsurface also had significant amplitude inmodes 10 to 50 (defects on length scalesof 100s of microns). Wall thickness mea-surements generally showed these repre-sented “ripples” in the wall rather thanthickness variations. It was suspectedthat these defects had multiple causes:collisions of the mandrels with each otherand/or the bath stirring device, surfacedistortions caused by large vacuoles(voids) within the mandrel wall, andsome kind of modulated stress resulting

solution and suspending this encapsulateddroplet in a stirred aqueous bath. During a multihour curing phase, the organic solvent slowly dissipates into the bath,leaving a solid polymer shell filled withwater, which can be removed by slow airdrying. Shells in the 2-mm-diam (or larg-er) size could be easily prepared; however,the quality of these shells did not satisfythe NIF specifications.

Figure 2 illustrates in cartoon fashionthe types of defects, their manifestation inexample atomic force microscope (AFM)equatorial traces of the shell, and therelated effect on the surface power spec-tra.4 First, shells had significant wallthickness variation, a nonconcentricity(NC) or P1 defect that does not manifestitself in AFM traces, but which can affect

nm

360300240180120600Angle

Pow

er (n

m2

)

10 100 1000

Mode number

High-frequencyroughness

NIF capsuleignition

requirement

(d)(c)(b)(a)

–2000

–1000

0

1000

2000

10 7

10 6

10 5

10 4

10 3

10 2

10 1

10 0

10 –1

10 –2

Middle-mode“bump”

Mode-2out-of-round

FIGURE 2. Shown at the top are exaggerated drawings of microencapsulated shell defects: (a) mode-1 wall thicknessvariation, (b) mode-2 out-of-round, (c) middle-mode roughness, and (d) high-frequency roughness due to surfacedebris and surface or near-surface vacuoles. Below left are example AFM SphereMapper traces (three parallel traces 40 mm apart). For a NIF shell, 1 degree represents about 17.5 mm of a surface trace. Thus the prominent features atabout 75, 145, 210, and 290 degrees are “bumps” that are 0.2 to 0.4 mm high and 100s of mm wide. These give rise to thepower over modes 10 to 50 in the power spectrum on the right. The features in the traces that appear as “narrowspikes” are due either to surface debris or surface vacuoles and are responsible for the high-frequency power.(NIF-0401-02077pb01)

3


UCRL-LR-105821-00-1

in shell wall buckling. Third, the shellsurface had a rather high amplitude inmodes >100. These high-frequencydefects were due in part to surface debrisand the presence of small-diam vacuolesin the polymer wall, some of which dis-rupted the surface.

In this article, we describe how theseproblems were overcome or at leastreduced, so that we are now able to pro-duce 2-mm mandrels that are beginning tomeet the design specifications. Our objec-tive is not to provide detailed procedures,but rather to discuss the scientific basis ofthe approaches we have taken and to doc-ument their effectiveness in meeting ourobjectives. In the final section, we summa-rize the current mandrel status.

MicroencapsulationMethod

The initial microencapsulated dropletsare prepared using a triple orifice dropletgenerator.5,6 As schematically shown inFigure 1, the innermost orifice that deliv-ers pure water is inside a larger orifice thatdelivers a nonaqueous polymer solutionresulting in the encapsulation of the innerdroplet. This compound droplet is thenstripped off the orifice by an outer aque-ous flow that carries it into an aqueousbath. The compound droplet size is con-trolled by the rate of this flow and the ori-fice dimensions, while the relativeamounts of inner water and oil phases,which determine the wall thickness, areprecisely controlled by syringe pumps.NIF-scale shells can be generated at a rateof about 2.5 s–1, and though metastable,are remarkably robust. They can, forinstance, be squeezed down a tube whoseinner diameter is ~20% smaller than theshell outside diameter (OD) without lossof the inner water phase. The typical batchsize is about 3000 shells, and the variationin final diameter (~2000 µm) and wallthickness (~15 µm) within a batch is lessthan 0.5% and 3%, respectively. The poly-mer used in our work is poly(a-methyl-styrene) (PaMS); its structure is shown inFigure 3. The polymer has a very narrow

molecular weight distribution centered atabout 400,000. PaMS is used because itcan be thermally decomposed to gaseousproducts at 300°C, a step in subsequentcapsule preparation.7 The polymer is dis-solved in fluorobenzene, a solvent pickedprimarily for its reasonably close densitymatch [r(25°C) = 1.024 g/cm3] to theaqueous media. The aqueous bath andstripping fluid must contain a “protectivecolloid” to prevent interaction andagglomeration of the compound droplets.This has typically been about 2 wt%poly(vinyl alcohol) (PVA), but for reasonsthat will be discussed later, we currentlyuse poly(acrylic acid) (PAA) at a muchlower concentration.

Following droplet generation, the com-pound fluid shells must be agitated forsome period of time to center the inneraqueous droplet in the oil shell. The exactmechanism of this centering is not wellunderstood, but Norimatsu8 has shown inmodel calculations that fluid dropletdeformation causes core centering.Experimentally, we have found that cen-tering can be achieved rapidly with vari-ous bath agitation methods. Initially, weused a simple open beaker with a stir pro-peller, but have since moved to a rotatingdrum device as pictured in Figure 4. Thisapproach tumbles the shells very effective-ly, but at the same time more gently, giv-ing higher batch yields of mandrels withvery uniform walls and also allows us toeasily control the rate of solvent loss fromthe fluid shells; that latter feature hasimportant consequences as described later.

When the shells have cured, the interiorwater phase must be removed. Shells areput in 25% ethyl alcohol solution to createan osmotic pressure and diffuse some ofthe water out of the interior water phase.This water removal puts a compressivestress on the shell that will increase until

( CH2 C

CH3

–

__ ) �Mw � 400,000

... _ _... n

FIGURE 3. PaMS structure.(NIF-0401-02078pb01)

4


UCRL-LR-105821-00-1

the shell buckles or a gas bubble nucleatesin the interior water phase and relieves thepressure. After two or three days, we mustnucleate the gas bubble with an ultrasonicbath to avoid the cracking or collapse ofthin wall (

5


UCRL-LR-105821-00-1

dependence on the droplet size and thatthe distortion scales with 1/g. It is clearfrom these simple models that good densi-ty matching (low Dr), attention to bathagitation, and maximization of the interfa-cial tension g are critical to minimizingMOOR.

Density MatchingOur initial studies showed us that the

basic mode-2 out-of-round was sensitive tothe density match of the bath to the com-pound droplet (inner water core plus oilphase), consistent with Eq. 1. Careful mea-surements of the density of fluorobenzenesolutions of PaMS as a function of tempera-ture and concentration were made to deter-mine the optimal density matchingconditions, at least at the time of dropletgeneration. Since the thermal expansioncoefficient of fluorobenzene is greater thanwater, it was possible to use temperature toadjust the density of the compound dropletto that of the bath density. However, thedensity of the compound drop is timedependent due to the continuous loss of thefluorobenzene during cure. Careful model-ing calculations showed that the variationin compound droplet density would be lim-ited to a few thousandths of a g/cm3, 6probably about as good as our absolute con-trol given small variations in the droplet todroplet size and wall thickness.

Application of these density-matchingcontrols and more gentle bath agitationtechniques certainly improved the qualityof our shells, but still left us somewhatabove the specification we were trying tomeet. Specifically, the mode-2 out-of-roundwas still a few microns in the best shells,somewhat larger than the desired onemicron. In addition, middle-mode rough-ness was still high, with shells generallyshowing a clear bump in the power cen-tered at modes 10 to 20, and vacuoles nearthe surface as well as surface debris werestill causing significant high-frequencyroughness. The ultimate solution to themode-2 problem is detailed in the next sec-tion; the middle- and higher-mode prob-lems are discussed in the sections“Solutions to the Mode-10 to –50 BumpProblem” and “Solutions to the High-Frequency Roughness” that follow.

Interfacial TensionIt was clear that an additional handle to

control the mode-2 out-of-round was toincrease the interfacial tension g. We beganby considering other organic solvents forthe oil phase,6 but the requirements fordensity matching, water insolubility, andpolymer solubility drastically limited ourchoices, and we determined there was notmuch to gain by this approach. Thus,effort was focused on modification of theaqueous bath phase.

As noted above, PVA has historicallybeen used as the protective colloid addi-tive to the bath. PVA acts as an entropical-ly driven steric stabilizer, resisting theapproach of two encapsulated droplet sur-faces because of the entropic consequencesof deforming the PVA random coils in theaqueous phase between them. This action,however, is independent of the effect thatPVA or any other polymeric stabilizermight have on the oil/aqueous interfacialtension. A typical value of the interfacialtension between a pure nonpolar organicfluid such as benzene and pure water isabout 35 dynes/cm, about half the valueof pure water against air. Interfacial ten-sion measurements showed that our rela-tively impure systems (fluorobenzenecontaining PaMS vs water containingPVA) had an interfacial tension abouttwenty times less (Table 1).

We have discovered that high molecu-lar weight PAA is an equally effectiveprotective colloid, while significantlyincreasing the droplet/bath interfacial tension. The differences between PAA andPVA with respect to interfacial tensionwere clearly demonstrated in a series ofexperiments based on homogeneous

TABLE 1. Interfacial tension measurements by droplet deformation of 2.5-mm-diam PaMS/fluorobenzene drops in various aqueous solutions. Measurements made at 45∞C.11

Additive wt% D diam (mm) Dr (g/cm3) g (dyne/cm)

None (0) 165 0.021 3.0PVA 2 221 0.016 1.7PAA 0.025 17 0.021 30.PAA 0.00625 29 0.021 17.PAA 0.00156 18 0.021 28.

6


UCRL-LR-105821-00-1

droplet deformation.11 Droplets 2.5 mmdiam of 15 wt% PaMS in fluorobenzenewere placed on a flat glass support in an aqueous bath containing pure water, 2 wt% PVA, or PAA at a variety of concen-trations as shown in Table 1. The dropletshape was recorded photographically, andfrom this image the horizontal and verticaldrop diameters were measured. Eq. 1 wasthen used to evaluate the value of theinterfacial tension g using independentlymeasured values of the fluid densities.6This method is a rough approximation tothe sessile drop method of determininginterfacial tension,12 and is adequate todemonstrate the marked differencebetween PVA and PAA solutions. We findthat the interfacial tension of the oil/PAAsystem is a factor of 10 or more higherthan that of the oil/PVA system, in factnear to the expected value for a pure non-polar solvent against water.

The structures of PVA and PAA areshown in Figure 5a. The effectiveness ofPAA as a protective colloid at very lowconcentrations (0.01 to 0.05 wt%) may bedue in large part to the very high molecu-lar weight, but the polymer molecularweight should have little effect on theinterfacial tension. The differences may bedue to the weak ionic character of PAA (incontradistinction to PVA) in aqueousmedia (Figure 5b). This polyelectrolytecharacter leads to strong interactionsbetween the macromolecules in solution,with the result that for concentrations at or

above 0.05 wt%, the quiescent solutionforms a thixotropic gel. Another manifes-tation of this strong interaction is in mea-surements of solution viscosity as shownin Figure 6. We have found that microen-capsulated shells can only be produced ata bath viscosity of less than about 10 to 20 cP (PAA concentrations no greater than0.05 wt%); at higher viscosity the shearfrom mixing causes the encapsulateddroplet to lose its inner aqueous core.

The increase in interfacial tension mani-fests itself in the microencapsulation pro-cess in shells with distinctly reducedmode-2 out-of-rounds as illustrated inFigure 7, where we show in histogramform the best PVA and PAA batch results.Also shown is the nonconcentricity (NC),which also shows a significant improve-ment. Figure 7 also demonstrates the sig-nificant increase in consistency madepossible by the use of PAA.

Solutions to the Mode-10to -50 Bump Problem

Almost all microencapsulation PaMSshells regardless of size have had aprominent peak or shoulder in the powerspectrum near modes 10 to 20, often 2 to 3orders of magnitude higher than the NIFspecification. Frequently, this defect can beseen clearly as oscillations in the AFM

( CH2 – C )n

OH__

_ _

H

OH

__

H

C_=O

PVA PAA

OH

_

H

C_=O O–

_

H

C_=O

(a)

(b)

( CH2 – C )n

( CH2 – C )n

... _ _ ... MW � 25,000 ... _ _ ... MW � 1.0 x. 10

6

... _ _ ... + H2O ( CH2 – C )n ... _ _ ... + H3O

+

FIGURE 5. (a) Structures of PVA and PAA. (b) Partial ionization of PAA.(NIF-0401-02080pb01)

10

100

1000

Vis

cosi

ty (c

P)

0.01 0.1 1Polymer conc (wt%)

PAA

PVA

FIGURE 6. Viscosity of PAA and PVA as a function of poly-mer concentration. (NIF-0401-02081pb01)

7


UCRL-LR-105821-00-1

equatorial traces with amplitudes of 100sof nm and wavelengths of ~500 µm.Simultaneous wall thickness measure-ments usually show that the largest com-ponent of the defect is a wall “wrinkle”rather than a thickness variation. Sincepower in modes between 10 and 50 is themajor driver of Rayleigh–Taylor instabili-ty in the implosion, it was essential toidentify the origin of the defect and elimi-nate its presence.

There have been multiple hypothesesfor the origin of this mode-10 to -20power, among them buckling due toosmotic stress during the curing13 or dueto unspecified shrinking stresses in thedrying (the focus on stress being motivat-ed by the very long wavelength nature ofthe defect and the view that this was theproduct of some global rather than localcause). We now believe that the seeds ofthis low-mode structure are set by convec-tion cells that form in the fluid shell wallduring the curing phase. The existence ofconvection cells is well known in the dry-ing of thin flat films. This phenomenon iscalled Marangoni convection and is drivenby surface tension gradients at the surfaceof the film.14 These gradients can be gen-erated by temperature (heat flow) or con-centration (mass flow) differences. In oursituation, we have a variation of surfacetension with polymer concentration. Thisconvection is analogous to Rayleigh con-vection in thicker films, where density gra-dients due to temperature are the source.15

Marangoni convection for heat transferhas been studied in thin flat films for

many years, but application of these prin-ciples to the drying of spherical shells isnew. Two important results can bederived.16 First, the theory yields the con-ditions under which Marangoni convec-tion is “turned on,” namely that theMarangoni number M be greater thansome critical value Mc. The Marangoninumber for our situation of a shell losingsolvent from its outer wall is defined as

(3)

where DC is the difference in polymer con-centration C from the inside to the outsideof the fluid wall of thickness w, (dg/dC) isthe change of the outer surface interfacialtension with respect to polymer concentra-tion, h is the oil phase viscosity, and D isthe diffusivity of fluorobenzene in the oilphase. Second, the theory allows the pre-diction of the spherical harmonic modethat should characterize the lateral lengthscale of the convection cells. In a flat filmthere is only one characteristic length, thethickness of the film, and this determinesboth the critical Marangoni number andthe dimension of the convection cell.However, for a spherical shell,17 there aretwo length scales of interest, the thicknessof the oil phase wall w and the circumfer-ence 2πr of the oil phase shell. These twolength scales give rise to a set of solutionsof the hydrodynamic equations, each solu-tion corresponding to a different sphericalharmonic mode l characterizing the relative

MCw d dC

D ,= D ( / )g

h

15% 14%19%

5

4

3

2

1

0

1059

2023

2025

2037

2047

2050

3011

3013

3015

3017

3035

3037

2 wt% PVA 0.05 wt% PAABatch numbers

5

4

3

2

1

0

NC

(%)

OO

R (µ

m)

FIGURE 7. Histogram pic-ture of OOR (black) andNC (gray) for 6 batcheseach of PVA and PAA pro-cessed shells.(NIF-0401-02082pb01)

8


UCRL-LR-105821-00-1

size of the convection cells. However, foreach mode, there is a unique criticalMarangoni number. Thus, the physicallyobserved l mode will be the one that givesthe minimum critical Marangoni number.Using our best estimates for our experi-mental process parameters, we find thatthis mode is approximately given by

(4)

Thus the characteristic size of theobserved convection cell is very close tofour times the initial film thickness w. The value of r/w is dependent only on theratio of the inner water and oil phase flowrates, and we find for typical encapsula-tion conditions that the predicted modebased upon the initial encapsulation conditions is between 8 and 17, consis-tent with the experimental results wehave seen.

These shells are not in steady state butrather are continually changing duringcure. As the solvent is removed, the inter-facial tension and probably also its gradi-ent are changing, the wall thickness isdecreasing, the viscosity is dramaticallyincreasing, and the diffusivity of fluo-robenzene probably decreasing. Thus,primarily because of the decrease in wand increase in h, the Marangoni numberfor the shell is decreasing during curing.Assuming M starts off above Mc, at sometime later its value drops below the criti-cal value and convection stops. If the oilphase shell is too viscous at this point to“relax out” distortions caused by the con-vection cells, their imprint will remain inthe final dry shell. Experimentally, wefind that the mode structure we see corre-sponds roughly with the compounddroplet conditions at the time when thedroplet is initially formed, when the con-vection is easiest due to low viscosity,rather than at some later time when M isstill greater than Mc, but the calculatedlob has changed due primarily to thethinning wall. The failure of the shell con-vection cells to “adjust” to the changinggeometry by decreasing their size (andsimultaneously increasing their number)is possibly due to an activation barrier.

Although we do not have quantitativevalues for many of the relevant terms, thefunctional relationships developed clearlypoint to processing changes that candecrease M and thus potentially shut offMarangoni convection while the shell isstill fluid enough to relax, or perhaps pre-vent it entirely. As described below, theeasiest parameters to control are the poly-mer concentration difference across thewall DC and the initial wall thickness w.

We can decrease DC by slowing theremoval of fluorobenzene during curing.Control of the rate of fluorobenzeneremoval is achieved by providing a flowof nearly saturated fluorobenzene vapor tothe space above the curing bath as shownin Figure 4. In principle, the level of satu-ration can be controlled exactly; however,in the experiments described here, wehave simply bubbled the N2 flow througha tube containing fluorobenzene at thesame temperature as the bath. As shownin Figure 8, we find that 2-mm OD shellscured in one day (without a fluorobenzenevapor flow) show a substantial mode-10feature compared to shells in which thecuring was extended to four days usingfluorobenzene vapor. By extending thedrying, we have decreased DC and pre-sumably dropped the shell Marangoninumber below the critical value, eliminat-ing convection, either from the time ofcompound droplet formation or while theoil layer was still fluid enough to relax.

Decreasing w also dramatically decreas-es the mode-10 power. Thinner-walledshells can be made by starting with moredilute polymer in the oil phase and/or byencapsulating with a thinner initial oilphase layer. The latter is preferable fromthe point of view of minimizing the initialshell M value, hopefully to a value belowMc so that convection is not turned on.However, the use of more dilute solutionis often necessary for the formation of sta-ble initial compound droplets by thedroplet generator. In these cases, the initialvalue of M may, in fact, be greater due tothe lower viscosity of the oil phase; how-ever, we believe M drops below Mc whilethe shell is still fluid enough to relax awaythe convection cell imprint. To demonstratethe effect of decreasing w, in Figure 9 weplot the observed mode-10 power for

lr

wob ,@ 2

4p

9


UCRL-LR-105821-00-1

individual shells as a function of the finaldry shell wall thickness for a set of 950-µm-diam shells all made with 8 wt%PaMS in fluorobenzene. For these shells,the variation in wall thickness was con-trolled by varying the relative oil to innercore water flow rates. Although shell-to-shell results vary significantly, the mode-10 power clearly increases dramatically(note log scale) with thicker-walled shells.

These recent experiments, though quali-tative in nature, demonstrate that we haveidentified Marangoni convection as thecontrolling mechanism that leads to themode-10 to -20 power seen on previouslyfabricated mandrels. Further, we haveshown that by process control of slowingthe curing process and/or reducing w, wecan either prevent the onset of Marangoniconvection or insure that it turns off whilethe shell is still fluid enough to relax.

Solutions to the High-Frequency Roughness

Vacuoles Polymer shells made by microencapsu-

lation have historically had a problemwith vacuoles. The vacuoles are presentas a dispersion of voids or bubbles in thefinal shell wall with diameters up to several microns. They affect the high-frequency surface finish by either

(b)(a)Po

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NIF capsule specification

–2000

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perturbing the surface if they lie close to it or by creating small “pits” if they breakthrough the surface as the shell dries.These very-high-frequency defects arethen amplified in subsequent coatingoperations to produce unacceptably rough surfaces.

It had long been understood that thevacuoles were caused by phase separationof water in the oil phase wall during thecuring step. However, the specific mecha-nism of this phase separation wasunknown. Initially, it was thought thatwhen the concentration of polymerincreased as the organic solvent dissipated

FIGURE 8. (a) Power spec-tra for two shells areshown, the light gray datafor a shell cured rapidly inone day, the dark gray datafor a shell cured moreslowly over four days.(b) Examples of AFM tracestaken from the two shellsclearly show a dramatic difference in long-lengthscale surface oscillations.(NIF-0401-02083pb01)

FIGURE 9. Shown aremeasurements of mode-10 power as a function of final shell wallthickness for a number of950-mm-diam shells. Wallthickness was controlledby varying the relative oil to inner core waterflow rates.(NIF-0401-02084pb01)

0.1

1

10

100

1000

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er (n

m2 )

252015105

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950-µm-diam shells

10


UCRL-LR-105821-00-1

into the bath, the solubility of water in theoil phase wall would decrease, resulting insupersaturation. Modeling of this processdemonstrated that this was the case;however, the predicted degree of super-saturation was very low, effectively pre-cluding homogeneous nucleation andsuggesting that heterogeneous nucleationpromoted by particulate or ionic impuri-ties was responsible for vacuole forma-tion.18 Subsequent to this modeling work,it was discovered that the addition ofinorganic salts to the aqueous bath wouldsuppress vacuole formation, presumablyby lowering the water activity in the bathrelative to possible water droplets in theoil phase.19 It was also observed thatwater droplets would spontaneouslyform in a fluorobenzene solution ofPaMS when placed in contact with water,indicating that supersaturation caused bysolvent removal was unnecessary andsupporting the concept of the presence ofa hydrophilic impurity in the organicphase driving aqueous droplet formation.Further analysis showed that the PaMScontained 20 to 50 parts per million lithi-um salts, a residue from the butyl lithiuminitiator used to prepare the polymerfrom monomer. Removal of this ionicimpurity by multiple reprecipitationsnow allows us to produce nearly vacuole-free shells without the use of inorganicsalts in the bath. There remain a variablebut small number of generally larger vacuoles that seem to have different origins—their elimination is the subject of ongoing efforts.

Surface Debris The presence of small amounts of sur-

face debris on the mandrels is problemat-ic. Although a 1-µm piece of dust on thesurface may be thought to add roughnessto the shell surface power spectrum atonly very high frequency, subsequentcoating operations can lead to a signifi-cant broadening of the bump resulting inunacceptable dome formation.20 Thus,cleanliness is of extreme importance. Notonly are all solutions carefully filtered,but the entire fabrication operation isconducted in a Class-100 clean-room

environment. With these techniques andthe use of PVA as the bath protective colloid, we have been able to produceshells essentially free of surface debris.

However, as discussed previously, theinterfacial tension benefits of using veryhigh molecular weight PAA as the bathadditive are significant. Unfortunately,we have found that shells produced inthese baths have what appears to beareas of thinly deposited PAA on theirsurfaces. In general, these deposits haveonly a very minor effect on the bare shellpower spectra, but are manifest moreseriously in subsequent coatings.

We are currently developing tech-niques to remove these deposits. Our ini-tial attempt involves making use of thehighly functionalized PAA structure.When used in the baths, PAA is dis-solved into pure water, thus it is onlyweakly ionized (Figure 5). However, inthe presence of base, the moleculebecomes a completely ionized polyelec-trolyte, and because of this, its chain con-formation changes radically.21 Likewise,it can be completely protonated by treat-ment with acid. In initial experiments,we have used washes with acid and baseto loosen and remove PAA from fullycured shell surfaces, expecting that thechanges in chain conformation will facili-tate the process. Some success has beenachieved, as is shown in Figure 10.Shown on the left are both Sphere-Mapper traces and an AFM patch scan ofa PaMS shell that was produced in aPAA bath and rinsed only with waterbefore drying. Note the high-frequencyroughness in the traces as well as themottled appearance of the patch scan.On the right is a shell from the samebatch that was also rinsed with diluteNaOH (2%), rinsed again with water,and then rinsed with dilute HCl (0.5%)followed by a final rinse with water. Thetrace profiles are clearly improved, andthe patch scan shows significantlyreduced deposits. However, capsulesmade from these washed PaMS man-drels are still too rough to meet ourrequirements, so development of tech-niques to prevent or remove thesedeposits is an ongoing activity.

11


UCRL-LR-105821-00-1

Current Status

In the course of solving the surfaceroughness problems, we have substantial-ly modified the mandrel production pro-cess, making use of our understanding ofthe important materials and processingparameters. Part of the solution involvednew chemical interactions and mechani-cal processes, and part was due to bettermaterials and processing control. Clearly,all aspects of the process are interrelated,and in some cases, the solutions to oneproblem have had consequences foranother.

In Figure 11, we show five powerspectra from representative 2-mm PaMSshells. Clearly, we are at or below thefinal capsule design requirements.However, as noted at the beginning ofthis article, these are just the initial man-drels, and one must be concerned withsubsequent coating operations. Of partic-ular importance is the PAA depositroughness described above, which isspread over the high-frequency modes.

FIGURE 11. (a) Shown arepower spectra for five ofthe best shells from recentbatches. The very lightgray line in the powerspectrum graph is theaverage of the five-shellpower spectra; it is at orbelow the final capsuledesign specification(shown in black). (b) A rep-resentative trace fromeach of the shells isshown. Visible on thesetraces is evidence of PAAsurface contamination.(NIF-0401-02086pb01)

FIGURE 10. Three parallelAFM SphereMapper traces40 mm apart [top, (a) and(b)] and AFM patch scans(bottom) of a PaMS man-drel cured in a PAA solu-tion (c) as-dried and (d)after washing in diluteNaOH and HCl solutions.(NIF-0401-02085pb01)

20

0 nm

50

100

(d) Washed(c) As-dried

(b) (a)

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20

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0 10 20µm

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105

104

103

102

101

100

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10–2

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er (n

m2 )

10 100 1000Mode number

Individual shells Average of 5 shells NIF capsule ignition

(a)

(b)

12


UCRL-LR-105821-00-1

We have found that coatings on theseshells produce lower-frequency power inthe critical central part of the spectrum,and for this reason, this is our primaryconcern at this time.

Notes and References1. R. Cook, “Production of Hollow Microspheres

for Inertial Confinement Fusion Experiments,”Mat. Res. Soc. Symp. Proc. 372, 101 (1995).

2. M. Takagi et al., “Development of DeuteratedPolystyrene Shells for Laser Fusion by Means ofa Density Matched Emulsion Method,” J. Vac.Sci. Technol. A 9, 2145 (1991).

3. R. Cook, R. McEachern, and R. B. Stephens,“Representative Surface Profile Power Spectrafrom Capsules Used in Nova and OmegaImplosion Experiments,” Fusion Technol. 35, 198(1999).

4. R. L. McEachern, C. E. Moore, and R. J. Wallace,“The Design, Performance, and Application ofan Atomic Force Microscope-Based Profilo-meter,” J. Vac. Sci. Technol. A 13, 983 (1995).

5. T. Norimatsu et al., “Cryogenic Targets andRelated Technologies at ILE Osaka University,”J. Vac. Sci. Technol. A 12, 1293 (1994).

6. R. C. Cook et al., Mandrel Development Update—1/98 to 12/98, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-ID-133144,February 1, 1999.

7. S. A. Letts et al., “Fabrication of Polymer ShellsUsing a Depolymerizable Mandrel,” FusionTechnol. 28,1797 (1995); B. W. McQuillan et al.,“The PaMS/GDP Process for Production of ICFTarget Mandrels,” Fusion Technol. 31, 381 (1997).

8. T. Norimatsu et al., “Modeling of the CenteringForce in a Compound Emulsion to MakeUniform Plastic Shells for Laser Fusion Targets,”Fusion Technol. 35, 147 (1999).

9. R. C. Cook, P. M. Gresho, and K. E. Hamilton,“Examination of Some Droplet DeformationForces Related to NIF Capsule Sphericity,” J.Moscow Phys. Soc. 8, 221 (1998).

10. P. M. Gresho, “Some Aspects of the Hydro-dynamics of the Microencapsulation Route toNIF Mandrels,” Fusion Technol. 35, 157 (1999).

11. M. Takagi et al., “Decreasing Out-of-Round inPoly(a-methylstyrene) Mandrels by IncreasingInterfacial Tension,” Fusion Technol. 38, 46 (2000).We note that the computed values of g in thispaper are high by a factor of 10 due to a calcula-tion error. They have been corrected in Table 1.

12. A. W. Adamson, “Physical Chemistry ofSurfaces,” John Wiley & Sons, New York, pp.27–36 (1982).

13. M. Takagi et al., “The Effects of ControllingOsmotic Pressure on a PaMS MicroencapsulatedMandrel During Curing,” Fusion Technol. 38, 54(2000).

14. M. J. Block, “Surface Tension as the Cause ofBenard Cells and Surface Deformation in aLiquid Film,” Nature 178, 650 (1956); C. V.Sternling and L. E. Scriven, “InterfacialTurbulence, Hydrodynamic Instability and theMarangoni Effect,” AICHE Journal 5, 514 (1959);J. C. Berg, A. Acrivos, and M. Boudart,“Evaporative Convection,” in Advances inChemical Engineering 6, 61, (1966).

15. Lord Rayleigh (John W. Strutt, Phil. Mag. (6) 32,529 (1916); P. G. Drazin and W. H. Reid,“Thermal Instability,” Chapter 6 in HydrodynamicStability, Cambridge University Press, 1981.Work on Rayleigh convection in spherical shellsis given in S. Chandrasekhar, “The ThermalInstability of a Fluid Sphere Heated Within,”Phil. Mag. (7) 43, 1317 (1952); S. Chandrasekhar,“The Onset of Convection by Thermal Instabilityin Spherical Shells,” Phil. Mag. (7) 44, 233 (1953);S. Chandrasekhar, “The Onset of Convection byThermal Instability in Spherical Shells—ACorrection,” Phil. Mag. (7) 44, 1129 (1953).

16. B. W. McQuillan, to be published.17. The essential hydrodynamics for this analysis

can be found in three papers: (a) O. Pirotte andG. Lebon, “Surface-Tension Driven Instability inSpherical Shells,” Appl. Microgravity Technology,I(4), 175–9 (1988); (b) H. C. J. Hoefsloot and H.W. Hoogstraten, “Marangoni Instability inSpherical Shells,” Appl. Microgravity Technology,II(2), 106–8 (1989); and (c) O. Pirotte and G.Lebon, “Comments on the Paper ‘MarangoniInstability in Spherical Shells,’” Appl.Microgravity Technology, II(2), 108–9 (1989).

18. G. Wilemski et al., “Prediction of PhaseSeparation During the Drying of PolymerShells,” Fusion Technol. 28, 1773 (1995).

19. B. W. McQuillan et al., “The Use of CaCl2 andOther Salts to Improve Surface Finish andEliminate Vacuoles in ICF MicroencapsulatedShells,” Fusion Technol. 35, 198 (1999).

20. S. A. Letts, D. W. Myers, and L. A. Witt,“Ultrasmooth Plasma Polymerized Coatings forLaser Fusion Targets,” J. Vac. Sci. Technol. 19, 739(1981).

21. R. Y. Lochhead, J. A. Davidson, and G. M.Thomas, “Poly(acrylic acid) Thickeners,” inPolymers in Aqueous Media, J. E. Glass, Ed.,American Chemical Society, Chapter 7 (1989).

13

Ignition of thermonuclear burn in iner-tial confinement fusion (ICF) experi-ments1 will require extremely precisecontrol of many laser and target parame-ters. The type of target currently envi-sioned for ignition experiments at theNational Ignition Facility (NIF) has afrozen deuterium-tritium (DT) ice layeradhering to the inner surface of an ablatorshell, and the specifications for the innersurface quality of this ice layer areextremely demanding.2,3 To achieve igni-tion on NIF, the DT ice layer must be well-characterized. In some target designs, theablator shell is transparent to visible light,greatly facilitating ice-surface characteriza-tion, while in other designs, the ablatorshell is opaque. Formation of suitablysmooth ice layers in opaque shells willprobably rely heavily on the experiencegained from the characterization of ice lay-ers in transparent shells. Optical character-

ization of ice layers in transparent shellswill, therefore, be critical to achieving igni-tion on NIF, and reliable diagnostics arerequired.

Currently, the primary optical diagnos-tic of DT ice-surface quality in sphericalshells is backlit shadowgraphy,4 and thegeometry of this technique is shown inFigure 1. In this technique, light that istotally internally reflected from the innerice surface is imaged in transmission as abright band, and the power spectrum ofthe radial variations of the bright-bandposition is assumed to be equal to thepower spectrum of the ice-surface radialprofile in the great-circle plane perpendic-ular to the shadowgraph optical axis. Thesquare of the rms surface roughness isthen inferred by summing the mode coeffi-cients of the bright-band power spectrum.

The details of how the bright bandmaps to the inner ice surface are complex

VALIDATING DT ICE-SURFACE ROUGHNESSDIAGNOSTICS FOR NIF INERTIAL

CONFINEMENT FUSION

J. A. Koch J. D. Sater

T. P. Bernat A. J. MacKinnon

D. N. Bittner G. W. Collins

B. J. Kozioziemski C. H. Still

UCRL-LR-105821-00-1

Backlight

Object plane Image plane Intensity

Shadowgraph lineout

Gas

Lens

Bright band

Ice

Shell

FIGURE 1. Schematic ofbacklit shadowgraphy,illustrating how light total-ly internally reflected fromthe inner ice surface formsa bright band in transmis-sion. Other ray groupsform weaker inner bandsnear the bright band;these inner bands appearconcentric and nearly cir-cular when the ice surfaceis very smooth.(NIF-0401-02035pb01)

and depend on many factors. Earlier ray-tracing work examined the behavior ofthe bright-band position in the presenceof localized surface imperfections andfound that the correlation depends on theheight and curvature of the imperfection.5In general, a first-principles mathematicalanalysis is intractable, and ray tracing uti-lizing localized surface imperfections doesnot obviously illuminate the general caseof many coupled surface modes. In thepresent work, we therefore take a differ-ent approach; we ignore the details ofhow the local bright-band position corre-lates to individual imperfections, andinstead, we use exact numerical ray trac-ing to examine how well the overallpower spectrum derived from the bright-band analysis corresponds to the actualice-surface power spectrum inside thespherical shell. This approach directlyaddresses the validity of backlit shadowgraphy, since ignition capsules will ulti-mately be qualified against specificationson the basis of power spectra and rmsmeasurements.

We considered experimental characteri-zation of a fabricated surrogate capsule asan approach to validating shadowgraphy,but this approach presents significant dif-ficulties. First, one must rely on calibra-tions from a separate inner-ice-surfacediagnostic that is known to be more reli-able than shadowgraphy, and no suchdiagnostic exists over the full range ofmode numbers accessible with shadowgraphy; ray tracing through a simulatedcapsule eliminates this problem by allow-ing mathematical ice surfaces to be speci-fied to arbitrary precision. Second, anexperiment would only allow validationwith a single surrogate ice-surface profile,and other profiles would require separatesurrogate shells to be fabricated; ray trac-ing provides infinite flexibility for choicesof simulated ice-surface parameters.Third, a diagnosable fabricated capsulewould necessarily have different charac-teristics than a real ignition-qualifiablecryogenic ICF capsule (and would likelyneed to be a noncryogenic multilayerhemisphere), and the impact of these dif-ferences upon the conclusions of theexperiments could not be known withoutray tracing to verify that the differences

14

VALIDATING DT ICE-SURFACE ROUGHNESS DIAGNOSTICS FOR NIF INERTIAL CONFINEMENT FUSION

UCRL-LR-105821-00-1

are quantifiable. Finally, a simulationcapability allows alternative optical diag-nostic techniques to be investigated andcompared with shadowgraphy, andallows for detailed analysis of any sub-tleties that might arise.

We have therefore developed a numeri-cal ray-trace code, SHELL3D, to addressthis issue.6 With SHELL3D, we simulateice surfaces with specified spherical-harmonic modal imperfections, and weproduce simulated shadowgraphs that are interpreted with the same data analy-sis code used to interpret real experimen-tal data. We find that shadowgraph-derived power spectra are reliable indicators of ice-surface power spectraand total rms out to Fourier mode num-bers as high as 80, provided the radial position of the bright band is defined with an appropriately fitting algorithm.We also find that the position fit previ-ously used to define the bright-band posi-tion produces erroneously high power inthe higher modes and overestimates thetotal rms by factors as large as 2; as acorollary, we find that our experimentallyproduced ice surfaces are smoother thanwe once thought they were. Finally, wefind that experimental diagnosticimprovements may be obtained by changing the illumination geometry andanalyzing other shadowgraph features,and that enhanced information may beobtained by utilizing backlit transmissioninterferometry instead of simple backlitimaging. The results have significantlyimproved our understanding of how DT ice surfaces may be characterized inorder to qualify them for ICF experimentson NIF.

Simulating BacklitImaging Data withSHELL3D

We begin by reviewing the operation ofSHELL3D. The simulated capsule geome-try is shown in Figure 2. In SHELL3D, theouter and inner shell surfaces are definedas perfect cocentered spheres, and theinner ice surface is defined as the sum of

real-valued spherical harmonics with arbi-trary values of l and m:

(1)

where R1 is the A0,0 coefficient, and theassociated Legendre functions Pl,m aredefined by the usual recursion relations.7,8The outer ice surface is assumed to beidentical to the inner shell surface, and thecode does not permit topological changessuch as cracks or gaps between the outerice surface and the inner shell surface.Furthermore, each layer is assumed to behomogeneous, nonpolarizing, and nonab-sorbing. The x-axis in Figure 2 is typicallyused for referencing q in the spherical har-monics, and all results discussed in thispaper use this orientation.

The general approach followed in thesimulation is shown schematically inFigure 3. SHELL3D is essentially an ana-lytical ray-tracing code; starting from aninitial source point (x0, y0, z0) and an initialray vector , the intersection point(x1, y1, z1) with the outer surface F(x, y, z)= 0 is determined by substituting the para-metric equations F(x0+at, y0+bt, z0+ct) = 0

15


UCRL-LR-105821-00-1

and solving for t. The transmitted andreflected ray vectors are determined basedon the incident vector, the surface normal—F(x1, y1, z1), and the indices of refraction.The choice of reflection or transmission isprobabilistic based on the ray polarization,angle of incidence, and indices of refrac-tion; the process then repeats from the newpoint and ray vector. Several features andsubtleties are important to note:

a. The choice of spherical-harmonicrecursion relations can have a signifi-cant impact on the numerical accura-cy of the code, and in particular, it iseasy to generate spurious high-fre-quency structures near the poles (q ≈0 and p) when using recursionrelations that involve the term ÷1 – cos2 q in the denominator. Wehave taken care to eliminate theseinstabilities from our algorithms,which arise from round-offs anddivide-by-zero errors.

b. The polarization of each ray is ran-domly chosen and fixed as S or P. Infact, the polarization with respect tothe local surface will generallyevolve as the ray propagates throughthe capsule if the inner ice surface isnot spherical. This effect is not treat-ed in the code, but the practicalresult of this simplification will be negligible for nearly smooth surfaces.

R12 1 +

Al,0 2l + 1Pl,0 (cosq ) +

2(2l + 1)(l - m)!(l + m)!

Pl,m (cosq ) *

Al,m cosmf + Al,- m sin mf( )m =1l

Â

Ï

Ì

ÔÔ

Ó

ÔÔ

¸

˝

ÔÔ

˛

ÔÔ

l =1Â

È

Î

ÍÍÍÍÍ

˘

˚

˙˙˙˙˙

x2 + y2 + z2 =

X

Z

Object plane

Final rayback-projected toobject plane

Disk source(diffuse or collimated)

Initial ray

FIGURE 2. Schematic ofthe ray-tracing geometryused in SHELL3D. The sim-ulation is nonsequential inthat each ray can reflectfrom or transmit throughthe surfaces in any orderbefore leaving the capsuleand being back-traced.(NIF-0401-02036pb01)

c. A wrapped transmitted phase map isgenerated along with the image array,and this map can be postprocessedby phase-unwrapping software togenerate a transmitted wavefrontmap, as will be discussed below.

d. The maximum number of surfaceseach ray can intersect is 16. This is sufficient to pass all forward-scattered, twice-reflected rays.

e. The effective imaging lens is perfectand has no distortion, but can be

16


UCRL-LR-105821-00-1

specified to have an effective point-spread function. In all cases dis-cussed here, the imaged plane is themidplane of the capsule.

f. For the spherical surfaces, intersectionpoints are determined analytically;there are generally two roots for eachintersection, and the correct choicecan be determined logically. For thespherical-harmonic surface, there arean unknown number of intersectionpoints that cannot be determined ana-lytically and that fall in an unknownorder. For this surface, the codeinstead propagates the ray forward insmall incremental steps in the regionof the inner ice surface9 until the firstroot is passed; this bounds the posi-tion of the root, which is then deter-mined iteratively using an imple-mentation of Brent’s algorithm.8

The output shadowgraph array is a 1024 ¥ 1024 pixelized image, which can beanalyzed as if it were real data by the sameanalysis code, LAYER,10 which is used toanalyze experimental bright-band data. Forcomparison to the bright-band-derivedpower spectrum and surface rms, a separatecode calculates the actual radial variationsof the mathematically generated ice surface11as a function of q in the great-circle planeperpendicular to the shadowgraph axis, andFourier-transforms DR(q) to obtain a one-sided power spectrum. In both cases, theFourier-mode coefficients sum to the squareof the rms surface deviation in one dimen-sion, which in turn can be related to the two-dimensional rms power spectrum most rele-vant to ICF ignition capsule simulations.12

All codes currently run on the LivermoreComputing Center DEC 8400 machines. Thecentral processing unit (CPU) time requiredto produce simulated images through two-dimensionally rough ice surfaces withSHELL3D scales approximately as L2,where L is the maximum cut-off modenumber. Good signal-to-noise ratios (>10throughout the full field of view) for L = 40 can be obtained after approximately 750 CPU hours. For such large problems,multiple versions of SHELL3D can be runsimultaneously using different randomnumber seeds, and the results can be addedto minimize the actual clock time required.

START

FINISH

Randomly choose initial point on disk source in vacuum

Randomly choose initial ray vector within specified limits

Randomly choose initial polarization S or P

Write image histogram (the shadowgraph) to a file

Randomly determine whether ray transmits or reflects based on polarization

and angle of incidence

Is the new ray into vacuum?

Propagate ray to surface intersection; calculate intersection point, normal vector, incident angle, reflected and transmitted angles, accumulated

optical path length

Increment a bin image histogram by one, OR create N new image points within a Gaussian point-spread function and increment the bin

image histogram with the N new points

For collimated sources only, create three 90-degree phase-shifted interferograms

referencing the bin field histogram against a plane wave

No YesIs the final ray vector within the specified collection angle limit?

No Yes

Back-propagate ray to specified imaged plane; is final image point within the

specified detector area?

No Yes

For collimated sources only, increment a bin field histogram by exp(ikp), where p is the

accumulated optical path length

No Yes

Final ray?

FIGURE 3. Logicalflowchart of SHELL3D.(NIF-0401-02037pb01)

SHELL3D Validation ofDT Ice Data

We described preliminary resultsobtained using a simplified rotationallysymmetric version of SHELL3D in an ear-lier paper;6 here we describe more recentresults we obtained using the full capabili-ties of the code to validate real experimen-tal DT data. In these simulations, wespecify the spherical-harmonic mode coef-ficients ΩAl,mΩ to be functions of l only,but with randomly chosen signs for eachvalue of l, m, and –m, and we use severalfunctional scalings for ΩAl,mΩ(l) in orderto vary the one-dimensional power spec-trum and total rms. In the simulationsdescribed in this section, we assume anisotropically emitting, nonpolarized, inco-herent, broadband diffuse backlight sourcethat subtends f/4 as viewed from the cap-sule center; this is comparable to currentexperimental configurations. In all cases,we image the midplane of the capsulewith an f/4 lens having a 3-µm-diameter(full width at half-maximum intensity)point-spread function.

Shadowgraph analysis is performedwith LAYER.10 In this analysis, the radialposition of the bright band can be definedby a steepest-slope fit to the inside edge ofthe bright band, or by a Gaussian centroidfit to the center of the bright band. Theedge fit has historically been used to analyze experimental data, while theGaussian fit was only recently implement-ed. LAYER outputs a linearly unfoldedbright-band curve and a one-dimensionalbright-band–derived power spectrum inunits of pixels-squared. The bright-band–derived power spectra can then beconverted to units of µm-squared usingthe known scaling of the shadowgraphdata for direct comparison to the knowninput ice-surface power spectrum.

Figures 4a and 4b show two simulatedshadowgraphs from SHELL3D, both ofwhich assume a 1-mm-diameter capsulewith a 10-µm-thick plastic shell and a 100-µm-thick DT ice layer. Figure 4a speci-fies 10 modes of one-dimensional (rota-tionally symmetric about the x-axis inFigure 2) surface structure, while Figure 4bspecifies 10 modes of two-dimensional

17


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surface structure with a comparable valuefor the total rms. Figures 4c and 4d showthe power spectra of the actual ice-surfaceprofiles from Figures 4a and 4b, respec-tively, together with bright-band–derivedpower spectra using both the edge fit andthe Gaussian fit to define the bright-bandposition.

Several features are important to note inthese figures. First, both the edge fit andthe Gaussian fit to the bright-band posi-tion in the rotationally symmetric case ofFigure 4c yield bright-band–derivedpower spectra that are in excellent agree-ment with the known input spectrum overthe 10 modes that are actually present, butthe edge fit diverges from the input spec-trum for mode numbers >10 while theGaussian-fit power spectrum falls rapidlyabove mode 10, in agreement with theinput spectrum. This behavior is generallyreproduced in the two-dimensional exam-ple in Figure 4d; however, the bright-band–derived power spectra do not matchthe input spectrum as well over the first 10 modes using either fit algorithm. Wehave found this to be a general feature ofthe two-dimensionally rough surfaces wehave modeled and analyzed and to repre-sent a difference from the rotationallysymmetric results reported earlier.6 Thispoorer peak-by-peak agreement likelyresults from polar-angle averaging (in thez-direction of Figure 2), which has a muchstronger effect in the two-dimensionallyrough case than in the rotationally sym-metric case, and is dominated by theeffective f/# of the diffuse backlight, aswill be discussed below. We return to thereasons for the generally poorer agree-ment between the input spectra and theedge-fit bright-band spectra later in thissection.

Recent experimental DT ice data13 hasshown approximately 1.5-µm total rmsroughness for modes 1–60 and approxi-mately 0.5-µm rms roughness for modes3–60, using beta layering in a 2-mm-diam-eter capsule with a 30-µm-thick shell and a200-µm-thick ice layer. This data was ana-lyzed using a Gaussian centroid fit todefine the bright-band position, and theresults are significantly smoother than ear-lier data (analyzed with an edge fit todefine the bright-band position) appeared

to indicate. We show here that the currentresults are almost certainly correct, andthat the earlier results were in errorbecause the edge fit analysis yielded spu-rious high-mode power.

Figure 5a is an experimental shadow-graph of a DT ice layer in a capsule,13 andFigure 5b shows bright-band–derivedpower spectra from both the Gaussiancentroid fit and the edge fit. The edge-fitpower spectrum clearly shows higherpower in the higher modes and has anrms that is 86% higher. As noted above,the Gaussian centroid fit spectrum wasexpected to be correct based on earliersimulation results.6 To verify this conclu-sion for the present case, we performed

two simulations that are shown in Figures 5c and 5e. The first simulation isderived from a mathematical ice surface(with the same capsule and ice thicknessparameters), which was specified to havea known power spectrum that nearlymatches the Gaussian-fit spectrum fromFigure 5b over the first 40 modes; the sec-ond simulation is derived from a mathe-matical ice surface (again with the samecapsule and ice thickness parameters),which was specified to have a knownpower spectrum that nearly matches theedge-fit spectrum from Figure 5b over thefirst 40 modes. Qualitatively, the shadow-graph in Figure 5c appears fairly smooth,whereas the shadowgraph in Figure 5e

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FIGURE 4. (a) Simulatedshadowgraph of a rota-tionally symmetric ice sur-face with 10 L-modes of(one-dimensional) asym-metry; (b) simulated shadowgraph of a two-dimensionally rough icesurface with 10 LM-modesof asymmetry; (c) great-circle ice-surface powerspectrum for the simula-tion of Figure 4a togetherwith edge-fit andGaussian-fit bright-bandpower spectra; (d) great-circle ice-surface powerspectrum for the simula-tion of Figure 4b togetherwith edge-fit andGaussian-fit bright-bandpower spectra.(NIF-0401-02038pb01)

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FIGURE 5. (a) Experimental shadowgraph of DT ice; (b) edge fit and Gaussian-fit bright-band power spectra from the data of Figure 5a; (c) simulatedshadowgraph of an ice surface with a great-circle ice-surface power spectrum nearly equal to the Gaussian-fit bright-band power spectrum from theexperimental data over the first 40 modes; (d) great-circle ice-surface power spectrum for the simulation of Figure 5c together with edge-fit andGaussian-fit bright-band power spectra; (e) simulated shadowgraph of an ice surface with a great-circle ice-surface power spectrum nearly equal tothe edge-fit bright-band power spectrum from the experimental data over the first 40 modes; (f ) great-circle ice-surface power spectrum for the simu-lation of Figure 5e together with edge-fit and Gaussian-fit bright-band power spectra. The shadowgraph image intensity scales have been adjusted tobring out the bright band and inner bands more clearly. (NIF-0401-02039pb01)

appears substantially more mottled thanthe experimental ice surface shown inFigure 5a. This suggests that the experi-mental ice surface cannot be as rough asthe edge-fit spectrum would indicate; thisis quantitatively supported by the resultsfrom analysis of the two simulated shad-owgraphs, which are shown in Figures 5dand 5f respectively. In both cases, theGaussian centroid fit to the bright-bandposition matches the input spectrum verywell, with total rms errors 1 and overestimates the rms byfactors of 1.5–2. We have reached similarconclusions from all other simulations wehave analyzed; we therefore conclude thatthe Gaussian centroid fit to the experimen-tal data is essentially correct, and that the

edge fits used to analyze older experimen-tal data were consistently overestimatingboth the higher-mode power and the total rms.

There appear to be two reasons for thepoor accuracy of the older edge-fit analy-sis algorithm. First, the edge fit appears tobe more susceptible to noise in the data,resulting in large spurious variations inthe fitted position of the bright band. Thisis clear from Figure 6, which shows aknown great-circle ice-surface profile for a10-mode two-dimensionally rough simula-tion (that of Figure 4b) together with linearly unfolded shadowgraph brightbands and the corresponding Gaussian-and edge-fit profiles. The edge fit clearlyshows spurious power in higher modesthat is not actually present in the simulat-ed ice surface, while the Gaussian fit

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FIGURE 6. (a) Great-circleice-surface profile fromthe 10-mode simulation ofFigure 4b; (b) unfoldedbright band and edge-fitprofile (thin white line)from the simulation ofFigure 4b; (c) unfoldedbright band and Gaussian-fit profile (thin white line)from the simulation ofFigure 4b. The horizontalaxis is the azimuth anglefrom 0° to 360°, and thevertical axis is the radius.The vertical scale varies inthese plots.(NIF-0401-02040pb01)

matches the known input spectrum muchmore closely. The reason for this differencemay be related to the lack of sharp edgesin the bright band that would tend to helpdefine the bright-band position for theedge fit. However, even the Gaussian fitdoes not exactly match the input profile,for reasons discussed below.

The second reason for the poorer accu-racy of the edge-fit analysis is averagingalong the surface in the direction of theoptical axis. Figure 7 is a map of bright-band radius vs polar angle on the ice sur-face (relative to the z-axis in Figure 2)showing where rays that contribute to thebright band at a particular radius haveintersected the ice surface. Each radius ofthe bright band consists of many rays thathave intersected the ice surface at variouspolar angles; for this example of an f/4diffuse backlight and f/4 imaging, a par-ticular radius in the shadowgraph brightband corresponds to light that reflects offthe ice surface over an ~12°-wide circularribbon symmetric about the z-axis inFigure 2. Surface structure on the ice sur-face along this direction (particularly withmode numbers greater than ~30, corre-sponding to the 12° width) will therefore

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broaden the bright band, and the edge fitwill track the inner edge of this broadeneddistribution. This adds spurious power tohigher surface modes by confusing struc-ture in the polar direction with structurein the azimuthal direction.

This effect is clear from Figure 8, whichshows a known great-circle ice-surfaceprofile for a 40-mode two-dimensionallyrough simulation (that of Figure 5e)together with linearly unfolded shadow-graph bright bands and the correspondingGaussian- and edge-fit profiles. The edgefit tracks scattering artifacts in the brightband along the lower boundary that donot correspond to actual great-circle-planeice-surface features along the azimuth, butrather correspond to structure in the polardirection that has been averaged, resultingin a locally broadened band. The Gaussianfit, in contrast, is less affected by polaraveraging and tracks the center of the dis-tribution regardless of its width. This aver-aging does affect the absolute accuracy ofthe Gaussian fit, however, and is likely tobe the reason why the Gaussian-fit powerspectrum does not exactly match the inputspectrum in two-dimensionally rough sim-ulations (this is clear, e.g., in Figure 6).

Progress towardsImproved DT IceCharacterization

Based on the simulation work describedabove, we believe that diffuse-backlitshadowgraphy is a valid diagnostic of cur-rently achievable DT ice-surface powerspectra for great-circle mode numbers atleast as high as 40, and perhaps6 as highas 80, provided a Gaussian centroid-posi-tion fit is used to define the local bright-band radius. We also find that the edge fitpreviously used to define the local bright-band radius yields erroneously highpower and overestimates the total rms byfactors as large as 2; as a corollary, we findthat our experimentally produced ice sur-faces are smoother than we once thoughtthey were.

Despite these successes, there are severalreasons to seek improved characterization

FIGURE 7. Points correspond to rays that appear at aparticular radius in the bright band and that havereflected off the inner ice surface at a particular polarangle relative to the z-axis of Figure 2. This particularexample is for an f/4 diffuse backlight and f/4 imag-ing, a 2-mm-diameter capsule, a 30-µm-thick shell,and a 150-µm-thick ice layer. The bright band clearlyaverages over an ~12°-wide circular ribbon in thiscase. (NIF-0401-02041pb01)

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techniques. Imaging with a diffuse back-light naturally increases polar averagingand eliminates any one-to-one correspon-dence between bright-band position andice thickness in a single perpendicularplane (see Figure 7). This averaging broad-ens the bright band, degrades the achiev-able position-fitting precision, and limitsour ability to observe and diagnoseshort–scale-length features. In addition,extremely smooth ice surfaces will becomeincreasingly difficult to quantitativelydiagnose since the radial variations in thebright-band position will become unob-servably small. Finally, we anticipate aneed to characterize DT ice surfaces insitu, in a hohlraum in the NIF targetchamber prior to an ignition experiment,and restricted access to the capsule willconstrain our ability to utilize existingcharacterization techniques.

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One simple improvement to currentbacklit shadowgraphy is to use a collimat-ed backlight rather than a diffuse back-light. Figure 9 shows SHELL3D simulatedsections of a bright band that would beobserved from the same ice surface underf/4 diffuse backlight conditions and undercollimated (e.g., laser) backlight condi-tions. The collimated-backlight geometryclearly produces a sharper bright band,the position of which can be defined moreprecisely. Perhaps more importantly, how-ever, the effects of polar averaging areminimized in the case of a collimatedbacklight, and a one-to-one relationshipcan be identified between ice-surface fea-tures in a single perpendicular plane andfeatures in the bright band, particularlyalong the outer edge (see Figure 10). Thissuggests that higher-frequency spatialstructure will be more easily observed at

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the outer edge of the bright band using acollimated-backlight geometry.

We also note that most shadowgraphs(e.g., Figures 5c and 5e) clearly show innerbands that are weaker but more distortedthan the bright band. These bands resultfrom other multiple-reflection ray pathsand appear visually to be more sensitiveindicators of ice-surface asymmetry thanthe bright band itself; however, the morecomplicated ray paths suggest that dis-cerning a quantitative correspondencebetween inner-band structure and ice-surface structure will be difficult.Additionally, the central portions of theshadowgraphs (e.g., in Figure 4b) showmottled structure that is clearly related toice-surface asymmetry; this structure mayprovide additional surface-quality infor-mation (particularly with a collimatedbacklight), though again the quantitativecorrespondence will probably be difficultto discern.

Finally, we note that bright-band trans-mission interferometry might be utilized toprovide ice-surface–quality information. Asimple implementation of this techniquewould be to interfere a plane-wave refer-ence beam with a collimated-backlight

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shadowgraph image; in this case, the raypaths are already understood from theabove analysis, and the quantitative

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FIGURE 9. Close-up of thebright-band structure;(a) uses a diffuse backlight,while (b) uses a collimatedbacklight. The collimatedbacklight produces asharper bright band, theposition of which can bemore precisely defined.(NIF-0401-02043pb01)

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FIGURE 10. Points correspond to rays that appear at aparticular radius in the bright band and that havereflected off the inner ice surface at a particular polarangle relative to the z-axis of Figure 2. This particularexample is for a collimated backlight and f/4 imaging,a 2-mm-diameter capsule, a 30-µm-thick shell, and a150-µm-thick ice layer. The inner edge of the brightband averages over an ~3°-wide circular ribbon in thiscase, while the outer edge of the bright band tracks asingle trace along the ice surface. (NIF-0401-02044pb01)

correspondence between bright-band phaseand surface structure is straightforward toderive for a given shell thickness, nominalice thickness, and capsule diameter. InFigure 11 we show a simulated bright-bandinterferogram obtained by interfering ashadowgraph image (that of Figure 4b)with a plane-parallel reference beam. Thebright-band phase varies significantly inazimuth and radius, and this phase corre-lates to the same surface structure thataffects the radial position of the peakbright-band intensity (in this particularcase, one wave of phase corresponds to 1.4 µm of ice-thickness radial variation).These phase variations may be more easilymeasured than radial variations of the position of the bright band, particularly forcases where the ice surface is nearly perfect.

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We are working towards developing phaseunwrapping software that can be used toanalyze bright-band interferograms, andwe plan to perform experiments to devel-op this and other ice-surface characteriza-tion techniques in the coming year.

AcknowledgmentsWe thank J. Burmann, E. M. Campbell,

S. Haan, B. Hammel, J. Hoffer, R. Jones, E.Mapoles, J. Pipes, and W. Unites for theircontributions and support.

Notes and References1. J. D. Lindl, Inertial Confinement Fusion (Springer-

Verlag, New York, 1998).2. T. R. Dittrich et al., Phys. Plasmas 5, 3708 (1998).3. T. R. Dittrich et al., Phys. Plasmas 6, 2164 (1999).4. J. K. Hoffer et al., Fusion Technol. 30, 529 (1996).5. Y. Lee, Lawrence Livermore National Laboratory,

Livermore, CA, personal communication.6. J. A. Koch et al., Fusion Technol. (in press).7. E. Butkov, Mathematical Physics (Addison-

Wesley, Reading, 1968).8. W. H. Press et al., Numerical Recipes in C

(Cambridge University Press, Cambridge, 1994).9. The region of the inner ice surface is defined by

two spheres that entirely contains the ice-sur-face profile; ray tracing within this region mustbe done carefully to avoid possible errorscaused by multiple intersection points.

10. E. R. Mapoles et al., Phys. Rev. E 55, 3473 (1997).11. We calculate the great-circle-plane, one-dimen-

sional power spectrum numerically using thesame spherical-harmonic algorithms that areused in SHELL3D; this approach minimizes thepotential impact of numerical errors in the algo-rithms on the comparison with the bright-band-derived power spectra.

12. S. M. Pollaine et al., 1994 ICF Annual Report,Lawrence Livermore National LaboratoryReport No. UCRL-LR-105820-94 (June 1995).

13. J. D. Sater, data from Lawrence LivermoreNational Laboratory beta-layered DT ice experiments.

FIGURE 11. Simulatedtransmission interfero-gram of a two-dimen-sionally rough icesurface with 10 LM-modes of asymmetry,using a collimated back-light but otherwise usingthe same model parame-ters as used for the simu-lated diffuse-backlightshadowgraph shown inFigure 4b. Phase infor-mation in the brightband relates to opticalpath length difference;this can be related to sur-face roughness and canperhaps be observedmore easily than radialposition variations.(NIF-0401-02045pb01)

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Our original ignition “point designs”1(circa 1992) for the National IgnitionFacility (NIF)2 were made energeticallyconservative to provide margin for uncer-tainties in laser absorption, x-ray conver-sion efficiency, and hohlraum–capsulecoupling. Since that time, extensive experi-ments on Nova3 and OMEGA4 and theirrelated analysis indicate that NIF couplingefficiency may be almost “as good as wecould hope for.” Given close agreementbetween experiment and theory/model-ing, we can credibly explore targetenhancements which couple more of NIF’senergy to an ignition capsule. Theseinclude using optimized mixtures of mate-rials to reduce x-ray wall losses, slightlyreduced laser entrance holes, and laseroperation strategies that increase theamount of energy we can extract from NIF.We find that 3–4¥ increases in absorbedcapsule energy appear possible, providinga potentially more robust target and ~10¥increase in capsule yield.

The NIF in the United States and LaserMegajoule (LMJ)5 in France, the next gen-eration of high-energy, high-power ICFlaser drivers, have the potential of achiev-ing thermonuclear ignition and gain in thelaboratory. One key element of achievingthat goal is coupling a significant fractionof the laser’s energy to a fuel capsule. Wecan relate the quantity of x-rays absorbedby an indirect-drive ignition capsule Ecapto the laser energy ENIF v

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