INERTIAL CONFINEMENT - Lasers, Photonics, and Fusion ... · Inertial Confinement Fusion Plasmas (S. H. Glenzer) 35 This article reports on a test of non-local thermodynamic equilibrium

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

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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 Be

require 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 (<20 µm) shells; thick-wall shellsare strong enough to nucleate a bubble ontheir own. Once bubbles have formed inthe shells, they are put in a vacuum ovenat low temperature to remove the rest ofthe interior water phase. At room temper-ature, that can take 5 to 7 weeks.

The Mode-2 Out-of-Round Problem

Theoretical Considerations Below is a review of some of the rele-

vant modeling results that have formedthe framework for our experimental work.The model used was initially a simplehomogeneous fluid droplet suspended ina second immiscible fluid,9 though moredetailed consideration of the compounddroplet has also been undertaken, both atLLNL10 and elsewhere.8 For the homoge-neous droplet, the only force promotingsphericity is due to the interfacial tensiong. The distorting forces examined included(a) deformation due to a density mismatchbetween the droplet and the supporting

bath and (b) deformation due to hydrody-namic interaction between the bath fluidand the droplet. For the first case one canshow that maximum out-of-round(MOOR), equal to the difference betweenthe maximum and minimum dropletdiameters, is given by

(1)

where g is the acceleration of gravity, r thedroplet radius, and Dr is the density dif-ference between the droplet and support-ing fluid. This calculation, which assumesan ellipsoidal deformation, was done for adroplet sitting on a surface, but is alsoaccurate for situations in which thedroplet deformation is more rapid thantranslational droplet motion. As an exam-ple of the effects of hydrodynamic interac-tions, the case of the fluid droplet in alinear shear gives

(2)

where µ is the bath viscosity and G is thelinear shear field experienced by thedroplet, related to both the method andintensity of the bath agitation method. Inboth examples note the greater-than-linear

Flow meterFlow fluorobenzenesaturated N2 gas

Fluorobenzenein bubbling trap

Temperature-controlled water bath

N2gas

Temperature-controlled water bath

Curing shells in rotating drumCuring shells in rotating drum

Rotation motor

N2gas

FIGURE 4. Shown is thetemperature-controlledrotating drum curingdevice. A flow of N2 gaspartially saturated withfluorobenzene vapor con-trols the rate of curing.(NIF-0401-02079pb01)

MOOR 8

,2

@ mgGr

MOOR 5

,@gr3

4Dr

g

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, 6

probably 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. 106

... _ _ ... + 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 ,@ 24

p

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

wer

(nm

2 )

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10 100 1000

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NIF capsule specification

–2000

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Fast curing

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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e-10

pow

er (n

m2 )

252015105

Dry shell wall thickness (µm)

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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µm

0 10 20µm

10

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–500

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0

500

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105

104

103

102

101

100

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10–2

10–3

Pow

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.7,8

The 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 <a, b, c>, 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 =1

l

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 surface11

as 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

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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 <35%, while inboth cases the edge fit to the bright-bandposition seriously overestimates the powerin modes >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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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 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 via the expression

Ecap = habshCEhHR-capENIF (1)

As indicated schematically in Figure 1,habs is the fraction of incident laser energyabsorbed by the hohlraum, hCE is the con-version efficiency of laser light into x-rays,and hHR-cap is the fraction of generated x-rays that are actually absorbed by thecapsule. Typically, habs is assumed to be 1 – (SBS + SRS) where SBS is the fraction of incident laser light reflected or scatteredout of the hohlraum by stimulated Brillouin scattering and SRS is the fractionreflected by stimulated Raman scattering.6

Since ENIF for NIF is nominally 1.8 MJ,standard “point design” capsules1,7

that absorb 150 kJ of x-rays requirehabshCEhHR-cap = 0.083. Additional constraints1

are that the hohlraum be gas filled, thelaser pulse shape be carefully tailored, andthe peak radiation temperature (TR) be 250 to 300 eV.

Numerical simulations of the ignitionpoint design’s hohlraum and capsule show

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FIGURE 1. The x-ray ener-gy absorbed by a capsuleis the product of the threeefficiencies shown and thelaser energy.(NIF-0401-02046pb01)

a theoretical conversion efficiency of ~80%and an hHR-cap of ~14%, producing a theoretical hCEhHR-cap of 0.11. Comparedto the 0.083 required efficiency, this pro-vides a 25% margin. This margin wasintentionally incorporated into the ignitionprogram in the early ’90s in order to com-pensate for uncertainties, allowing us tobe off somewhat in our assumptions andstill be able to achieve ignition. For exam-ple, if habs = 1 and hCEhHR-cap = 0.11, thenENIF = 1.35 MJ would successfully driveour ignition design. Or if stimulatedbackscattering losses proved to be asmuch as 25% but hCEhHR-cap = 0.11, thenthe expected 1.8 MJ will successfully drive the ignition design. Similarly if habs > 0.75 and ENIF = 1.8 MJ, then valuesof hCEhHR-cap < 0.11 would also work.

Since the original point design wasspecified, an extensive experimental effort,first on Nova3 and, more recently, on theOMEGA4 laser, has significantly reducedthe uncertainties in coupling. Indeed,these experiments and their related analy-sis indicate that NIF coupling efficiencywill be almost as good as we had hopedfor. Ongoing experiments studying stimu-lated Brillouin and Raman backscattering(also known as Laser Plasma Interactionsor LPI) in ignition hohlraum “plasmaemulators” imply that the total backscat-tered losses from these two processesshould be <~5% [Ref. 8]. Complementingthis work are experiments studying theradiation drive9-11 and symmetry12-14 inlaser-heated hohlraums. Analysis of theseexperiments shows that x-ray productionand capsule coupling is very close to ourmodeling. We conclude that for a capsuleof given area and albedo, an ignitionhohlraum’s hCEhHR-cap will be ~1.04±0.12of coupling predicted by our simulations.Applying that to the NIF point designgives an estimated coupling of 0.115±0.012[Ref. 10].

Given coupling that is close to model-ing, we can credibly explore ways toincrease capsule absorbed energy.Referring to Equation 1, we can increasecapsule energy by increasing hCE , hHR-cap,and/or ENIF. In the section below, wedescribe improvements to the hohlraumthat allow us to increase the overallhohlraum coupling efficiency hCEhHR-cap.

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In the section “Increasing ENIF,” wedescribe strategies that allow us toincrease the laser energy.

Improving HohlraumCoupling Efficiency

The energy that a capsule absorbs is justone part of the overall hohlraum energybalance. For a given amount of total x-rayproduction in the hohlraum, hCE(habsENIF),we can write

hCE(habsENIF) =

EWALL + ELEH + ECAP =

(EWALL/ECAP + ELEH/ECAP + 1)ECAP (2)

where EWALL is the the x-ray energyabsorbed by the high-Z walls of thehohlraum (a diffusive, radiative heat flow)and ELEH is the radiation losses throughthe laser entrance hole (LEH). We useratios in Equation 2 to emphasize that wecan increase capsule coupling by decreas-ing the fractional energy absorbed by thewall relative to the capsule absorption,and by decreasing the fractional energythat escapes the LEH relative to the cap-sule absorption. Since the wall losses areproportional to the hohlraum area, we canreduce EWALL/ECAP by making changesthat decrease the heat flow/unit area aswell as by decreasing the total area of thewall while leaving the capsule size fixed(the need to maintain good implosionsymmetry limits the degree to which wecan shrink the hohlraum). Similarly, wecan reduce ELEH/ECAP by decreasing thearea of the laser entrance hole while leav-ing the capsule size fixed. Finally, we notethat hohlraum improvements that eitherdirectly or indirectly increase x-ray con-version efficiency hCE or hohlraumabsorption habs will also increase ECAP.

To understand the improvements thatcan be made to ignition hohlraum cou-pling efficiency, consider as a case study a target based on a 600-kJ variant of a

250-eV target with a beryllium ablator1 asshown in Figure 2. This capsule has anouter radius of 1.77 mm and produces70–120 MJ of yield, depending on thedetailed drive profile and the amount ofDT fuel assumed. We can drive this targetwith a continuous radiation temperaturevs time as shown in Figure 3. At 600-kJabsorbed energy, the target is rather for-giving to changes in timing. The capsuleproduces high yield for drive profiles withplateau-time parameter t ranging between11 and 16 ns. The hohlraum size and,therefore, the wall area for this targetdepends on our choice of “case-to-capsuleratio,” RCC = (Ahohl/Acap)0.5. Virtually allthe NIF point design work, to date, hasbeen done at RCC = 3.65. This case:capsuleratio would place the capsule in ahohlraum 8.8 mm diameter and ~13.3 mmlong (this is approximately a 5.55¥ scale-

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UCRL-LR-105821-00-1

up of a standard Nova hohlraum, or “scale5.55”). Standard NIF design practice callsfor the laser entrance holes to have a diam-eter of 50% of the hohlraum diameter.

Had we examined this 600-kJ capsule inthe early ’90s when we were first explor-ing NIF possibilities, we would have concluded the capsule/hohlraum combi-nation requires too much energy. At thattime we would have assumed pure goldwalls, a scale 5.55 hohlraum and 50% laserentrance holes. The energy budget for thistarget, Case A in Table 1, shows that itrequires 3.3 MJ of x-rays. In the early ’90s,when there was considerable uncertaintyabout hohlraum physics, we hoped thathohlraum x-ray conversion efficiencymight be as high as 70%. Using that value,we would have concluded that this targetwould require ~4.7 MJ of laser energy—well beyond our expectations for NIF.

However, there are several improve-ments that can be made to the hohlraum

Be1.845 g/cm3

Na + Brdoped layer

DT ice0.25 g/cm3

DT gas0.3 mg/cm3

1.769 mm

1.589 mm

1.408 mm

1.539 mm

FIGURE 2. Be ignition capsule designed to operate at250 eV. The 50-mm-thick doped layer next to the DT ice isBe with 2% (atomic fraction) Na and 0.4% Br on theinside of the layer, linearly decreasing to 0.5% Na and0.1% Br on the outside of the layer. The yield is ~75 MJwith the amount of DT ice shown and the pulse shape ofFigure 3. By increasing the ice thickness and adjustingthe pulse shape, yields up to 120 MJ are achieved in sim-ulations. (NIF-0401-02047pb01)

FIGURE 3. The 250-eV Becapsule can be driven witha continuous pulse shapeparameterized by a“plateau time” t. The func-tional form is T 4 = T0

4 + (TF

4 – T04)(t/t)n for t < t.

n = 5 typically allows igni-tion over the widest rangeof t. (NIF-0401-02048pb01)

300

200

100

00 5 10 15 20

t (ns)

TR

(eV

)

TABLE 1. Energy budget for three different assumptions of hohlraum wall material, laser entrance hole, and conversion efficiency. Capsule-absorbed energy remains fixed.

Case A Case B Case C

EWALL(MJ) 1.8 1.2 0.95ELEH (MJ) 0.9 0.55 0.4ECAP (MJ) 0.6 0.6 0.6Total x-rays (MJ) 3.3 2.35 1.95CE 0.7 0.9 0.9Laser energy (MJ) 4.7 2.6 2.2

coupling. Wall losses/unit area can be significantly reduced by using hohlraumsmade of material mixtures. The basic ideais simple: single materials have opacitythat is quite high in some parts of the x-ray spectrum but low elsewhere in thespectrum. Radiation will preferentiallyflow through these opacity “holes.”However, by making the walls from mix-tures of complementary materials theseopacity holes can be filled in.15-17 Forexample, experiments on Nova showedthat ~240-eV radiation will flow through amixture of gold and gadolinium moreslowly than through pure gold.16 Theincrease in Rosseland opacity inferredfrom the measurements is close to whatwas expected from theory.

For ignition pulse shapes that span avery large range in temperature, very sig-nificant decreases in wall losses can beachieved by using mixtures of severalmaterials. For example, Figure 4 showswall loss vs time for three different wallmaterials exposed to the TR vs time ofFigure 3. These estimated wall losses werecalculated with the LASNEX18 code usingan average atom19 of an atomic physicsmodel. The losses plotted in Figure 4 cor-respond to the area of a scale 5.55 Novahohlraum made out of the indicated materials. Mixtures can very significantly

28


UCRL-LR-105821-00-1

reduce losses throughout the pulse,including the foot of the pulse.Quantitatively, wall losses ~2/3 that ofpure Au may be possible. Also shown inFigure 4 are plots of wall albedo vs timefor a pure Au wall and the cocktail mix-ture. At early times there can be a very sig-nificant increase in albedo that not onlysaves energy but also serves to reduce thehot-spot:wall emission ratio. This, in turn,should reduce both intrinsic asymmetryand random asymmetry due to laser beampower imbalance.20

Table 2 lists a variety of cocktail mix-tures we have explored and, in the secondcolumn, our estimated wall losses for the600-kJ case-study capsule in a hohlraumwith RCC = 3.65. The third column showsthe ratio of a given mixture’s estimatedwall loss to that of gold. The final row inthe table is an estimate of the lowerbound to wall loss, found by forcing theRosseland opacity of a Z = 75 wall to beequal to the Bernstein-Dyson upperbound of opacity.21 Although this sug-gests that further improvements may befound, it must be recalled that theBernstein-Dyson limit is a very extremeupper bound.

Equation 2 also shows that we can alsoincrease ECAP by decreasing the energylost through the laser entrance hole. In ahohlraum of fixed case:capsule ratio thatmeans that we must decrease the laserentrance hole diameter from its standardvalue of 50% of the hohlraum diameter.There are at least two techniques foraccomplishing this. One is to simply makethe holes smaller. The other is to allow theholes to partially close as high-Z blowoffmoves inward from the rim of the LEH.Our current work utilizes the latter tech-nique. In our two dimensional (2D)LASNEX simulations of ignitionhohlraums, we find that the simulatedlaser entrance holes partially close if wedo not coat them with a low-Z layer (aswas used in the original designs,1 where itwas assumed that hole closure should beavoided). The x-radiation losses throughthe LEH of all our integrated simulationsof ignition hohlraums are consistently50–60% of the losses we would expectfrom sTR(t)4Ageometric , where TR(t)4 is the radiation flux that is imploding the

0 5 10 15 20

2.0

1.5

1.0

0.5

0

Au: Gd

U:Pb:Ta:Dy:Nd

Au

E (M

J) a

nd a

lbed

o

t (ns)

FIGURE 4. Solid lines: x-ray energy (MJ) absorbed by walls of various materials vs timewhen exposed to the temperature vs time of Figure 3. Area of all three corresponds tothat of a scale 5.55 hohlraum. Dotted lines: albedo vs time for gold and for a multi-component cocktail. (NIF-0401-02049pb01)

capsule, Ageometric is the initial area of theLEH, and s is the Stefan-Boltzmann con-stant. This corresponds to decreasing theeffective LEH diameter from the standard50% of the hohlraum diameter to ~35–40%of the hohlraum diameter. Independentcalculations of LMJ ignition hohlraums byFrench researchers using their 2D codeFCI-2 corroborate this finding.22 The“automatic” decrease in the fractionalLEH loss ELEH/Ecap reduces our casestudy’s x-ray requirement by 350 kJ. Notethat although the fractional diameter ofthe LEH may have decreased from 50% to35–40% of the hohlraum diameter, theactual size of the hole in our case study islarger than the standard point design’s1,7

because the hohlraum is bigger.The potential benefits of reducing the

specific wall losses via cocktails andallowing the laser entrance hole to close to60% of its geometric area are summarizedin Table 1 as Case B. We see that these twochanges reduce the x-ray energy require-ment to ~2.35 MJ. Additionally, we canachieve further savings of x-ray energy byshrinking the hohlraum size while keep-ing the capsule fixed; i.e., reduce RCC.Case C in Table 1 is for a hohlraum wherewe decreased RCC to 3.28 (=90% of theconventional 3.65 value). The total x-rayrequirements drop to ~2 MJ.

We convert hohlraum x-ray energyrequirements to laser energy requirementsby dividing by the average x-ray conver-

29


UCRL-LR-105821-00-1

sion efficiency. We mentioned above thatin the early ’90s we had hoped that thehohlraum x-ray conversion efficiencywould be as high as 70%. Since then abroad range of experiments and the asso-ciated modeling have shown thathohlraum x-ray conversion efficiency can,in fact, be as high as 85% in Novahohlraums.9 In the 1D and 2D simulationsof the ignition hohlraums described here,we find effective conversion efficiencies of approximately 90%. As described inReference 9, such high conversion efficien-cies are a result of the confined nature ofthe system; plasma blowoff energy thatwould be lost in open geometry remainsin the hohlraum where it can “find” itsway into becoming radiation. Using 90%conversion efficiency, the estimated laserrequirements for Cases B and C of Table 1are 2.6 and 2.2 MJ, respectively. This, aswe shall see, puts such a target withinNIF’s design performance envelope.

Integrated Design Analysis

In addition to x-ray and laser energyestimates, as summarized by Table 1, ouranalysis of the hohlraums’s x-ray budgetalso produces x-ray power requirementsthat we readily convert to laser powerrequirements using estimated time-depen-dent conversion efficiency. We validateand refine these laser power estimateswith 1D and 2D LASNEX integrated simu-lations1,7,14 that include detailed hohlraumspecifications, wall materials, capsule, andlaser irradiation. Figure 5 shows a laser

FIGURE 5. Laser power(which drives a 600-kJ,250-eV capsule inside ascale 5.0 hohlraum madewith cocktail walls) vstime.(NIF-0401-02050pb01)

300

200

100

0

PN

IF (T

W) ENIF = 2.25 MJ

1050 15 20

t (ns)

TABLE 2. A variety of mixtures of materials canreduce x-ray wall losses to ~2/3 that of pure Au.

Material Wall loss (kJ) Wall loss/Au

Au 1850 1.00Au:Gd 1540 0.83U:At:W:Gd:La 1200 0.65U:Bi:W:Gd:La 1200 0.65U:Bi:Ta:Dy:Nd 1170 0.63Th:Bi:Ta:Sm:Cs 1250 0.68U:Pb:Ta:Dy:Nd 1170 0.63U:Ta:Dy:Nd 1240 0.67U:Au:Ta:Dy:Nd 1190 0.64U:Au:Ta:Dy:Nd 1220 0.66U:Nb.14:Au:Ta:Dy 1230 0.66Bernstein-Dyson 800 0.44

power that successfully implodes our 600-kJ case-study capsule in a scale 5.0hohlraum (RCC = 3.28) made of cocktailmaterials such as the ones listed in Table 2.It has a total energy of 2.25 MJ. The yieldfrom our 2D simulations of this target,which include the effect of time-depen-dent 2D asymmetries and non-Planckianspectra, is 65–70 MJ; comparable to the75–80 MJ found for this capsule in 1D sim-ulations using the Planckian drive ofFigure 3. Although these design simula-tions at RCC = 3.28 do show a somewhatgreater tendency for an axial jet of fuel todevelop at late time than is typicallyfound at the more standard RCC = 3.65, thesimulated capsules consistently ignite andburn to high yield over a range of tunings.

Besides the 70-MJ–yield capsule, wehave also been studying a 115-MJ–yieldversion of the same 250-eV, Be capsule. Ithas more DT fuel and is driven on a some-what lower adiabat (i.e., the foot TR is90 eV vs the 110 eV shown in Figure 3).This capsule also absorbs ~600 kJ. It isdriven by a 2.55-MJ laser pulse into ahohlraum of the more typical case:capsuleratio, RCC = 3.65. This target consistentlyproduces 110–115 MJ in our 2D simulationsthat include time-dependent asymmetries,giving a target gain of ~44. Our estimatedlaser power does not result in a perfectreproduction of the original drive; here the

30


UCRL-LR-105821-00-1

peak hohlraum radiation temperature is~270 eV vs the 250 eV in the originaldesign. The ease with which we are able to get our 2D simulations of this target toignite is an indication that targets of thissize may indeed be quite robust.

Besides the 600-kJ capsule used for ourcase study, we have examined scaled ver-sions of this capsule, which absorbbetween 265 and 1000 kJ of x-rays for RCCranging between 3.65 and 2.98. Our analy-sis includes validating the estimated laserpower with 1D and 2D integrated simula-tions. (Here the 2D simulations are donewith the capsule flux numerically forced tobe uniform. This allows us to rapidlyassess the energetics of an extensive rangeof hohlraums without also needing tosimultaneously control symmetry.) Figure 6 summarizes the hohlraum cou-pling efficiency, hCEhHR-cap of Equation 1,for this survey. At the standard case:cap-sule ratio, cocktails and slightly reducedLEHs together with longer pulse lengthscombine to produce coupling efficiencies~20–22% vs the ~11% of the original pointdesign. If we can successfully reduce thecase-to-capsule ratio without introducingunacceptable asymmetry, then couplings~26–28% are plausible at RCC = 3.28 and~30–33% at RCC = 2.98.

In evaluating the increase of hohlraumcoupling efficiency from ~11% to ~25%,

40

30

20

10

0E

CA

P/E

lase

r (%)

ECAP (kJ)

4002000 600 800 1000

2.98 Rcc

3.65 Rcc

3.28 Rcc

250-eV designs

300-eV point design

FIGURE 6. Hohlraumcoupling efficiency

(hCE hHR-cap) vs capsule-absorbed energy for vari-ous scales of the 250-eVBe capsule. The couplingefficiency ranges between20 and 33%, dependingon the case:capsule ratio.(NIF-0401-02051pb01)

we find that it is due to the simultaneouscombination of many relatively smallimprovements. We cannot point to anyone key change. The steady accumulationof small improvements is summarized inTable 3. This collection of modestimprovements produces, in concert, morethan a factor of 2 increase in overallhohlraum coupling.

Increasing ENIF

NIF is a glass laser that is capable ofproducing up to ~4.8 MJ (4MJ) of 1-mm(infrared) wavelength laser light when it iscompleted with 7 (5) slabs of glass in thefinal booster amplifiers. (The number ofslabs that will ultimately be installed isunder discussion. The amplifiers beingbuilt will accommodate seven.) This 1-mmlight is converted to the 1/3-mm (blue)light used to irradiate hohlraums in thefinal optics assembly (FOA), where it isalso focused and aimed onto the target.Two fundamental questions that must beanswered in order to assess NIF’s capabili-ty to produce any given pulse shape are:

1. Is there enough 1-mm light to createthe needed blue pulse shape?

2. If so, how much “damage” will theblue light cause in the FOAs?

The answer to the first questiondepends not only on the intensity-depen-dent conversion efficiency of the potassi-um dihydrogen phosphate (KDP) crystals

31


UCRL-LR-105821-00-1

(which convert the infrared light to bluelight) but also on the operational strategythat we use to produce a given pulseshape at the target. In the case of the 2.25-MJ pulse shape of Figure 5, if we electto generate it by simply running an appro-priately shaped, continuous 1-mm pulseshape through the KDP crystals, then wefind that we need 4.5 MJ of 1-mm laserlight. This is well within the energeticscapability of NIF with seven booster slabsbut not with five. However, there are oper-ational strategies for significantly reducingthe 1-mm requirements. These strategiesare all based on the “picket fence”approach,23 which replaces a continuouspulse with a train of short, high-powerpulses that convert to blue light muchmore efficiently in the KDP crystals duringthe low-power, early time “foot” of thepulse. Now there is a concern, based onsimulations, that hohlraums irradiated bywidely spaced pickets will have symmetryproblems related to cooling of thehohlraum’s bulk plasma between pickets.However, it is possible to take advantageof NIF’s architecture to produce temporal-ly skewed pickets that convert well in theKDP crystals but provide a continuouspulse after being focused onto the target.24

Moreover, by taking advantage of NIF’sarchitecture in which a “quad” (a 2¥2array of four beams) can be treated as asingle beam that irradiates the hohlraum,it is possible to interleave four relativelyshort pulses from each of the four beamsto form a continuous pulse. Using tech-niques such as this, we can envision aver-age 1/3-mm conversion efficiencies as highas 70%, as measured at the target. For thepulse shape of Figure 5, this “ultrafastpicket” technique could lower the 1-mmenergy requirement to ~3.5 MJ. Indeed,such advanced conversion schemes allowus to contemplate even larger capsules.Table 4 summarizes 1/3-mm and 1-mmenergy requirements for several targets.Using advanced conversion schemes andreduced case:capsule ratios, we can con-sider driving capsules that absorb as muchas 1 MJ of x-rays.

The second fundamental question abouta given pulse shape is how much “damage”will it cause in the FOA? A basic problemis that surface imperfections will slightly

TABLE 3. Hohlraum efficiency can be significantlyincreased by a combination of many relatively smallimprovements.

Hohlraum Efficiency (%)

300 eV, 150 kJ, 3 ns 11250 eV, 600 kJ, 7.5 ns 14.5Reduce LEH only 16.2Cocktails only 17.7Both cocktails and reduced LEH 20.3CE rises from ~80% to ~90% 22.9Reduce Rcc by 10% 25.3

absorb blue light causing local heating.Too much heating produces local damage.The figure of merit for this process, knownas the “damage integral,” increases withfluence (J/cm2) but decreases with pulselength as 1/t0.5, since heat can diffuseaway from the absorbing imperfections.NIF’s specification for damage integral is8 J/cm2, 3 ns Gaussian equivalent. Thismeans that a 3-ns Gaussian pulse of8 J/cm2 passing through the FOA wouldbe acceptable. Likewise, the t0.5 scalingmeans a 12-ns pulse of 16 J/cm2 couldalso be acceptable. For an arbitrary pulseshape,25

(3)

where I is the blue-light intensity in unitsof GW/cm2, t and s are in ns. The finalcolumn in Table 4 lists the damage integral

32


UCRL-LR-105821-00-1

values for several higher absorbed energydesigns. All are within NIF’s 8 J/cm2 3 nsGaussian equivalent damage specification.

Discussion

The 600-kJ capsule driven at 250 eV thatwe used as a case study is part of a largerstudy exploring the limits of capsule cou-pling energy. This work indicates that NIFmay be able to drive some surprisinglyenergetic targets. Figure 7 is an “engineer-ing plot” that summarizes our findings at250 eV. It relates capsule absorbed energyto laser performance. The solid lines repre-sent the three case:capsule ratios we stud-ied: RCC = 3.65, 3.28, and 2.98. The brokenline at the upper right shows where wewould run out of 1-mm energy using anadvanced pulse-shaping technique such asthe ultrafast pickets described above. At

TABLE 4. One-µm energy needed to drive various targets, assuming two different operational strategies, and1/3-µm damage integral for each target’s pulse shape.

1/3-µm energy 1-µm energy 1-µm energy Damage integralTarget ECAP/Yield/Rcc (MJ) CW pulse (MJ) fast pickets (MJ) (J/cm2 3 ns equiv)

600 kJ/70 MJ/3.28 2.25 4.5 3.5 7.2600 kJ/120 MJ/3.65 2.55 5 3.9 7.8850 kJ/150 MJ/2.98 2.65 5.1 4 7.81000 kJ/380 MJ/2.98 3 6 4.5 8

Damage integral = 1.1 0

¥-Ú I s

t sds

t( )

8

10

6

4

2

00 200 400 600 800 1000

2.98 Rcc

3.28 Rcc

3.65 Rcc

4.8 MJ 1 limit with advanced-conversion

220-eV capsule(Tabak/Hammer)

NIF 3spec

J/cm2 3 ns Gaussian equivalent at the KDP

250-eV designs

Capsule-absorbed energy (kJ)

FIGURE 7. Energyabsorbed by the 250-eVcapsule vs 3w damageintegral (cf Equation 3).Solid lines indicate threedifferent case:capsuleratios. Broken line indi-cates the limit set by NIF’savailable 1-mm energy,assuming seven boosteramplifier slabs andadvanced conversionschemes. NIF’s designspecification for 3w dam-age integral is “8 J/cm2

3 ns Gaussian equivalent.”(NIF-0401-02052pb01)

RCC = 3.65, we may be able to implode acapsule that absorbs 600 kJ before exceed-ing NIF’s 8-J/cm2 blue-light fluence speci-fication. If we can successfully implodecapsules in hohlraums with reducedcase:capsule ratio, then absorbed energiesapproaching 800 kJ to 1 MJ are possible.The star on the plot indicates one 220-eVtarget we investigated. It is based on a1000-kJ absorbed energy capsule that pro-duced 380 MJ of energy.26

Although we allow the laser entrancehole to close to ~80% of its initial diameter,it is important to realize that thesehohlraums are bigger than the typicalpoint design hohlraum1,7 (a scale 3.45hohlraum). Consequently, the laserentrance holes are bigger, even after thepartial closure. This, coupled with a lowerpeak power (~300–350 TW vs 450 TW)leads to the prospect of relatively lowintensities in the LEH; ~2–4¥101 4 W/cm2

may be possible.Returning to Figure 7, we see that at

250 eV, there is a reasonably good matchbetween NIF’s damage specification and the1-mm light potentially available. Figure 8 isa similar plot for 300-eV targets, based on a Cu-doped Be capsule design.27 At300 eV we find some mismatch between

33


UCRL-LR-105821-00-1

the damage specification and the 1-mmenergy potentially available. We are begin-ning to explore ways to possibly redressthis mismatch, including evaluating theuse of green light, which is believed tohave a damage limit considerably higherthan that of blue light.

Finally, Figure 9 is a plot of yield vs cap-sule-absorbed energy, which demonstrates

15

10

5

00 200 400 600 800 1000

2.95 Rcc

3.28 Rcc

3.65 Rcc4.8-MJ 1 limit with advanced

conversion

NIF 3spec

Estimated 2 limit

Capsule-absorbed energy (kJ)

J/cm2 3 ns Gaussian equivalent at the KDP

FIGURE 8. A similar plot to Figure 7 but for a capsule driven at 300 eV. (NIF-0401-02053pb01)

FIGURE 9. Yield vs cap-sule-absorbed energyfrom 1D simulations of acapsule driven at 250-eVpeak radiation tempera-ture and a capsule drivenat 300 eV. Significantlyincreasing the capsule-absorbed energy willmove us away from theignition “cliff,” therebyproviding a more robusttarget.(NIF-0401-02054pb01)

100

10

1

0.10 200 400 600 800 1000

Capsule energy (kJ)

TR = 300 eV

TR = 250 eV

Y (MJ)

Possible designs400 kJ, 300 eV600 kJ, 250 eV

Original point designs(150–200 kJ @ 300 eV)

some of the benefits of increased absorp-tion. We see that a factor of two to fourincrease in absorption over the original150–200 kJ moves us much further fromthe “cliff” where the penalty for smallerrors in understanding can be very large.These increases in absorbed energy canalso very significantly increase the capsuleyield.

AcknowledgmentsMuch of this work was engendered

during an evening’s discussion withR. Kauffman and L. Powers. We wouldlike to acknowledge useful discussionswith J. Lindl, B. Hammel, M. Tabak, andJ. Edwards. We would like to thank E. M.Campbell, in particular, for his enthusias-tic support and encouragement.

Notes and References1. S. W. Haan, S. M. Pollaine, J. D. Lindl, et al.,

Phys. Plasmas 2, 2480 (1995). 2. J. A. Paisner, E. M. Campbell, and W. J. Hogan,

Fusion Technol. 26, 755 (1994).3. J. T. Hunt and D. R. Speck, Opt. Eng. 28, 461

(1989).4. J. M. Soures, R. L. McCrory, C. P. Verdon, et al.,

Phys. Plasmas 3, 2108 (1996).5. M. Andre, M. Novaro, and D. Schirmann,

“Technologie pour un Laser Megajoule,” ReviewScientifique et technique de la direction des applica-tions militaires, Chocs, Numero 13, 73, Avril 1995.

6. See, for example, W. Kruer, The Physics of LaserPlasma Interactions (Addison-Wesley, New York,1988).

7. W. J. Krauser, N. M. Hoffman, D. C. Wilson, etal., Phys. Plasmas 3, 2084 (1996).

8. B. J. MacGowan, R. L. Berger, S. I. Glenzer, et al.,“Laser Beam Smoothing and Backscatter

34


UCRL-LR-105821-00-1

Saturation Processes in Plasmas Relevant toNational Ignition Facility Hohlraums,”Proceedings of the 17th IAEA Fusion EnergyConference, Yokohama, Japan (October 1998),International Atomic Energy Agency, Vienna.

9. L. J. Suter, R. L. Kauffman, C. B. Darrow, et al.,Phys. Plasmas 3, 2057 (1996).

10. L. J. Suter et al., “Status of Our Understandingand Modeling of Ignition Hohlraum X-RayCoupling Efficiency,” ICF Quarterly Report 8 (4),171–178, Lawrence Livermore NationalLaboratory, UCRL-LR-105821-98-4 (1998).

11. R. L. Kauffman, L. J. Suter, C. B. Darrow, et al.,Phys. Rev. Lett. 73, 2320 (1994).

12. A. Hauer et al., Rev. Sci. Instrum. 66, 672 (1995).13. P. Amendt et al., Phys. Plasmas 4, 1862 (1997).14. L. J. Suter et al., Phys. Rev. Lett. 73, 2328 (1994).15. H. Nishimura et al., Appl. Phys. Lett. 62, 1344

(1993).16. T. J. Orzechowski, M. D. Rosen, H. N.

Kornblum, et al., Phys. Rev. Lett. 77, 3545 (1996).17. D. Colombant, M. Klapisch, and A. Bar-Shalom,

Phys. Rev. E 57, 3411 (1998).18. G. B. Zimmerman and W. L. Kruer, Comments

Plasma Phys. Controlled Fusion 2, 51 (1975).19. D. E. Post et al., Atom. Data Nucl. Data Tables 20,

397 (1977).20. O. J. Jones, Lawrence Livermore National

Laboratory, Livermore, CA, private communica-tion (1999).

21. See, for example, J. Bond, K. Watson, and J.Welch, Atomic Theory of Gas Dynamics (Addison-Wesley, New York, 1965) p. 371.

22. E. Dattolo, CEA Bruyeres-Le-Chatel, France, pri-vate communication (1999).

23. D. J. Kuzienga, Opt. Commun. 22, 156 (1977).24. J. Rothenberg, Lawrence Livermore National

Laboratory, Livermore, CA, private communica-tion (1999).

25. J. Trenholm, Lawrence Livermore NationalLaboratory, Livermore, CA, private communica-tion (1998).

26. J. H. Hammer et al., Phys. Plasmas 6, 2129(1999).

27. T. R. Dittrich et al., Fusion Technol. 31, 402(1997).

35

We have tested spectroscopic model-ing of the helium-like and lithium-

like argon x-ray emission in dense gasbagplasmas by comparing measured spectrawith kinetics calculations using plasmaparameters that have been accurately mea-sured with Thomson scattering. In particu-lar, we have measured the line radiation inthe wavelength region of the He-like Ar1s2 – 1s3l transition (He-b). This spectrumis of interest to diagnose gas targets, ne ~1021 cm–3 (Refs. 1–3), laser ablation plas-mas, ne ~ 1022 cm–3 (Ref. 4), and has previ-ously been applied to diagnose electrondensities and temperatures of inertial con-finement fusion (ICF) capsule implosions,ne ~ 1024 cm–3 (Refs. 5,6).

The ICF implosions produce plasmaconditions of extremely high densities sim-ilar to those of stars and therefore requirex-ray emission or neutron diagnostics.7

The spectrum of the He-b transition ofAr XVII together with its dielectronicsatellites arising from the Li-like Ar states1s2 nl – 1s nl n'l', referred to below as the He-b complex, has been found to be avaluable diagnostic of electron densitiesand temperatures. The He-b line is Stark-broadened so that densities can be inferredfrom the width of the spectral line.Moreover, the upper states of the observ-able dielectronic satellites on the red wingof the He-b line are predominantly popu-lated by dielectronic recombination so thattheir relative intensity is sensitive to theelectron temperature.8,9 Some of the higher-n satellite features overlap with the

He-b transition and consequently need tobe self-consistently included in the fit ofthe whole line shape with a Stark-broaden-ing code coupled to a kinetics (collisional-radiative) model.10,11 This procedureapplies kinetics modeling to very highdensities where the codes have not beentested against independent measurements.In this study, we perform critical compar-isons of kinetics calculations with experi-mental data from well-characterizedplasmas at the highest possible densitieswhere independent optical diagnostics,i.e., Thomson scattering, can be used tomeasure the electron temperature.12,13 Thisis a necessary first step toward a criticalevaluation of the diagnostic proceduresused at the highest measured plasma density of ne > 1024 cm–3.

We have performed our experiments inwell-characterized gasbag plasmas at den-sities ne = 0.6 ¥ 1021 cm–3 and ne = 1.1 ¥1021cm–3. The densities of these gasbagplasmas are independently diagnosed withstimulated Raman scattering,1 and theelectron temperatures are measured withtemporally and spatially resolvedThomson scattering.13 The Thomson scat-tering measurements indicate that the gas-bags are homogeneous with slowlyincreasing electron temperatures duringthe first 0.6 ns of the 1-ns-long heater beampulse. These data are also consistent withhydrodynamic LASNEX modeling14 sug-gesting that gasbag plasmas are suitablesources to test our kinetics modeling capability.

ON THE ACCURACY OF X-RAY SPECTRAMODELING OF DENSE INERTIAL CONFINEMENT

FUSION PLASMAS

S. H. Glenzer B. A. Hammel

K. B. Fournier R. W. Lee

B. J. MacGowan

UCRL-LR-105821-00-1

To compare the experimental spectrawith synthetic spectra, we employ theHULLAC suite of kinetics codes.15 Wefind for the two different electron densitiesthat the kinetics modeling accurately pre-dicts the intensity ratio of the Li-likedielectronic capture satellite transitionsand of the He-b transition (consisting ofthe sum of the resonance line, He-b1: 1s21S0 – 1s3p 1P0

1, and the less intense inter-combination line from the triplet to thesinglet system of He-like argon, He-b2: 1s21S0 – 1s3p 3P0

1). On the other hand, spec-tral line emission originating from levelswhose population is primarily determinedby electron collisional processes showsdiscrepancies of up to a factor of two com-pared to the modeling. In particular, this isobserved for inner-shell excited satellitetransitions that are populated from the Li-like ground state. We have examinedpossible explanations for this discrepancyand found that the most likely one iserrors in the calculated ionization balancebetween the He- and Li-like state.

In spite of these remaining discrepan-cies between calculated and measuredinner shell satellite intensities, the fact thatthe strongest satellite features (the dielec-tronic capture satellites) are well modeledby the HULLAC code may affect the inter-pretation of ICF capsule implosions exper-iments. Our findings indicate that weshould revisit the analysis of the higherdensity implosions to find if the kineticsmodeling is consistent with the resultsobtained here. Preliminary calculations forimplosion conditions show that variouskinetics codes result in a factor of two dif-ferent prediction for the ratio of the cap-ture satellites to the He-b transition. Moreanalysis using line shape calculations willbe required to investigate whether the pre-vious interpretation of spectra from cap-sule implosions is affected.6 Moreover,having proven the technique to bench-mark kinetics calculations in laser-pro-duced plasma conditions, one can hope to extend this method to verify criticallyimportant aspects of indirectly driven capsule physics by testing the conditionscreated inside of ICF hohlraums.

36

ON THE ACCURACY OF X-RAY SPECTRA MODELING OF DENSE INERTIAL CONFINEMENT FUSION PLASMAS

UCRL-LR-105821-00-1

Experiment

The experiments were performed withthe Nova laser facility at the LawrenceLivermore National Laboratory.16 ThisNd:glass laser was operating at 1.055 mm(1w) and could be frequency converted to3w with energies of ~30 kJ. The applicationof these large laser energies has enabled usto produce large-scale–length andextremely homogeneous plasmas (DTe/Te< 20%). We used nine f/4.3 laser beams toilluminate gasbag targets from all sides.Gasbags consist of two 0.35-mm-thickpolyimide (C14H6O4N2) membranes thatare mounted on either side of a 0.4-mm-thick aluminum washer with an innerdiameter of 2.75 mm (Figure 1). In thisstudy, the membranes have been inflatedwith propane (C3H8) or neopentane(C5H12) plus a small amount of Ar (1% byatomic number in each case) as a spectro-scopic test element. The concentration ofAr atoms of 1% was chosen to obtain optically thin conditions for the Li- andHe-like Ar emission.The heater beams provided 2.3-kJ energy per beam at

2.3 kJ@ 3

2.3 kJ@ 3

2.3 kJ@ 3

2.3 kJ@ 3

FIGURE 1. Gasbag target before it was pressurized withC3H8 or C5H12. The thickness and the inner diameter ofthe washer were 0.4 mm and 2.75 mm, respectively. Thegasbags were heated with nine 1-ns-long heater beamsof 2.3 kJ per beam at 3w. (NIF-0401-02069pb01)

3w (l0 = 351 nm) in a 1-ns-long squarepulse. A diverging focus resulted in anintensity of I = 1014 W cm–2 on target.

The x-ray spectra have been measuredwith a crystal spectrometer17 coupled to agated microchannel-plate detector(MCP).18 The x-ray emission is observedthrough a slit cut in a copper shield andmounted on the target at a distance of8 mm, effectively limiting the plasma sizeseen by the spectrometer. This slit allows aview through the gasbag center. We used apentaerythritol (PET) crystal to spectrallydisperse the plasma emission and detectedthe spectra with the MCP detector with atemporal resolution of 80 ps, a spatial res-olution of 22 mm, and a resolving power ofl/Dl = 800. Examples of the spectra mea-sured in this way are presented in the nextsection. The gated MCP detector was fur-ther employed for 2D x-ray imaging of thegasbag emission with photon energies ofE > 2 keV. For this purpose, we used 10-mm pinholes with a Be filter in front ofthe MCP camera. Figure 2 shows an exam-ple of three successive measurements. Forearly times (t < 0.3 ns) during the 1-ns-long heating pulse, the initial imprint ofthe heater beams can be identified. For t >0.4 ns, these measurements indicate thatthe gasbag plasmas become homogeneous.

For a more quantitative investigation ofthe plasma homogeneity, we measured theelectron temperature at various distancesfrom the target center with Thomson scat-

37


UCRL-LR-105821-00-1

tering. A 50-J, 4w (l0 = 263 nm) probebeam has been used for the Thomson scat-tering experiments.13 Due to the stronglaser light absorption, stray light, andstimulated Raman side-scattering from theheater beams in the wavelength regionaround the longer Nd:glass wavelengthharmonics: 2w and 3w , a short-wavelengthprobe is required to characterize opengeometry large-scale–length ICF plasmas.The probe laser was focused into the gas-bag target to a spot of 60 mm ¥ 120 mmresulting in an intensity of I ~ 3 ¥1014 W cm–2 (at 4w). In separate experi-ments, we have shown that this probedoes not influence the plasma when it ishot and heated by kJ-laser beams.

The Thomson scattered light has beenimaged at an angle of 90˚ with f/10-opticsonto the entrance slit of a 1-m (SPEX)spectrometer. We employed an S-20 streakcamera to record spectra with a temporalresolution of 50 ps and a wavelength reso-lution of 0.05 nm. The imaging setupresulted in a cylindrical scattering volumewith a scale length of ~100 mm. The scat-tering volume is small compared to thesize of the plasma. The choice of the probelaser wavelength of 263 nm and of thescattering angle of 90˚ results in collectiveThomson scattering from fluctuationscharacterized by wave numbers ksuch that the scattering parameter isa = 1/klD > 2 for the gasbag electron den-sities and temperatures. The Thomson

FIGURE 2. Temporallyresolved 2D x-ray imagesof the gasbag emissionwith energies E > 2 keV.The gasbags show ahomogeneous emissionshortly after the begin-ning of the heater pulse(for t > 0.4 ns).(NIF-0401-02070pb01)

Rad

ius

(mm

)

1 0 –1 1 0 –1

Minor radius (mm)

1

0

–1

1 0 –1

t = t0 + 250 ps t = t0 + 750 ps t = t0 + 1250 ps

scattering spectra are dominated by thenarrow ion feature which shows scatteringresonances at the ion-acoustic wave fre-quencies shifted from the incident probelaser frequency on either side on the fre-quency scale (redshift and blueshift forwaves copropagating and counterpropa-gating along the scattering vector k.

Figure 3 shows an example of Thomsonscattering spectra at t = 0.35 ns and t =0.9 ns measured at a radius of 800 mmfrom the gasbag center. The electron tem-perature can be inferred from the frequencyseparation of the two ion-acoustic peaks.Each peak consists of two unresolved ion-acoustic waves, one belonging to carbon(slow mode) and one belonging to hydro-gen (fast mode) giving the ion tempera-ture of the plasma from the relativedamping of these waves. With increasingtime, the ion-acoustic peaks showincreased separation and broadening indi-cating increasing electron and ion temper-atures during the heating of the gasbagplasma. To accurately infer temperaturesfrom these spectra, we convolute the formfactor S(k,w) for multi-ion species19 withthe experimental instrument function andfit the resulting profile to the data.Examples of these fits are also shown inFigure 3. We obtain an error estimate forthe electron temperature of <10% from thefitting procedure by varying the calculatedprofile within the noise of the experimen-tal data.

38


UCRL-LR-105821-00-1

Figure 4 shows the electron tempera-ture as a function of the radius for two dif-ferent times during the heating of thegasbag plasma. The experimental datashow mutual agreement between theresults from the temporally and spatiallyresolved Thomson scattering techniqueand with temporally and spatiallyresolved x-ray spectroscopy using theintensity ratio of the He-like Ar 1s2 – 1s2l(He-a) line to the Li-like jkl dielectronicsatellites.2 These two techniques are com-pared together with hydrodynamic LASNEX and FCI2 simulations. The errorbars for the spectroscopically derived tem-peratures are in the range of 15% to 20%depending on the noise amplitude of theindividual spectra at various times. TheThomson scattering data are accurate towithin 10%. We find that the results of thesimulations are close to the experimentaldata. For this comparison, we include theheater beam scattering losses by stimulat-ed Brillouin and stimulated Raman scat-tering. The results presented in Figure 4clearly show a homogeneous plasma atthe time of the measurements of the He-btransition plus satellites, i.e., 0.3 ns < t <0.5 ns, with DTe/Te < 20%. At the time

263 264 265Wavelength (nm)

1

0

2

t = 0.9 ns

t = 0.35 ns

Te = 2.5 keVTe/Ti = 4

Te = 1.3 keVTe/Ti = 7.4

Inte

nsi

ty (

arb.

un

its)

FIGURE 3. ExperimentalThomson scattering spec-tra from a C5H12-filled gas-bag measured from a radialdistance of 0.8 mm fromthe gasbag center.Thespectra show increasingelectron temperatures anddecreasing electron-to-iontemperature ratios.Theparameters are inferredfrom the theoretical fits tothe experimental data.(NIF-0401-02071pb01)

FIGURE 4. Experimental electron temperature data forvarious radial positions measured at t = 0.35 ns and at t = 0.9 ns. The temperatures from Thomson scatteringshow excellent agreement with the results from x-rayspectroscopy and are consistent with the hydrodynamicmodeling using the codes LASNEX and FCI2. At t = 0.35 nsthe electron temperature profile is flat indicating the utili-ty of gasbags for spectroscopic investigations.(NIF-0401-02072pb01)

0 0.5 1Radius (mm)

1

0

Te

(keV

)

1.5

2

3

t = 0.35 ns

t = 0.9 ns

LASNEX

FCI2

Thomson scattering He-/jkl

close to peak temperature, i.e., t = 0.9 ns,we find a homogeneous center with adiameter of 2 mm, DTe/Te < 30%.

While the electron and ion tempera-tures in these gasbag plasmas are wellknown from the measurements describedabove, the electron density is principallyknown by the density of the gas fill.Measurements of the wavelength of theRaman scattered light that occurs at thefrequency of the electron plasma wavegive a value for the electron density that isconsistent with the gas fill density.1 Theline intensity ratio of the resonance andintercombination line of He-like Ar hasalso been shown to be in agreement withthe expected densities.2 In summary, thedetailed measurements and the generalagreement with the simulations indicatethat the plasma conditions in these gasbagtargets are known with good accuracy sothat it provides a spectroscopic source thatis very suitable to test kinetics codes.

Experimental Results andDiscussion

Figure 5 shows an example of a tempo-rally resolved x-ray spectrum in the wave-length region 0.332 nm < l < 0.345 nmmeasured at t = 0.35 ns from a gasbag thathas been filled with C5H12 and 1% Ar. Thedata have been measured spatiallyresolved along the slit height and aver-aged over the region r < 1.2 mm to reducenoise. The averaging does not influencethe interpretation of plasma conditionsbecause at the time of the measurementsthe gasbag plasma is homogeneous asshown above. In Figure 5 we also show asynthetic spectrum calculated with theexperimental resolution and with a higherresolution using the HULLAC suite ofcodes for the experimental plasma param-eters: Te = 1.3 keV, ne = 1.1 ¥ 1021cm–3.

The spectrum is dominated by the1s – 3p resonance line of He-like argonAr XVII at l = 0.3364 nm, He-b, the theo-retical transition energy of which has beenused to determine the absolute wave-length scale of Figure 5. A number of spectral lines can be identified on the low-

39


UCRL-LR-105821-00-1

energy, or red, wing of the He-b transition.These are the intercombination line at l = 0.337 nm, dielectronic satellites with an = 3 spectator electron at l = 0.3381 nmand four dielectronic satellites with a n = 2spectator electron labeled 1 through 4(Refs. 4, 20). For a quantitative comparisonbetween the experiment and the spectramodeling, we fit the experimental datawith a multi-Gaussian profile using aleast-squares method (Figure 5). We obtainan estimate for the error bar of the experi-mental intensities of the various spectrallines by varying the fit within the noise ofthe data. This error is in the range of 5%for the intense transitions (e.g., feature 4)to 20% for the weak transitions (e.g., feature 1). In Figure 5, the n = 3 dielectron-ic satellites at 0.3381 nm have not beenincluded in the fit since we do not com-pare it to modeling. However, we verifiedthat the n = 3 feature, as well as n = 4satellites,11,20 do not influence the intensityof the He-b line for our conditions.

Figure 6 compares the measured inten-sity ratio with the results of the HULLACcalculations. It shows the ratio of the

3.36 3.4 3.44Wavelength (0.1 nm)

Inte

nsit

y (a

rb. u

nits

)

Te = 1.3 keV

ne = 1021 cm–3

1

He-

4

2,3

FIGURE 5. Experimentaland synthetic spectra ofthe Ar He-b complex.(NIF-0401-02073pb01)

dielectronic capture satellite (labeled 4) tothe He-b transition as function of the mea-sured electron temperature for the two dif-ferent electron densities. The dielectroniccapture satellite 1s2 + e– Æ 1s 2l 3l' is pri-marily populated by collisional excitationfrom the He-like ground state and simul-taneous capture of a free electron into anexcited bound state. This process is knownto be sensitive to the electron temperature,and kinetics modeling shows no depen-dence on electron density for the densityrange of this study. We find that the exper-imental data are in excellent agreementwith the kinetics modeling if the fully colli-sional-radiative HULLAC model is used.

The HULLAC calculations15 includeall singly and doubly excited energy levelswith principal quantum number n ≤ 5. Thecode generates atomic wave functionsusing a fully relativistic, parametric poten-tial method that calculates the multicon-figuration, intermediate coupled levelenergies and radiative transition rates, A.In addition, the code also computessemirelativistic autoionization transitionrates to the ground and excited levels ofan adjacent ion. The electron-impact exci-tation rates between all levels of eachcharge state mentioned above are calculat-ed in the distorted wave approximation.The ionic transition rates include theautoionization rates from the Li- to He-likeand He-like to H-like ions, as well asdirect, impact ionization and radiativerecombination rate coefficients. Radiativerecombination from and collisional ioniza-

40


UCRL-LR-105821-00-1

tion to the bare nucleus Ar18+ are alsoincluded. These rates are used to constructthe collisional-radiative rate matrix. Theinverse of each ionization process, namelydielectronic capture and three-bodyrecombination have been found accordingto the principle of detailed balance. Therelative populations of the four chargestates and the population, N, in each levelof each ion are then found in steady state.

From these calculations we obtain theintensity of the spectral line emission and thus the intensity ratios shown inFigures 6 and 7. In general, for opticallythin plasmas, the intensity of a radiativetransition Iul from the upper level u to thelower level l is given by the integral of theemission coefficient e over the plasmapath length:

where e is given by the atomic transitionprobability Aul, the population density ofthe upper atomic state Nu, and a lineshape function F that is normalized to oneif integrated over the whole line profile infrequency space.

The comparison shows that the HULLAC calculations agree on averagewithin 6% with the experimental intensityof the dielectronic capture satellite. Alsoshown in Figure 6 are two simplified calcu-lations using a coronal approximation, i.e.,for low densities, the population of theupper states is determined by electron col-lisional excitation from the ground state Ngand de-excitation by radiative transitions.

These two simplified models,15,20 whichuse slightly different estimates for Aul andthe averaged cross section for electron col-lisional excitation <sn>, overestimate theexperimental ratio by 12% to 22%. This

Te (keV)

Rat

io: 4

/H

e-

0 1 2 30

0.1

0.2

0.3

Fully kineticsHULLAC model

Corona model(Ref. 20)

Corona modelwith HULLACatomic physics

C5H12 dataC3H8 data

FIGURE 6. Comparisonbetween the experimentalline ratios from C3H8-filled(ne = 6 ¥ 1020cm–3) andC5H12-filled (ne = 1.1 ¥1021cm–3) gasbags withsteady-state kinetics (colli-sional-radiative) modeling.The intensity ratio of theHe-b transition (resonanceplus intercombination line)to satellite feature 4, whoseupper state is populated bydielectronic capture, showsexcellent agreement withthe fully kinetics modeling.(NIF-0401-02074pb01)

I x dxu ul l( ) ( , )n e n= Ú

e n np

nu u uxh

A N x xl l( , ) )=4

( ) ( , F

NN n

Aug

u=

Â

e sn

l

comparison indicates that a full kineticscalculation is required to model thesespectra. We observe good agreementbetween the experimental dielectronic cap-ture satellite intensities and the full kinet-ics model indicating that the populationsof atomic states within one ionizationstage are well understood.

On the other hand, we find that inner-shell collisional excited satellite lines arenot as well modeled. These satellites areexcited by collisions of free electrons withions in the Li-like ionization state: 1s2 2l + e– Æ 1s 2l 3l' + e–. Figure 7 showsthe ratio of the inner-shell excited satellitefeature 1 with the fully collisional-radia-tive HULLAC kinetics modeling.

In this case, we observe discrepanciesbetween the data and the modeling of upto a factor of two. To ascertain the poten-tial effects of the hot electrons and nonsteady-state populations, we use time-dependent calculations to model theexperimental conditions described above.Only for times t < 0.1 ns, when there is asignificant fraction of Li-like ions in theplasma, do these calculations show thathot electrons increase the collisional exci-tation and therefore the intensity of theHe-b transition as well as the inner-shellcollisional excited satellites. However, at

41


UCRL-LR-105821-00-1

later times when the spectra have beenmeasured, i.e., 0.3 ns < t < 0.5 ns, the effectof the hot electrons is found to be negligi-ble because He-like ions begin to domi-nate the charge state distribution so thatthermal electrons dominate the collisionalexcitation process (e.g., Ref. 21). Further,the same time-dependent calculationsshow that deviations from steady state aresmall for the gasbag plasma conditionsand cannot account for the discrepancyobserved in Figure 7.

The most likely explanation for theobserved discrepancies arises from differ-ences in the ion balance between modeland experiment. The calculations indicatethat at the time of the measurements about80% of the argon ions are in the He-likeionization state while only 1%-2% of theions remain in the Li-like state. Smallerrors in the calculation of the absolutenumber of Li-like ions can therefore resultin large errors in the ratio of collisionalexcited satellites (e.g. feature 1) to the res-onance transition (the He-b transition).

Conclusions

We have performed x-ray spectroscopicexperiments in homogeneous gasbag plas-mas where we independently measure thetemperature with Thomson scattering. Wefind that collisional radiative (kinetics)modeling of the intensities of the He-b lineand its dielectronic capture satellites isgenerally in agreement with the measuredspectra. On the other hand, for the partic-ular case of satellites arising from inner-shell electron collisional excitation, wefind discrepancies of up to a factor of twobetween experiment and kinetics models.We have ruled out possible effects on theline emission due to plasma gradients,radiative transport, and suprathermal elec-tron excitation, leaving errors in the atom-ic physics modeling to be the most likelyexplanation.

The determination that there are prob-lems with the collisionally populatedstates is important for the interpretation of inertial confinement fusion capsuleimplosions where electron densities andtemperature have been measured using

Te (keV)

Rat

io: 1

/H

e-

0 1 2 30

0.02

0.04C5H12 dataC3H8 data

FIGURE 7. Comparison between the experimental lineratios from gasbags with steady-state kinetics (collisional-radiative) model calculations. The intensity ratio betweenthe He-b transition (resonance plus intercombinationline) to satellite feature 1, whose upper state is populatedby inner-shell collisional excitation, shows discrepanciesof up to a factor of two compared with the fully kineticsmodeling. (NIF-0401-02075pb01)

1263 (1993). B. A. Hammel et al., J. Quant.Spectrosc. Radiat. Transfer 51, 113 (1994).

6. N. C. Woolsey et al., Phys. Rev. E 56, 2314 (1997).Ibid., Phys. Rev. E 57, 4650 (1998). N. C. Woolseyet al., Phys. Rev. E 53, 3696 (1996). Ibid., J. Quant.Spectrosc. Radiat. Transfer 58, 975 (1997).

7. M. D. Cable et al., Phys. Rev. Lett. 73, 2316 (1994).8. A. H. Gabriel, Mon. Not. R. Astron. Soc. 160, 99

(1972).9. R. W. Lee, B. L. Whitten, and R. E. Strout, II,

J. Quant. Spectrosc. Radiat. Transfer 32, 91 (1984).10. C. F. Hooper, Jr., et al., Phys. Rev. Lett. 63, 1267

(1989). C. F. Hooper et al., Quant. Spectrosc.Radiat. Transfer 44, 79 (1990).

11. R. C. Mancini et al., Rev. Sci. Instrum. 63, 5119(1992). D. A. Haynes et al., Phys. Rev. E 53, 1042(1996). I. E. Golovkin and R. C. Mancini,J. Quant. Spectrosc. Radiat. Transfer 65, 273 (2000).

12. H.-J. Kunze, in Plasma Diagnostics, edited byW. Lochte-Holtgreven (North-Holland,Amsterdam, 1968), p. 550.

13. S. H. Glenzer et al., Phys. Plasmas 6, 2117 (1999).S. H. Glenzer et al., Rev. Sci. Intrum. 70 1089(1999). S. H. Glenzer et al., Phys. Rev. Lett. 82 97(1999).

14. G. Zimmerman and W. Kruer, Comments PlasmaPhys. Controlled Fusion 2, 85 (1975).

15. A. Bar-Shalom and M. Klapisch, Computer Phys.Comm. 50, 375 (1988). M. Klapisch, ComputerPhys. Comm. 2, 239 (1971). M. Klapisch et al.,J. Opt. Soc. Am. 67, 148 (1977). J. Oreg et al.,Phys. Rev. A 44, 1750 (1991). A. Bar-Shalom et al.,Phys. Rev. A 38, 1773 (1988).

16. E. M. Campbell et al., Rev. Sci. Intrum. 57, 2101(1986).

17. C. A. Back et al., Rev. Sci. Instrum. 66, 764 (1995).18. J. D. Kilkenny, Laser Part. Beams 9, 49 (1991). 19. J. A. Fejer, Can. J. Phys. 39, 716 (1961). D. E.

Evans, Plasma Phys. 12, 573 (1970). S. H. Glenzeret al., Phys. Rev. Lett. 77, 1496 (1996).

20. P. Beiersdorfer et al., Phys. Rev. E 52, 1980 (1995).21. F. B. Rosmej, J. Phys. B 28, L747 (1995). F. B.

Rosmej, J. Quant. Spectrosc. Radiat. Transfer 51,319 (1994).

42


UCRL-LR-105821-00-1

the spectral line shape of the He-btransition of Ar XVII. The analysis of theimplosion data has required Stark broad-ening calculations coupled to a kineticsmodel to calculate the detailed line inten-sities and widths. Despite remaining dis-crepancies, the good agreement betweenthe experimental dielectronic capturesatellites and the HULLAC calculationssuggests that HULLAC is a more appro-priate code for the construction of thekinetics models of the He-b complex fromhigh-density plasmas than previouslyused codes (e.g., MCDF). HULLACresults in somewhat higher temperaturesfor the implosion conditions of Refs. 5 and6 that are in closer agreement with the 2Dradiation hydrodynamic modeling andother spectroscopic techniques. Theseresults indicate that benchmarking kineticscodes with Thomson scattering is animportant area in present ICF research.

AcknowledgmentsWe would like to thank A. L. Osterheld,

C. Decker, L. Lours, and P. E. Young forhelpful discussions.

Notes and References1. B. J. MacGowan et al., Phys. Plasmas 3, 2029,

(1996). 2. S. H. Glenzer et al., Phys. Rev. E 55, 927 (1997).3. P. G. Burkhalter et al., J. Appl. Phys. 50, 4532

(1979).4. V. A. Boiko et al., Mont. Not. R. Astr. Soc. 185,

789 (1978).5. B. A. Hammel et al., Rev. Sci. Instrum. 61, 2774

(1990). B. A. Hammel et al., Phys. Rev. Lett. 70,

43

In indirect-drive inertial confinementfusion (ICF), x-rays are used to deliver

energy to the surface of a capsule whichcontains deuterium-tritium fuel.1 The cap-sule surface is ablated by the x-rays, andthe resulting pressure implodes theremaining capsule and fuel to the densitiesand temperatures required for efficientthermonuclear fusion.

The x-rays are produced by directingmultiple laser beams onto specific loca-tions on the interior wall of a high-Z cavity(hohlraum) surrounding the capsule,where they are efficiently absorbed, reradi-ating much of the energy as soft x-rays.1, 2

These x-rays, in turn, heat the remainderof the hohlraum wall, which then reradi-ates as well. The centrally located implo-sion capsule is thus heated by radiationfrom the laser absorption region (“hotspot”) and the less intense radiation fromthe heated hohlraum wall, while the laser-entrance holes (LEHs) in the hohlraumproduce no radiation. Different points onthe capsule’s surface view different solidangle-weighted proportions of hot spots,wall, and LEH. The objective is to haveany point on the capsule’s surface absorbthe same amount of drive energy, at anygiven time, as any other point, in order toproduce a uniform implosion. Analytic

calculations and simulations1-4 haveshown that high spatial frequency drivevariations are effectively smoothed by thehohlraum environment. What remains isto smooth the lowest spatial frequencyvariations, which, for the cylindricalhohlraum geometry considered here, areusually expressed in terms of a Legendreseries [ S AnPn(cosq), (n = 0, 2, 4, …),where q is the angle relative to the symme-try axis]. The odd terms vanish due to thebasic symmetry of the geometry. It hasbeen shown2 that for a given wall-to-hotspot temperature ratio, and hohlraumgeometry, the lowest (P2) mode coefficientcan be made equal to zero by an appropri-ate choice of hot spot location.

Unfortunately, these parameters changewith time. For example, the power fractionreradiated by the indirectly heated wall(“albedo”) rises with time. Also, thehohlraum wall expands inwardly, inter-cepting the laser beams at new locationsand thus causing the hot spots to movecloser to the hohlraum axis. It is this lattereffect that is of interest to us in this article.An example of this spot motion is shownin Figure 1. The concern is that the result-ing large P2 excursions are predicted tolead to intolerable higher spatial ordercapsule shell density and velocity pertur-bations which will impede full conver-gence and thwart fusion ignition. Theobvious solution—to change the pointing ofthe beams in a time-dependent fashion—can effectively be accomplished by pointing

DEMONSTRATION OF TIME-DEPENDENTSYMMETRY CONTROL IN HOHLRAUMS BY

DRIVE-BEAM STAGGERING

R. E. Turner P. Amendt O. L. Landen S. G. Glendinning P. Bell

C. Decker B. A. Hammel D. Kalantar D. Lee R. Wallace

D. Bradley* M. Cable R. S. Craxton* R. Kremens* W. Seka*

J. Schnittman* K. Thorp* T. J. Murphy† N. Delamater† C. W. Barnes†

A. Hauer† G. Magelssen† J. Wallace†

UCRL-LR-105821-00-1

*Laboratory for Laser Energetics, University of Rochester,Rochester, NY†Los Alamos National Laboratory, University of California,Los Alamos, NM

different beams to different locations,while tailoring the pulse shape differently on the different beams, so thatthe average laser pointing moves in time,as required, to counteract the wall motionand maintain drive symmetry. This tech-nique is referred to as beam phasing.1

Experiment

In the experiments reported here wehave used a simpler variation, referred toas beam staggering. Different pointingsare used for different sets of beams, andthere is a timing offset between the twogroups of beams. However, there is noindividual laser pulse shape control forthe different groups of beams. This tech-nique provides a single, midcourse correction for the time-dependent drivesymmetry.

To demonstrate the effect, we havemade time-resolved drive symmetry mea-surements for two different sets of laserpointings. Both are calculated to give time-integrated symmetry for implosion timesof order 2 ns. One set of pointings(“reduced swing”) is designed to givegood drive symmetry (low P2) at all times,while the second (“enhanced swing”) iscalculated to give significant P2 symmetryswings in time. The results are in goodagreement with calculations.

The experiments were conducted on theUniversity of Rochester’s OMEGA lasersystem,5,6 using 30 of the possible 60beams to drive a cylindrical goldhohlraum7 1.6 mm in diameter, 2.1 mm in length, with 1.2-mm-diameter laserentrance holes at either end. The geometry,

44

DEMONSTRATON OF TIME-DEPENDENT SYMMETRY CONTROL IN HOHLRAUMS BY DRIVE-BEAM STAGGERING

UCRL-LR-105821-00-1

shown in Figure 2, is such that five laserbeams at each end are incident at 42degrees to the hohlraum axis, and are des-ignated as “cone 2.” The remaining tenbeams at each end are incident at 58.8degrees and are designated as “cone 3.”The cone 3 beams are further subdividedinto two, interleaved in azimuth, referredto as cones 3a and 3b. All beams had simi-lar power profiles: 480 J per beam at351 nm, in a 1.1-ns-long, constant powerpulse. The cone 3a beams were on fromtime zero to t = 1.1 ns; the cone 3b andcone 2 beams were on from t = 1 to t = 2.1ns. The resulting total laser power is a 2.1-ns-long stepped pulse, with a 1:2 con-trast ratio, as shown by the dashed line in Figure 3.

One measure of symmetry is the shapeof the fuel region in imploded capsules8,9

obtained by direct pinhole imaging of thex-ray emission (3- to 6-keV photons) ontoa gated microchannel plate (MCP)camera.10 The emission is enhanced bydoping the 50 atmospheres of deuteriumfuel in the 440-µm-inner-diameter capsulewith 0.8 atmospheres of argon. (In thethinnest walled capsules, deuterium fillpressure was limited to 10 atmospheresdue to material strength concerns.) Theconvergence ratio of the targets is limitedby design to ≈8, leading to an ≈55-µm-diameter imploded core, easily resolvedby a 12-µm resolution pinhole camera. Theobserved asymmetry of the core is theresult of the drive asymmetry integratedover the duration of the implosion. Forthese experiments this integration timewas varied by changing the capsule wallthickness from 10 mm to 55 mm. The

t = 0.8 ns t = 1.2 ns

3a3b

2

3a 3b

2

Reduced Enhanced

FIGURE 1. Gated x-rayimages (hn ~ 5 keV) oflaser–plasma interactionregions, with original wallpositions superimposed,show movement of x-rayemission region due to wallmotion for early beams (left)and later beams (right). Notethe strong x-ray emissionfrom the laser entrance holeobscures some spots in thelate-time image.(NIF-0401-02055pb01)

FIGURE 2. Schematic of OMEGA hohlraum geometry,showing laser pointing for the three cones in the twoconfigurations. Cone 3a is the “early” cone. (Only right halfis shown.) (NIF-0401-02056pb01)

size (FWHM) of the implosion core’s vertical (a) and horizontal (b) axes wasrecorded, and the ellipticity ratio (a/b) wasused as a measure of the lowest order P2asymmetry averaged over the implosiontime. Knowledge of the time-dependentasymmetry can be inferred by examiningthe results of targets with varying implo-sion times, as shown in Figure 4.

The second technique uses an x-raybacklit surrogate foam (0.3 g/cm3 SiO2aerogel) ball, which yields a continuousrecord of hohlraum asymmetry.11,12 As thex-ray drive ablates the foam ball’s surface,the ablation pressure drives a shock front

45


UCRL-LR-105821-00-1

into the ball. Simulations show that theasymmetry of the ball, as measured by thex-ray transmission inflection points in abacklit image, is a good measure of thedrive asymmetry imposed up to that time.The asymmetry of the ball at differing timesis obtained from analysis of backlit imagesrecorded with the time-resolved pinholecamera described previously. Examples ofthese images are shown in Figure 5. The x-ray backlighting source is a titanium foilwhich, in a novel arrangement, is mounteddirectly over a hole in the side of thehohlraum wall. The foil is illuminated for2 ns with eight staggered laser beams on itsrear surface. The Ti is 5 mm thick, whichallows the 4.7-keV He-like line radiationgenerated on the outside to pass throughthe foil and backlight the foam ball. At thesame time, the inner side of the Ti absorbsand reemits, with reasonable efficiency, thesofter drive radiation, reducing the asym-metry an open hole would produce. Thediagnostic observation hole, opposite the Tifoil, is covered with a very thin (0.2-mm)layer of Ta, to help reduce the drive pertur-bation due to that hole.

The two diagnostic techniques are com-plementary in time. The foam ball workswell for the first 2 ns, but after that theshock has reached the center. The capsulesof varying wall thickness (“symmetry cap-sules”) work well for the time-integratedmeasurements ending between 1.4 to2.7 ns; it is not possible to make capsuleshells thin enough to integrate over an earlier time frame.

Experiment

Simulation

0

50

100

150

200

250

300

0

2

4

6

8

10

12

–0.5 0 0.5 1 1.5 2 2.5

a 0 sh

ock

traj

ecto

ry (µ

m)

Las

er p

ower

(TW

)

Time (ns)

Power

a

b

Ablator thickness ≈20 µm ≈35 µm ≈50 µm

Enhanced swing

Reduced swing

100

µm

Foam ball t (ns)1 2

Reduced symmetry swing

Enhanced symmetry swing

FIGURE 5. Examples of time-resolved x-ray backlitimages of foam ball targets. Enhanced swing case showsobservable P2 (note horizontal size > vertical) at earlytimes, and observable P4 asymmetry at 2 ns (note dia-mond shape). (NIF-0401-02059pb01)

FIGURE 4. Schematic of symmetry capsule principle.Thicker capsules integrate over longer times; ratio of vertical to horizontal size of imploded image (a/b) is used as a measure of symmetry. (NIF-0401-02058pb01)

FIGURE 3. Total laser power (dashed), and measured andsimulated average ablation front trajectory, versus time.Data is from enhanced swing configuration; reducedswing configuration gives identical results.(NIF-0401-02057pb01)

In all shots, the beams were pointed topositions which produce a nearly roundimplosion for capsules designed toimplode in approximately 2 ns. For theexperiment attempting to minimize P2symmetry swings, the cone 3a beams areturned on first, and are aimed at the loca-tion which minimizes P2 during the firstnanosecond. During that time, the goldwall expands inward, and the hot spot, asseen from the capsule, moves back towardthe laser-entrance holes. At the end of thefirst nanosecond, the cone 3a beams areturned off, and the remainder of thebeams are turned on. These are aimed at anew location—more inward, or toward thecapsule—to account for the fact that thegold wall has moved, and will continue tomove, inward some 150 mm. As seen fromthe capsule, the hot spot from these laterbeams begins in approximately the sameangular position as the initial cone 3a hotspot location. This is shown schematicallyin Figure 2. This midcourse repointing actsto restore the drive symmetry whichwould have otherwise been lost due towall motion, had all the beams been point-ed similarly. The actual pointings, definedas the point of intersection of the laserbeam with the hohlraum symmetry axis,measured from the hohlraum center, areshown in Table 1.

For the experiment designed toenhance the time-dependent symmetryswing, the beams were repointed to posi-tions which would give poor symmetryover any given half of the pulse whilestill maintaining time-integrated symme-try over the whole pulse. This wasaccomplished by pointing the early cone3a beams further inward. The later cones

46


UCRL-LR-105821-00-1

2 and 3b beams were then pointed moreoutward, to compensate in a time-averaged sense (see Figure 2). Beam timing and pulse shape were not changedbetween experiments.

Simulations and Analysis

The above-described experimental con-ditions are simulated with a two-dimen-sional radiation-hydrodynamics code.13

Integrated modeling techniques, whichtreat the hohlraum, capsule or surrogatetarget, laser deposition, and x-ray conver-sion as a coupled physical system, areused.14 Following completion of the simu-lations, postprocessing is used to generatesynthetic images of the capsule or surro-gate target for direct comparison withexperiment.

For the low-convergence implosions,the ellipticity ratio (a/b) of the syntheticimage’s 50%-of-peak-emission contour isextracted, in the same manner as is donefor the data, as shown in Figure 4.

For the foam ball simulations, theinflection point contour for transmissivitythrough the target is extracted and writtenas a partial sum of Legendre polynomialswith coefficients an (n = 0, 2, 4).12,15 Foreach Legendre coefficient, a fit through thesimulated data is performed and then dif-ferentiated in order to extract informationabout the ablation pressure history. For aconstant or increasing pressure, the shockspeed in a material is proportional to thesquare root of the pressure. Expandingthis relationship in a Legendre series andkeeping only the lowest order terms, thevarious Legendre coefficients of ablationpressure PAn are related to the shock fronttrajectory as follows15:

(1a)

(1b)

(1c)

where r is the foam ball density, g is theratio of specific heats, and overdots denote

TABLE 1. Laser beam pointing configurations forthe two cases studied. Numbers shown are the distances from the center of the hohlraum to thepoints where the beams cross the axis of symmetry.

Cone 2 Cone 3a Cone 3bExperiment (mm) (mm) (mm)

Reduced swing 1175 1100 900

Enhanced 1450 950 1150

P a

P P a a

P P a a

A

A A

A A

0

2 0

4 0

= ( )[ ]=

=

2 / + 1

2

2

02

2 0

4 0

r g ˙

/ ˙ / ˙

/ ˙ / ˙

differentiation with respect to time.However, we do not measure the shockfront trajectory but rather the x-ray transmissivity inflection point trajectory.Simulation studies indicate that this latterquantity provides a representative measureof the location of the shock.15 Although notstrictly correct, the association of shockfront and inflection point provides a sim-ple relation for estimating ablation pres-sure asymmetry without invoking detailedradiation-hydrodynamic simulations. Infact, comparison of this estimate of instan-taneous ablation pressure asymmetry withsuch simulations shows fairly good agree-ment for the second order coefficient, asshown in Figure 6. It is in this spirit that

47


UCRL-LR-105821-00-1

shock front and inflection point are usedinterchangeably.

The measured average ablation fronttrajectory a0(t) provides a direct means ofdiagnosing the x-ray drive.16 Figure 3shows the measured and simulated trajec-tories, and the laser power history, for theenhanced swing case. We note an increasein velocity after 1 ns, indicating the nearlyinstantaneous onset of increased x-raydrive. A direct measurement of the emit-ted x-rays17 is shown in Figure 7. It showsthe drive rising from an effective black-body temperature of 130 eV during thefoot to 190 eV by the end of the pulse, ingood agreement with the a0(t) data andsimulation shown in Figure 3. The error inmeasuring a0 is small, and does not signifi-cantly contribute to the error in deducingPA2 from equation (1b).

Results

Figure 4 shows examples, and Figure 8shows the quantitative results, of the sym-metry capsule experiments and simula-tions, plotting the (a/b) eccentricity of theimploded cores as defined earlier versusthe observed x-ray emission time. Thesimulations are overplotted on Figure 8.Each data point is the average of twoshots. Note that the (a/b) distortions forthe two pointing schemes cross each

(a)

Simulations

0 0.5 1 1.5 2

(b)

P2 p

ress

ure

(%

) P

2 pre

ssu

re (

%)

Time (ns)

0 0.5 1 1.5 2

Semianalytic

Simulations

–20

–15

–10

– 5

0

5

10

– 4

– 2

0

2

4

6

8

10

12

Semianalytic

0 10.5 1.5 2.52 3

T (

eV)

Time (ns)

100

120

140

160

180

200

FIGURE 6. Comparison between hydrodynamic code sim-ulations and simple analytic expression for 2nd ordercoefficient; (a) reduced swing case, (b) enhanced swingcase (note expanded vertical scale). (NIF-0401-02060pb01)

FIGURE 7. Measured x-raydrive flux as a function oftime, expressed as aneffective Planckian tem-perature.(NIF-0401-02061pb01)

other at ≈2 ns, as designed. However, thecapsules driven with reduced-swing beampointing show good implosion symmetryfor shorter implosion times, while theenhanced P2 swing pointing case does not.The experiment attempting to reduce thesymmetry swing shows (a/b) decreasingbetween 1.5 and 2 ns, a clear qualitativeindication that the normal symmetryswing due to spot motion, which wouldincrease (a/b), has been reversed. It shouldbe noted that the thickest capsules shownimploded long (>0.8 ns) after all laserbeams were off. For these capsules, sym-metry control is not maintained after 2 nsfor either pointing.

48


UCRL-LR-105821-00-1

Figures 3, 9, and 10 show the reduceddata from the foam balls; a0 (Figure 3), a2(Figure 9), and a4 (Figure 10) are thezeroth, second, and fourth order Legendrepolynomial coefficients, respectively, ofthe fit to the inflection point contours ofthe backlit images. The simulation resultsare overplotted on these figures. The time-dependence of the zeroth order coefficient(corresponding to an average radius)yields information on the average x-raypower, as previously discussed. The sec-ond order coefficient a2 quantifying ellip-ticity, yields continuous information onthe time-integral of the P2 flux asymmetryexperienced near the center of thehohlraum.15 For the data presented here,the values of a2(t) are small enough thatany initial a2(0) distortion present in thefoam ball can cause a substantial offset inthe results. We have removed this offsetfrom the data, to clarify the importantresult, the demonstrated control of time-dependent variations in a2. The offsets aretoo small (0, 0.5, 0.5, and 2.5 mm) to havebeen noticed during initial target charac-terization; we have inferred them from thevalues required to make the changes in a2extrapolate to zero, at time zero, for eachshot. In any case, the instantaneous fluxasymmetry is derived from the slope ofthe a2(t) history and not its absolute value.The error bars shown are statistical only,from the curve fitting process for eachimage.11,12

The results show a large excursion in a2for the case where the symmetry swingwas intentionally enhanced, reaching apeak of ≈5 µm, or 3% of the average radiusat that time. For the case attempting toreduce the symmetry swing, the a2 varia-tion is significantly reduced in magnitude,and shows the expected shift following thechange in beam pointing at t = 1 ns. Thefollowing simple argument18 shows thatapplying a single midterm pointing cor-rection should significantly reduce (by≈4¥) the maximum a2. Consider the P2swing approximated as linear in time.2 Then a2 is a ∫P2dt, hence at2.Therefore, halving the time over which theP2 swing is left uncorrected reduces the a2 by 4¥. Generalizing, applying n correc-tions by staggering beams n times wouldreduce a2 by n2.

FIGURE 8. Measured andsimulated a/b elliptical dis-tortion of imploded cap-sule core versus peakx-ray emission time, forthe different pointings.(NIF-0401-02062pb01)

FIGURE 9. Time variationof second Legendre coef-ficient of ablation fronttrajectory, with inferred t = 0 offsets subtracted(see text). Solid (short-dashed line) and open(long-dashed line) symbolsshow data (simulations)from the reduced swingand enhanced swingpointings, respectively.(NIF-0401-02063pb01)

1 1.5 2 2.5 3

Imag

e d

isto

rtio

n (

a/b)

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Enhanced (sims)

Reduced (data)

Reduced (sims)Enhanced (data)

X-ray bang time (ns)

–4

–2

0

2

4

6

0 0.5 1 1.5 2Time (ns)

∆a 2 (

µm

)

The fourth order coefficients shown inFigure 10 have been adjusted for an initialoffset (up to 1.5 mm) in the same manneras described above for the second orderdata. The simulations are overplotted. Asthe results indicate, this experiment didnot attempt to control the fourth ordercoefficients; that will be the subject offuture work.

Conclusions

The simulations of a2(t) for the two dif-ferent pointings are, as shown in Figure 9,in good agreement with the measurements.The inferred ablation pressure asymmetriesPA2(t), obtained by differentiating the simu-lations as described above, are shown inFigure 6. The ratio of the P2/P0 pressurecoefficients vary from –0.13 to +0.12 for theenhanced swing case, while the maximum

49


UCRL-LR-105821-00-1

extremes for the reduced swing case are–.025 and +.08, a factor of two and one-halfreduction in total symmetry swing. Themagnitude of the PA2 symmetry swing forthe reduced swing case is less than 10%over a 2-ns duration, which is the requiredlevel of control calculated for ignition tar-gets on the National Ignition Facility.1,2

In summary, we have shown how low-est order hohlraum drive asymmetries dueto plasma wall motion and changing wall-to-hot spot temperature ratios can be con-trolled in a time-dependent fashion, usinga multicone beam geometry.

AcknowledgmentsWe wish to thank the OMEGA opera-

tions staff, led by S. Loucks, S. Morse, andG. Pien, for their work in support of thisexperiment.

Notes and References1. J. Lindl, Phys. Plasmas 29, 3933 (1995).2. L. J. Suter et al., Phys. Rev. Lett. 73, 2328 (1994).3. S. Haan, Radiation Transport between Concentric

Spheres, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-ID-118152(1994); reprints available to the public from theNational Technical Information Service, U.S.Department of Commerce, 5285 Port Royal Rd.,Springfield, VA 22161.

4. A. Caruso and C. Strangio, Jpn. J. Appl. Phys. 30,1095 (1991); J. A. Fleck, Jr., and J. D. Cummings,J. Comput. Phys. 8, 313 (1971).

5. T. R. Boehly et al., Opt. Commun. 133, 495 (1997).6. J. M. Soures et al., Phys. Plasmas 3, 2108 (1996).7. T. J. Murphy et al., Phys. Rev. Lett. 81, 108 (1998).8. A. Hauer et al., Rev. Sci. Instrum. 66, 672 (1995).9. A. Hauer et al., Phys. Plasmas 2, 2488 (1995).

10. J. D. Kilkenny et al., Rev. Sci. Instrum. 59, 1793(1988).

11. P. Amendt et al., Rev. Sci. Instrum. 66, 785(1995).

12. S. G. Glendinning et al., Rev. Sci. Instrum. 70, 536(1999).

13. G. B. Zimmerman and W. L. Kruer, CommentsPlasma Phys. Control. Fusion 2, 51 (1975).

14. J. D. Kilkenny, Laser Part. Beams 9, 49 (1991).15. P. Amendt et al., Phys. Plasmas 4, 1862 (1997).16. P. Amendt et al., Phys. Rev. Lett. 77, 3815 (1996).17. C. Decker et al., Phys. Rev. Lett 79, 1491 (1997).18. O. L. Landen et al., Phys. Plasmas 6, 2137(1999).

FIGURE 10. Time variation of fourth Legendre coefficientof ablation front trajectory. Each data point (symbols) hasbeen averaged over several shots and corrected for initialoffset. Solid and open symbols show data from thereduced swing and enhanced swing pointings, respec-tively. Solid lines show simulations. (NIF-0401-02064pb01)

0 0.5 1 1.5 2

∆a 4 d

isto

rtio

n (

µm

)

Time (ns)

0

–1

1

2

3

4

5

Reduced swing

Enhanced swing

51

We report an experiment whichdemonstrated for the first time

that exceptionally intense and well-colli-mated proton beams are produced whenthin-foil targets are irradiated at ultrahighintensity with ultrashort laser pulses.1

The generation of fast protons fromlaser-irradiated solid surfaces is wellunderstood2,3 and attributable to electro-static fields produced by hot electrons acting on protons from adsorbed hydrocarbons.3 An empirical power lawrelationship between the mean protonenergy and intensity ¥ (wavelength)2 (Il2)was identified, and proton energies up to afew MeV were observed for Il2 up to1018 W cm–2 mm2 in nanosecond pulses.2

Chirped pulse amplification (CPA) lasertechnology4 enabled widespread genera-tion of terawatt (TW) power and the firstpetawatt (PW) laser.5 CPA lasers generatepulses in the range 20 fs to 1 ps. Protonswith 10-MeV energy were observed with a1-ps CPA laser at Il2 = 1019 W cm2 mm2,consistent with the previous scaling.6

New mechanisms of ion accelerationhave been studied with CPA lasers.Ponderomotive pressure of the laser radia-tion causes radial acceleration when laserbeams are focused in gas jets and in sub-critical density plasmas7 and also causesaxial acceleration into solid targets.8

Coulomb explosion of molecules9 andclusters10 has produced energetic ions. Theion energies from these newly studied pro-cesses have been <1 MeV/nucleon.

We report a laser-induced proton beamwith much higher particle energy and bet-ter collimation than previously observedwith the distinctive feature that it is emit-ted perpendicular to the rear unirradiatedsurface(s) of the target. The high protonenergy, up to 58 MeV, opens up access tonuclear processes.

The experiments used a CPA laser sys-tem generating 1-PW pulses of 500-fsduration.5 With f/3 parabolic mirror focusing, the peak intensity was3 ¥ 1020 W cm–2 in a focal spot of 9-mm fullwidth at half maximum (FWHM), with 30% of the energy inside the firstminimum. Amplified spontaneous emis-sion in a 4-ns period before the main pulse had 10–4 of the main pulse energy,and there was a 3 ¥ 10–4 prepulse 2 nsbefore the main pulse. This precursor radiation generated a plasma that wasmeasured by subpicosecond optical inter-ferometry. The on-axis electron densitywas 3 ¥ 1019 cm–3 in a plane 70 mm from a

INTENSE HIGH-ENERGY PROTON BEAMSFROM PETAWATT LASER IRRADIATION

OF SOLIDS

R. A. Snavelya,b M. H. Key a S. P. Hatchetta T. E. Cowana

M. Rothc T. W. Phillipsa M. A. Stoyera E. A. Henrya

T. C. Sangstera M. S. Singha S. C. Wilksa A. MacKinnona

A. Offenbergerd D. M. Penningtona K. Yasuikee A. B. Langdona

B. F. Lasinskia J. Johnson f M. D. Perrya E. M. Campbella

UCRL-LR-105821-00-1

aUniversity of California, Lawrence Livermore NationalLaboratory, PO Box 808, Livermore, CA 94550bUniversity of California, Davis, Department of Physics,Davis, CA 94616 cVisiting from GSI Laboratory, Darmstadt, GermanydVisiting from University of Alberta, Edmonton, Alberta, T6G2G7, CanadaeVisiting from ILE, Osaka University, Suita, Osaka 565, JapanfUniversity of Texas, Huntsville, Texas

flat CH target with an approximatelyexponential fall to lower densities havinga scale length of 40 µm.11

The proton beam was recorded withradiochromic (RC) film, which changesthrough polymerization of a diacetyleneactive layer from transparent to dark blue(dark to white in Figures 1 and 4) in pro-portion to the dose (rads) of ionizing radi-ation (1 rad = 100 ergs/g). A 90° conicalassembly of alternating Ta foils and sheetsof RC film was used. The cone is 4 cmdeep at its apex, which was placed 4.2 cmbehind the target on the laser axis so thedetector covered the forward hemisphere.The RC film response was calibrated abso-lutely, and the image data were analyzedby digital densitometry and transformedgeometrically to produce contour plots ofdose as a function of angle illustrated inFigure 1.

The data in Figure 1 show a collimatedintense proton beam emitted perpendicu-lar to the rear target surface of a target at45° to the laser axis. Its angular width nar-rows to 10° in the image through 600 µmof Ta. The beam is rather uniform in inten-sity with near-circular, sharp boundaries.There is a low-intensity wide-angle back-ground, discussed elsewhere, that is dueto escaping relativistic electrons.12 Similarresults are seen for normal incidence,S polarization, and target thickness downto 20 µm. The beam profiles from CH tar-gets have nonuniform edges and exhibitinternal fine structure as illustrated in

52

INTENSE HIGH-ENERGY PROTON BEAMS FROM PETAWATT LASER IRRADIATION OF SOLIDS

UCRL-LR-105821-00-1

Figure 2 for a 100-µm-thick CH target atnormal incidence. There was typically a5 times greater dose recorded from CH relative to Au targets. The proton identityof the beam was first suggested by analy-sis of etched tracks in CR39 plastic behind7 mm of Al, which gave evidence of >30-MeV protons.

The response of each RC film layer as afunction of proton energy was calculatedfrom stopping powers obtained with theSRIM code.13 (An example for a similardetector package is shown in Figure 2.)The integrated rad cm2 in each image ofthe proton beam was determined from theRC film data. A deconvolution procedurewas then used to relate these data to thefilm response (in rad cm2 per proton) togive the absolute proton energy spectrum.Figure 3a shows an example in which the energy spectrum has a cutoff at about58 MeV, with a near-exponential slopetemperature of 4 MeV. The conversionfraction of laser energy to protonsE > 10 MeV is 12% at 48 J. The extrapola-tion of the energy spectrum below 10 MeVis uncertain because the detector did notrecord protons of lower energy.

The sharp cutoff of the energy spectrumwas also measured at 45° to the laser axisvia a hole in the RC film detector using amagnetic spectrometer. These energy spec-tra were obtained from densitometry ofphotographic film as illustrated inFigure 3b. For targets irradiated at 45°

incidence, the recorded spectrum was on

(a) (b)180°

a E >17 MeV b E >24 MeV

c E >30 MeV d E >35 MeV

650

100

10

1

0.06

0.1

0Angle (degrees)

krad

s

–10 10 20–20

500

100

10

50

5

1

a

b

c

d

FIGURE 1. (a) Contourplots (a to d) of dose inkilorads (color bar units) asa function of angle afterpenetration throughrespectively 0.2-, 0.4-, 0.6-,and 0.8-mm Ta in thedetector.The target was a1-mm-square, 125-µm-thick Au foil irradiated with465 J at 45o P polarizedincidence. (b) Plot of beamprofile lineouts showingkilorads as a function ofangle in the vertical direc-tion through the center ofthe proton beam alongpath as indicated in (a).(NIF-0401-02065pb01)

the axis of the proton beam, and in the example shown, there is a cutoff at55 MeV. For normal incidence, the record-ed spectrum was at 45° off axis, and theexample shown has a cutoff at 15 MeV,consistent with the reduced cone angle forhigher proton energies seen in Figure 1.The photographic film is saturated so onlythe cutoffs in energy are significant in theplots. An estimate of the apparent sourcesize of the proton emission (400 µm) wasobtained from penumbral shadowing at

53


UCRL-LR-105821-00-1

the edge of the high-energy end of thespectrum when a rectangular slit aperturewas used, and a 4-mm-square, 125-µm-thick Au foil was irradiated.14

Direct evidence that the beam is madeup of protons rather than other ionspecies was obtained from observation ofnuclear reactions induced by protons. Amultilayer detector was used consisting of 3-cm-diameter flat discs of 50-µm Ti, followed by three repeats of 1.2-mm Be, 250-µm Ti, and 250-µm RC film, then

FIGURE 2. Data for a nor-mal incidence, 445-J shoton 100-µm CH from the Tinuclear activation and RCfilm detector describedlater in the text: Ti foilautoradiographs (top row) and RC film images(middle row). The plotsshow Monte Carlo model-ing (bottom left) of the RCfilm detector response inkilorad cm2 per proton,normally incident in thefilm layers, and the nuclearactivation response (bottom right) of the Tilayers to protons throughthe successive filter layersof the detector.(NIF-0401-02066pb01)

FIGURE 3. (a) Proton ener-gy spectrum deduced fromradiochromic film imagesfor a 423-J shot at normalincidence on 100-µm CH.(b) Spectrum of protonenergy recorded on filmwith a magnetic deflectionspectrometer. Plots showthe spectrum on axis andfrom another shot at 45°.The detector is saturatedabove the cutoff region.(NIF-0401-02067pb01)

B C D E

Deposited krad per proton

3

2

1

00 10 20 30 40 50

Proton energy (MeV)

* 10

–9 k

rad

s cm

2

B C DA

(A) (B) (C) (D) (E)

48V activation per proton

0.5

0.3

0.4

0.1

0.2

00 10 20 30 40 50

Proton energy (MeV)

* 10

–4 a

tom

s 48

V p

er p

roto

n

10,000

0.1 0.1

1

10

100

1

10

100

1,000

N*1

09 p

roto

ns p

er M

eV

Inte

gral

joul

es a

bove

E

45° 0°

0.1

1

1 10Proton energy (MeV)

Inte

nsit

y (a

.u.)

100

10

100

(a) (b)

100 20 30 40 50 60Proton energy (MeV)

Proton spectra

1.5-mm Be and 250-µm RC film, placed4.5 cm behind the target. The yield of the nuclear process, 48Ti(p,n)48V wasmeasured absolutely from the characteris-tic gamma emission of the activated48V nuclei. The cross section has a thresh-old at 5 MeV and peaks at 13 MeV,500 mbarn.15 The number of activatednuclei in each Ti layer was determinedfrom the gamma emission. The activationwas modeled using the stopping pow-ers13 and cross sections15 to give theresponse of the detector in activations perproton in each Ti layer, as in Figure 2. Adeconvolution procedure similar to thatused for the RC film gave the absoluteenergy spectrum of the protons, and closeagreement was obtained comparing bothmethods.

In the example shown in Figure 2 (445 Jat normal incidence on 100-µm CH), therewas an integrated energy of 30 J (3.5 ×1013 protons or 7% of the laser energy),and the Boltzmann temperature was 6MeV. Autoradiographic images of the 48Vactivation in the Ti foils shown in Figure 2show a one-to-one correspondence to theRC film images recorded on the same shotfrom adjacent layers in the detector, givingfurther evidence that the RC film shows aproton beam. Another nuclear processobserved was the production of 3 × 1010

neutrons on this shot (data from an Agactivation detector). This efficient yield(7 × 107 neutrons per joule) was from theseveral neutron-producing channels ofproton interaction with Be nuclei16 and

54


UCRL-LR-105821-00-1

was an order of magnitude greater thanneutron yields observed on shots withoutthe Be discs.

Whether the beam was normal to thefront or the rear surface of the target wasassessed using a 2-mm-wide, 30° wedgetarget of CH, as illustrated in Figure 4.That the emission was normal to the rearsurface is seen in the two separate protonbeams in directions corresponding to thenormals to major and minor “rear” sur-faces of the wedge.

RC images from 1-mm-square thin foiltargets through 25-µm Al (recording pro-tons with energy >4 MeV) showed in addi-tion to the intense beam, a weaker sheet ofproton emission in the horizontal plane.We attribute this emission to the verticaledges of the target. This suggests that thereis proton emission from an extended areaof the rear surface of the target with lower-energy protons emitted further from thecenter of the emitting surface.

Cones of RC film placed both behindand (with a central hole for the laserbeam) in front of a CH target for a targetat 45° established that protons above the12-MeV threshold energy for detectionintegrated over the forward hemispherehad less than 5% of the energy recorded inthe proton beam from the rear surface.

We interpret the process generating theproton beam as electrostatic accelerationfollowing hot electron generation. Thefocused main pulse generates an intenserelativistic electron source. Relativisticself-focusing in the preformed plasma17

650

100

10

1

0.1

0.06

Laser

CH2 target

FIGURE 4. Contours ofdose in kilorads as afunction of angle record-ed on an RC film through300-µm Ta (proton E > 18 MeV). The imageclearly shows two protonbeams, the larger fromthe major face and thesmaller from the minorface of the wedge.(NIF-0401-02068pb01)

enhances the intensity. This is evidenced inour work by an invariant x-ray emissionspot of about 20-µm diameter, as the focalplane was displaced as much as 300 µm infront of the target.18 We have previouslyreported on measurements of the energyspectrum of electrons emitted from therear surface of Au targets.18 Data showelectron energies up to 100 MeV with anexponential slope temperature of 5 to10 MeV. The RC film data shown inFigure 1 revealed the angular pattern ofrelativistic electron emission as a diffusebackground. The approximate source tem-perature and energy content of this elec-tron emission were determined bycomparison of quantitative analysis of theRC film and Monte Carlo modeling.Typical results were 1 to 2 J of electronsand a Boltzmann temperature of 3 to4 MeV. The total emitted energy corre-sponds to the maximum charge that canleave the target before the Coulomb potential traps the major fraction of the electrons. The angular pattern is broad. A similar pattern of >100° coneangle was observed in bremsstrahlung x-rays emitted from thick Au targets.Analysis of the measured total yield ofbremsstrahlung at photon energies>0.5 MeV suggests that more than 40% of the laser energy is converted to rela-tivistic electrons.12,19

We have adapted the standard model of fast ion generation by hot electrons3

for very short pulse duration and for theexistence at the time of creation of the hot electrons of a preformed long-scale-length plasma on the front of the targetand a short-scale-length at the unirradiat-ed back surface.

A full discussion of the accelerationmodel has been presented elsewhere.19,20

Briefly described, electrons penetratingthrough the target ionize H and otheratoms at the rear surface. Although the hot electron temperature Th, the ion scalelength Li, and the Debye scale length Ldrapidly change with time, one can estimatethe accelerating field by considering theirinitial values. By applying Poisson’s equation and assuming a Boltzmann distri-bution for the hot electrons, one obtainsthe result that the electric field acting on

55


UCRL-LR-105821-00-1

the ions21 is given by E = Th/e max (Li, Ld).This shows there will be much strongeracceleration at the sharp density interfaceon the back of the target than on the front,where the preformed plasma scale lengthis very long as shown by our optical probedata discussed previously. The rate of ener-gy transfer to the ions is therefore initiallymuch greater on the back of the target.Since the initial scale length on the back ofthe target is roughly a micron, we see thatelectric fields of MeV/micron are generat-ed. This model, modified by the fact thatthere are two electron temperatures pre-sent,3,22 is qualitatively consistent with ourdata. Two-dimensional particle-in-cell sim-ulations have further confirmed these find-ings and begin to address the relationbetween cutoff energy and angle in ourdata (e.g., Figure 1).

We have concluded that processes atthe front surface focal spot on the targetcould not generate the observed ionsbecause of the clear evidence that the pro-tons are emitted perpendicular to the rearsurface of the target. The observation ofproton emission from the edges of the tar-get supports a model of emission over anextended area much larger than the focalspot. The protons detected from Au targetscould not come from the front surfacefocal region of our targets because of theprepulse-induced blowoff-adsorbedmonolayers of hydrocarbon. Moreover, anarea that is much larger than the 10–6 cm2

focal spot area is needed to supply theobserved number of protons from anadsorbed layer.

Proton beams of the high energy,power, and collimation observed herecould be of interest for numerous applica-tions. They may be applicable to medicalproton beam cancer therapy or to the pro-duction of short-lived radionuclides. Morework is needed to characterize the emit-tance, which will determine the focusabili-ty of the beam and its usefulness, forexample, in replacing the front end oflarge accelerators or as an ignitor in fastignition. The ion acceleration process isnot restricted to protons, and with suitablepreparation of the target surface, moremassive ions could be accelerated to simi-lar energy per nucleon.

AcknowledgmentWe are grateful to C. Brown for his

skilled operation of the Petawatt LaserSystem.

Notes and References1. R. Snavely et al., Phys. Rev. Lett. 85, 2945 (2000).2. S. J. Gitomer et al., Phys. Fluids 29, 2679 (1986).3. Y. Kishimoto et al., Phys. Fluids 26, 2308 (1983),

and references therein.4. M. D. Perry and G. Morou, Science 264, 917

(1994). 5. M. Perry et al., Opt. Lett. 24, 160 (1999).6. A. P. Fews et al., Phys. Rev. Lett. 73, 1801 (1994),

and F. N. Beg et al., Phys. Plasmas 4, 447 (1997).7. G. Pretzler et al., Phys. Rev. E 58, 1165 (1998).8. M. Zepf et al., Phys. Plasmas 3, 3242, (1996). 9. K. Codling and L. J. Frazinski, Contemp. Phys.

35, 243 (1994). 10. T. Ditmire et al., Nature 398, 489 (1999).

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11. A. J. MacKinnon et al., UP2.65, Bull. Am. Phys.Soc. 44, 7 (1999).

12. M. H. Key et al., Inertial Fusion Sciences andApplications ‘99, C. Labaune, W. Hogan, andK. Tanaka, Eds., Publ. Elsevier, p. 392 (1999).

13. J. F. Ziegler et al., The Stopping and Range of Ionsin Solids (Pergamon Press, New York, 1996).

14. T. E. Cowan et al., Nucl. Instr. and Methods inPhys. Res. A 455, 130 (2000).

15. H. I. West, Jr., et al., Lawrence LivermoreNational Laboratory, Livermore CA, UCRL-ID-115738 (1993).

16. J. K. Blair et al., Nuc. Phys. 53, 209 (1964). 17. A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev.

Lett. 76, 3975 (1996).18. M. H. Key et al., Proc. of 17th IAEA Fusion Energy

Conference, Publ. IAEA Vienna, Vol. 3. p. 1093(1999).

19. S. Hatchett et al., Phys. Plasmas 7, 2076 (2000).20. S. Wilks et al., Phys. Plasmas 8, 542 (2001).21. J. Denavit, Phys. Fluids 22, 1384 (1979).22. L. M. Wickens et al., Phys. Rev. Lett. 41, 243

(1978).

A-1

AAdams, J. J., Bibeau, C., Page, R. H., Krol,D. M., Furu, L. H., and Payne, S. A.,4.0–4.5 mm Lasing of Fe:ZnSe below 180 K, aNew Mid-Infrared Laser Material, LawrenceLivermore National Laboratory, CA,UCRL-JC-135419; also in Opt. Lett. 24(23),1720–1722 (1999).

Amendt, P., Landen, O., Pollaine, S., Suter,L. J., and Hammel, B., Implosion TargetSurrogacy Studies on OMEGA for theNational Ignition Facility: Backlit Foamballsand Thinshells, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138241-ABS. Prepared for 30thAnnual Anomalous Absorption Conf, OceanCity, MD, May 21–26, 2000.

Amendt, P., Turner, R. E., Bradley, D.,Landen, O., Haan, S., Suter, L. J., Wallace,R., Morse, S., Pien, G., Seka, W., andSoures, J. M., High-Convergence Indirect-Drive Implosions on OMEGA in the Absenceof Argon Fuel-Dopant, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138240-ABS. Prepared for 30thAnnual Anomalous Absorption Conf, OceanCity, MD, May 21–26, 2000.

BBack, C. A., Bauer, J. D., Landen, O. L.,Turner, R. E., Lasinski, B. F., Hammer, J. H.,Rosen, M. D., Suter, L. J., and Hsing, W.H., Detailed Measurements of a DiffusiveSupersonic Wave in a Radiatively HeatedFoam, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-135062; also in Phys. Rev. Lett. 84(2),274–277 (2000).

Back, C. A., Grun, J., Decker, C. D., Davis,J., Laming, M., Feldman, U., Landen, O. L.,Suter, L. J., Miller, M., Serduke, F., andWuest, C., X-Ray Sources Generated fromGas-Filled Laser-Heated Targets, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138111-ABS.Prepared for 12th American Physical SocietyTopical Conf on Atomic Processes in Plasma,Reno, NV, Mar 19–24, 2000.

Baker, K. L., Drake, R. ., Estabrook, K. G.,Sleaford, B., Prasad, M. K., La Fontaine, B.,and Villeneuve, D. M., “Measurement ofthe Frequency and Spectral Width of theLangmuir Wave Spectrum Driven byStimulated Raman Scattering,” Phys.Plasmas 6(11), 4284–4292 (1999).

Banks, P. S., Dinh, L., Stuart, B. C., Feit, M.D., Komashko, A. M., Rubenchik, A. M.,Perry, M. D., and McLean, W., Short-PulseLaser Deposition of Diamond-Like CarbonThin Films, Lawrence Livermore NationalLaboratory, CA, UCRL-JC-134974; also inAppl. Phys. A 69(SUPPS), S347–S353.

PUBLICATIONS AND PRESENTATIONSOCTOBER 1999–MARCH 2000

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Banks, P. S., Feit, M. D., Rubenchik, A. M.,Stuart, B. C., and Perry, M. D., MaterialEffects in Ultra-Short Pulse Laser Drilling ofMetals, Lawrence Livermore NationalLaboratory, CA, UCRL-JC-133743; also inAppl. Phys. A 69 (SUPPS), S377–S380(1999).

Bayramian, A. J., Bibeau, C., Schaffers, K.I., Marshall, C. D., and Payne, S. A., GainSaturation Measurements of Ytterbium-DopedSr5(PO4)3F, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-133980; also in Appl. Optics 39(6), 982–985(2000).

Berger, R. L., Divol, L., Hinkel, D. E.,Kirkwood, R. K., Glenzer, S., Langdon, A.B., Moody, J. D., Still, C. H., Suter, L.,Williams, E. A., and Young, P E., Modelingthe Backscatter and Transmitted Light Spectraof High Power Smoothed Beams with pF3D, aMassively Parallel Laser Plasma InteractionCode, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137900-ABS. Prepared for 26th EuropeanConf on Laser Interaction with Matter,Prague, Czech Republic, Jun 12–16, 2000.

Berger, R. L., Langdon, A. B., Hinkel, D. E.,Still, C. H., and Williams, E. A., Influence ofNonlocal Electron Heat Conduction on theInduced Incoherence of Light Transmittedthrough Plasma, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136373. Submitted to Phys. Rev.Lett.

Bernat, T., Nobile, A., and Schultz, K.,Fabrication of Indirect Drive Ignition Targetsfor the NIF: Recent Developments, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138259-ABS.Prepared for 18th IAEA Fusion Energy Conf,Sorrento, Italy, Oct 4–10, 2000.

Boehly, T. R., Bradley, D. K., Fisher, Y.,Meyerhofer, D. D., Seka, W., and Soures, J.M., Effects of Optical Prepulse on Direct-Drive Inertial Confinement Fusion TargetPerformance, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137876. Submitted to Phys. Plasmas.

Bradley, D. K., Bell, P. M., Dymoke-Bradshaw, A. K. L., Hares, J. D., and Bahr,R., Development and Characterization of aSingle Line of Sight Framing Camera,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-138002-ABS.Prepared for High Temperature DiagnosticsMtg, Tucson, AZ, Jun 18–22, 2000.

Bryant, R., NIF ICCS Network Design andLoading Analysis, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-ID-135920.

Bullock, A. B., Landen, O. L., and Bradley,D. K., 10 mm and 5 mm Pinhole-AssistedPoint-Projection Backlit Imaging for NIF,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137904-ABS.Prepared for High Temperature DiagnosticsMtg, Tuscon, AZ, Jun 18–22, 2000.

Bullock, A. B., Landen, O. L., and Bradley,D. K., Relative X-Ray Backlighter IntensityComparison of Ti and Ti/Sc Combination FoilsDriven in Double-Sided and Single-SidedLaser Configuration, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137906-ABS. Prepared for HighTemperature Diagnostics Mtg, Tuscon, AZ,Jun 18–22, 2000.

Burnham, A., Runkel, M., Demos, S.,Kozlowski, M., and Wegner, P., Effect ofVacuum on the Occurrence of UV-InducedSurface Photoluminescence, Transmission Loss,and Catastrophic Surface Damage, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-137123-ABS.Prepared for Society of Photo-OpticalInstrumentation Engineers 45th Annual Mtg,San Diego, CA, Jul 30–Aug 4, 2000.

CCampbell, J. H., and Suratwala, T. I., Nd-Doped Phosphate Glasses for High-Energy/High-Peak-Power Lasers, LawrenceLivermore National Laboratory, Livermore,CA, UCRL-JC-132911 Rev 1; also in J. Non-Cryst. Solids 263(1-4), 318–341 (2000).

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PUBLICATIONS AND PRESENTATIONS

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Campbell, J. H., Suratwala, T. I.,Thorsness, C. B., Hayden, J. S., Thorne, A.J., Cimino, J. M., Marker, A. J., Takeuchi,K., Smolley, M., and Ficini-Dorn, G. F.,Continuous Melting of Phosphate Laser Glass,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-134194; also in J.Non-Cryst. Solids 263(1-4), 342–357 (2000).

Cauble, R., Remington, B. A., andCampbell, E. M., Laboratory Measurementsof Materials in Extreme Conditions: The Useof High Energy Radiation Sources for HighPressure Studies, Lawrence LivermoreNational Laboratory, CA, UCRL-JC-131079; also in J. Impact Engr. 23(1) Pt.1,87–99 (1999).

Celliers, P. M., Collins, G. W., Da Silva, L.B., Cauble, R., Moon, S. J., Wallace, B. A.,Hammel, B. A., and Hsing, W. W.,Multiple-Shock Compression of LiquidDeuterium, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136861 ABS. Prepared for AmericanPhysical Society March Mtg, Minneapolis,MN, Mar 20, 2000.

Cherfils, C., Glendinning, S. G., Galmiche,D., Remington, B. A., Richard, A. L., Haan,S., Wallace, R., Dague, N., and Kalantar, D.H., Convergent Rayleigh–Taylor Experimentson the Nova Laser, Lawrence LivermoreNational Laboratory, CA, UCRL-JC-135371; also in Phys. Rev. Lett. 83 (26),5507–5510 (1999).

Collins, G. W., Bradley, D. K., Celliers, P.,Silva, L. B., Cauble, R., Moon, S. J.,Hammel, B. A., Wallace, R. J., Koenig, M.,and Benuzzi-Mounaix, A., ShockCompressing H2O into an ElectronicConductor, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136738 ABS. Prepared for AmericanPhysical Society March Mtg, Minneapolis,MN, Mar 20, 2000.

Colvin, J. D., Remington, B. A., Kalantar,D. H., and Weber, S. V., ExperimentalEvidence for Shock Softening and Hardeningof Metals at High Strain Rate, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-136707.Submitted to Phys. Rev. Lett.

Cook, R., Models of Polyimide SprayCoatings, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136289. Submitted to Fusion Technol.

Crichton, S. N., Tomozawa, M., Hayden, J.S., Suratwala, T. I., and Campbell, J. H.,Subcritical Crack Growth in a Phosphate LaserGlass, Lawrence Livermore NationalLaboratory, CA, UCRL-JC-131864; also in J.Am. Ceramic. Soc. 82(11), 3097–3104 (1999).

DDattolo, E., Suter, L., Monteil, M.-C.,Jadaud, J.-P., Dague, N., Glenzer, S.,Turner, R., Juraszek, D., Lasinski, B.,Decker, C., Landen, O., and MacGowan,B., Status of Our Understanding andModeling of X-Ray Coupling Efficiency inLaser Heated Hohlraums, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-137622.Submitted to Phys. Plasmas.

Delage, O., Lerche, R. A., Sangster, T. C.,and Arsenault, H. H., SIRINC: a Code forAssessing and Optimizing the NeutronImaging Diagnostic Capabilities in ICFExperiments, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137922-ABS. Prepared for 13th Topical Confon High-Temperature Plasma Diagnostics,Tucson, AZ, Jun 18–22, 2000.

EEder, D. C., Pretzler, G., Fill, E., Eidmann,K., and Saemann, A., Spatial Characteristicsof Ka Radiation from Weakly Relativistic LaserPlasmas, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-133236; also in Appl. Phys. B 70(2), 211–217(2000).

Edwards, J., Glendinning, S. G., Suter, L. J.,Remington, B. A., Landen, O., Turner, R.E., Shepard, T. J., Lasinski, B., Budil, K.,Robey, H., Kane, J., Lewis, H., Wallace, R.,Graham, P., Dunne, M., and Thomas, B. R.,Turbulent Hydrodynamic Experiments Usinga New Plasma Piston, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136317-REV-2; also in Phys.Plasmas 7(5), 2099–2107 (2000).

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Ehrmann, P. R., Campbell, J. H., Suratwala,T. I., Hayden, J. S., Krashkevich, D.,Takeuchi, K., Optical Loss and Nd3+ Non-Radiative Relaxation by Cu, Fe and SeveralRare Earth Impurities in Phoshate LaserGlasses, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-132910 Rev 1; also in J. Non-Cryst. Solids263(1-4), 251–262 (2000).

GGlendinning, S. G., Cherfils, C., Colvin, J.,Divol, L., Galmiche, D., Haan, S., Marinak,M. M., Remington, B. A., Richard, A. L.,and Wallace, R., Ablation FrontRayleigh–Taylor Growth Experiments inSpherically Convergent Geometry, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-134966. Preparedfor 41st Annual Mtg of the Div of PlasmaPhyics, Seattle, WA, Nov 15, 1999.

Glenzer, S. H., Berger, R. L., Divol, L. M.,Kirkwood, R. K., MacGowan, B. J., Moody,J. D., Rothenberg, J. E., Suter, L. J., andWilliams, E. A., Laser–Plasma Interactions inInertial Confinement Fusion Hohlraums,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-136632.Submitted to Phys. Rev. Lett.

Glenzer, S. H., Chambers, D., Wolfrum, E.,Wark, J., and Young, P. E., ThomsonScattering on Astrophysical Plasmas,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137687-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics with Intense Laser, Houston,TX, Mar 30–Apr 1, 2000.

Glenzer, S. H., Fournier, K. B., Decker, C.,Hammel, B. A., Lee, R. W., Lours, L.,MacGowan, B. J., and Osterheld, A. L.,Accuracy of K-Shell Spectra Modeling inHigh-Density Plasmas, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137905. Submitted to Phys. Rev. E.

Glenzer, S. H., Fournier, K. B., Hammel, B. A., Lee, R. W., MacGowan, B. J., andWilson, B. G., Accuracy of X-Ray SpectraModeling for Inertial Confinement FusionPlasmas, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137557-ABS. Prepared for 12th AmericanPhysical Society Topical Conf on AtomicProcesses in Plasmas, Reno, NV, Mar 19–23, 2000.

Glenzer, S. H., Suter, L. J., Berger, R. L.,Estabrook, K. G., Hammel, B. A.,Kauffman, R. L., Kirkwood, R. K.,MacGowan, B. J., Moody, J. D., andRothenberg, J. E., Holhraum Energetics withSmoothed Laser Beams, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136356. Submitted to Contrib.Plasma Phys.

Goldman, S. R., Barnes, C. W., Caldwell, S.E., Wilson, D. C., Batha, S. H., Grove, J. W.,Gittings, M. L., Hsing, W. W., Kares, R. J.,Klare, K. A., Kyrala, G. A., Margevicius, R.W., Weaver, R. P., Wilke, M. D., Dunne, A.M., Edwards, M. J., Graham, P., andThomas, B. R., Production of EnhancedPressure Regions due to Inhomogeneities inInertial Confinement Fusion Targets,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137588.Submitted to Phys. Plasmas.

Goldman, S. R., Caldwell, S. E., Wilke, M.D., Wilson, D. C., Barnes, C. W., Hsing, W.W., Delamater, N. D., Schappert, G. T.,Grove, J. W., Lindman, E. L., Wallace, J. M.,Weaver, R. P., Dunne, A. M., Edwards, M.J., Graham, P., and Thomas, B. R., ShockStructuring due to Fabrication Joints inTargets, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137462. Submitted to Phys. Plasmas.

HHaan, S. W., Dittrich, T. R., Marinak, M. M., and Hinkel, D. E., Design of IgnitionTargets for the National Ignition Facility,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-133510. Preparedfor 1st Intl Conf on Inertial Fusion Sciencesand Applications, Bordeaux, France, Sep 12, 1999.

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Haan, S. W., Dittrich, T., Hinkel, D.,Marinak, M., Munro, D., Strobel, G., Suter,L., Pollaine, S., Jones, O., and Lindl, J.,Hydrodynamic Instabilities andThermonuclear Ignition on the NationalIgnition Facility, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137000-ABS. Prepared forAmerican Physical Society April Mtg 2000,Long Beach, CA, Apr 29–May 2, 2000.

Haber, I., Callahan, D. A., Friedman, A.,Grote, D. P., and Langdon, A. B.,Transverse-Longitudinal TemperatureEquilibration in a Long Uniform Beam,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-136630.Prepared for Inst of Electrical andElectronics Engineers, Inc. ParticleAccelerator Conf, Dallas, TX, May 1, 1995.

Hammel, B. A., Recent Advances in IndirectDrive ICF Target Physics, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138130-ABS.Prepared for 18th Fusion Energy Conf,Sorrento, Italy, Oct 4–10, 2000.

Hartemann, F. V., Landahl, E. C., Troha, A.L., Van Meter, J. R., Baldis, H. A., Freeman,R. R., Luhman, N. C., Song, L., Kerman, A.K., and Yu, D. U. L., The Chirped-PulseInverse Free-Electron Laser: A High-GradientVacuum Laser Accelerator, LawrenceLivermore National Laboratory, CA,UCRL-JC-134073; also in Phys. Plasmas6(10), 4104–4110 (1999).

Hatchett, S. P., Brown, C. G., Cowan, T. E.,Henry, E. A., Johnson, J., Key, M. H., Koch,J. A., Langdon, A. B., Lasinski, B. F., andLee, R. W., Electron, Photon, and Ion Beamsfrom the Relativistic Interaction of PetawattLaser Pulses with Solid Targets, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-135029.Prepared for 41st Annual Mtg of the Div ofPlasma Physics, Seattle, WA, Nov 15, 1999.

Hawley-Fedder, R., Robey, H., Biesiada, T.,DeHaven, M., Floyd, R., and Burnham, A.,Rapid Growth of Very Large KDP and KD*PCrystals in Support of the National IgnitionFacility, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137102-ABS. Prepared for Society of Photo-Optical Instrumentation Engineers 45th Annual Mtg, San Diego, CA, Jul 30–Aug 4, 2000.

Hayden, J. S., Marker, A. J., Suratwala, T.I., and Campbell, J. H., Surface Tensile LayerGeneration during Thermal Annealing ofPhosphate Glass, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-134690; also in J. Non-Cryst.Solids 263(1-4), 228–239 (2000).

Hayden, J. S., Tomozawa, M., andCrichton, S., OH Diffusion Measurements inPhosphate Laser Glasses, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-ID-136007.

Hicks, D. G., Li, C. K., Seguin, F. H., Ram ,A. K., Petrasso, R. D., Soures, J. M.,Meyerhofer, D. D., Roberts, S., Schnittman,J. D., and Sorce, C., Studies of MeV FastProtons Produced in Laser FusionExperiments, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136746. Submitted to Phys. Rev. Lett.

Hinkel, D. E., Haan, S. W., Pollaine, S. M.,Dittrich, T. R., Jones, O. S., Suter, L. J., andLangdon, A. B., Scaled Targets for theNational Ignition Facility, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138284-ABS.Prepared for 30th Annual AnomalousAbsorption Conf, Ocean City, MD, May21–26, 2000.

KKalantar, D. H., Belak, J., Colvin, J. D.,Remington, B. A., Weber, S. V., Allen, A.M., Loveridge, A., Wark, J. S., Boehly, T. R.,and Paisley, D., Dynamic X-Ray Diffractionto Study Compression of Si and Cu beyond theHugoniot Elastic Limit, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138108-ABS. Prepared for High-Temperature Plasma Diagnostics Mtg,Tucson, AZ, Jun 18–20, 2000.

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Kalantar, D. H., Bell, P. M., Perry, T. S.,Sewall, N., Diamond, C., Piston, K.,Optimizing Data Recording for the NIF CoreDiagnostic X-Ray Streak Camera, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138107-ABS.Prepared for High Temperature PlasmaDiagnostics Mtg, Tucson, AZ, Jun 18–20,2000.

Kalantar, D. H., Remington, B. A.,Chandler, E. A., Colvin, J. D., Gold, D. M.,Mikaelian, K. O., Weber, S. V., Wiley, L. G.,Wark, J. S., Hauer, A. A., and Meyers, M.A., High Pressure Solid State Experiments onthe Nova Laser, Lawrence LivermoreNational Laboratory, CA, UCRL-JC-129810; also in J. Impact Engr. 23(1) Pt. 1,409–419 (1999).

Kalantar, D. H., Remington, B. A., Colvin,J. D., Mikaelian, K. O., Weber, S. V., Wiley,L. G., Wark, J. S., Loveridge, A., Allen, A.M., and Hauer, A., Solid State Experimentsat High Pressure and Strain Rates, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-136355. Preparedfor 41st Annual Mtg of the Div of PlasmaPhysics, Seattle, WA, Nov 15, 1999.

Kauffman, R., Inertial Confinement FusionMonthly Highlights, November 1999,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-TB-128550-00-02.

Kauffman, R., Inertial Confinement FusionMonthly Highlights, October 1999,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-TB-128550-00-01.

Kauffman, R., Inertial Confinement FusionMonthly Highlights, September 1999,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-TB-128550-99-12.

Key, M. H., Campbell, E. M., Cowan, T. E.,Hatchett, S. P., Henry, E. A., Koch, J. A.,Langdon, A. B., Lasinski, B. F., Lee, R. W.,and Mackinnon, A., Studies of theRelativistic Electron Source and RelatedPhenomena in Petawatt Laser–MatterInteractions, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-135477 Rev 1. Prepared for 1st Intl Conf onInertial Fusion Sciences and Applications,Bordeaux, France, Sept 12, 1999.

Kirkwood, R. K., Montgomery, D. S.,Afeyan, B. B., Moody, J. D., MacGowan, B.J., Joshi, C., Wharton, K. B., Glenzer, S. H.,Williams, E. A., Young, P. E., Kruer, W. L.,Estabrook, K. G., and Berger, R. L.,Observation of the Nonlinear Saturation ofLangmuir Waves Driven by PonderomotiveForce in a Large Scale Plasma, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-128298; also inPhys. Rev. Lett. 83(15), 2965–2968 (1999).

Koch, J. A., Presta, R., Sacks, R., Zacharias,R., Bliss, E., Dailey, M., Feldman, M., Grey,A., Holdener, F., and Salmon, T.,Experimental Comparison of a Shack-Hartmann Sensor and a Phase-ShiftingInterferometer for Large-Optics MetrologyApplications, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136743. Submitted to Appl. Opt.

Koch, J. A., Sater, J., Bernat, T., Bittner, D.,Collins, G., Hammel, B., Lee, Y., andMackinnon, A., Quantitative Analysis ofBacklit Shadowgraphy as a Diagnostic ofHydrogen Ice Surface Quality in ICFCapsules, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136266. Prepared for 13th Target FabricationMtg, Catalina Island, CA, Nov 8, 1999.

Koch, J., X-Ray Interferometry withSpherically Bent Crystals, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138023-ABS.Prepared for 13th Topical Conf on High-Temperature Plasma Diagnostics, Tucson, AZ,Jun 18–22, 2000.

Komashko, A. M., Feit, M. D., Rubenchik,A. M., Perry, M. D., and Banks, P. S.,Simulation of Material Removal Efficiencywith Ultrashort Laser Pulses, LawrenceLivermore National Laboratory, CA,UCRL-JC-133744; also in Appl. Phys. A69(SUPPS), S95–S98 (1999).

Kozlowski, M. R., Battersby, C. L., andDemos, S. G., Luminescence Investigation ofSiO2 Surfaces Damaged by 0.35 mm LaserIllumination, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136870. Prepared for 31st Annual Symp onOptical Materials for High Power Lasers,Boulder, CO, Oct 4, 1999.

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LLandahl, E. C., Hartemann, F. V., Le Sage,G. P., White, W. E., Baldis, H. A., Bennnett,C. V., Heritage, J. P., Kolner, B. H.,Luhman, N. C., and Ho, C. H., Phase NoiseReduction and Photoelectron Acceleration in aHigh-Q RF Gun, Lawrence LivermoreNational Laboratory, CA, UCRL-JC-139029; also in IEEE Trans. Plasma Sci.27(5), 1547 (1999).

Landen, O. L., Amendt, P. A., Back, C. A.,Berger, R. L., Bradley, D. K., Bullock, A. B.,Cauble, R. C., Chandler, G. A., Collins, G.W., Decker, C. D., Edwards, M. J.,Glendinning, S. G., Glenzer, S. H., Haan, S.W., Kalantar, D. H., Kirkwoood, R. K.,Moody, J. M., Munro, D. H., Olson, R. E.,Perry, T. S., Pollaine, S. M., Remington, B.A., Robey, H. R., Sanchez, J., Suter, L. J.,Turner, R. E., Young, P. E., Wallace, R. J.,Hammel, B. A., and Hsing, W. W., RecentProgress in ICF and High Energy DensityExperiments, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-138000-ABS. Prepared for 26th EuropeanConf on Laser Interaction with Matter,Prague, Czech Republic, Jun 12–16, 2000.

Landen, O. L., and Glenzer, S. H., Warm,Dense Matter Characterization by X-RayThomson Scattering, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138258-ABS. Prepared for IntlWorkshop on Warm Dense Matter,Vancouver, Canada, May 29–31, 2000.

Landen, O. L., Bradley, D. K., Amendt, P.A., Pollaine, S. M., Glendinning, S. G.,Bullock, A. B., Turner, R. E., Suter, L. J.,Jones, O. S., Wallace, R. J., and Hammel, B. A., Symmetry Diagnosis and Control for NIF-Scale Hohlraums, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137874-ABS. Prepared for 26thEuropean Conf on Laser Interaction withMatter, Prague, Czech Republic, Jun 12–16, 2000.

Landen, O. L., Bradley, D. K., Pollaine, S.M., Amendt, P. A., Glendinning, S. G.,Suter, L. J., Turner, R. E., Wallace, R. J.,Hammel, B. A., and Delamater, N. D.,Indirect-Drive Time-Dependent SymmetryDiagnosis at NIF-Scale, LawrenceLivermore National Laboratory,

Livermore, CA, UCRL-JC-136297.Prepared for 1st Intl Conf on Inertial FusionSciences and Applications, Bordeaux, France,Sep 12, 1999.

Landen, O. L., Ze, F., Lobban, A., Tutt, T.,Bell, P. M., and Costa, R., AngularSensitivity of Gated Micro-Channel PlateFraming Cameras, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137879-ABS. Prepared for 13thTopical Conf on High-Temperature PlasmaDiagnostics, Tucson, AZ, Jun 18–22, 2000.

Langdon, A. B., Berger, R. L., Cohen, B. I.,Decker, C. D., Hinkel, D. E., Kirkwood, R.K., Still, C. H., and Williams, E. A., PowerTransfer between Smoothed Laser Beams,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-138282-ABS.Prepared for 30th Annual AnomalousAbsorption Conf, Ocean City, MD, May 21–26, 2000.

Lehmberg, R. H., and Rothenberg, J. E.,“Comparison of Optical Beam SmoothingTechniques for Inertial ConfinementFusion and Improvement of Smoothing bythe Use of Zero-Correlation Masks,” J.Appl. Phys. 87(3), 1012–1022 (2000).

Lukasheva, N. V., Niemela, S., Neelov, I.M., Darinskii, A. A., Sundholm, F., andCook, R., Conformational Variability of HelixSense Reversals in Poly(Methly Isocyanates),Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137206.Submitted to Macromolecules.

MMcCallen, D., Acceleration Amplifications inNIF Structures Subjected to Earthquake BaseMotions, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-ID-136812.

McKinnon, A., Shigemori, K., Ditmire, T.,Remington, B. A., Yanovsky, V., Ryutov, D.,Estabrook, K. G., Edwards, M. J., Keilty, K.A., and Liang, E., Radiative ShockExperiments Relevant to Astrophysics,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137569-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics on Intense Lasers, Houston, TX,Mar 29–Apr 1, 2000.

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Montgomery, D. S., Johnson, R. P., Cobble,J. A., Fernandez, J. C., Lindman, E. L.,Rose, H. A., and Estabrook, K. G.,“Characterization of Plasma and LaserConditions for Single Hot SpotExperiments,” Laser and Particle Beams17(3), 349–359 (1999).

Moody, J. D., MacGowan, B. J., Glenzer,S. H., Kirkwood, R. K., Kruer, W. L.,Montgomery, D. S., Schmitt, A. J.,Williams, E. A., and Stone, G. F.,Experimental Investigation of ShortScalelength Density Fluctuations in Laser-Produced Plasmas, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136401-REV-1. Prepared for 41stAnnual Mtg of the Div of Plasma Physics,Seattle, WA, Nov 15–19, 1999.

Murray, J. E., Milam, D., Boley, C. D., andEstabrook, K. G., Spatial Filter PinholeDevelopment for the National Ignition Facility,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-134647; also inAppl. Optics 39(9), 1405–1420 (2000).

NNoble, C. R., Hoehler, M. S., and Sommer,S. C., NIF Ambient Vibration Measurements,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-ID-136914.

PPerry, M. D., and Shore, B. W., PetawattLaser Report, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-ID-124933.

Pollaine, S., Bradley, D., Landen, O.,Amendt, P., Jones, O., Wallace, R.,Glendinning, G., Turner, R., and Suter, L.,P6 and P8 Modes in NIF Hohlraums,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-133888-ABS. -REV-2. Prepared for 30th AnnualAnomalous Absorption Conf, Ocean City,MD, May 21–26, 2000.

Pollaine, S., Radiation Transport between TwoConcentric Spheres, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137279. Submitted to NuclearFusion.

RRegan, S. P., Delettrez, J. A., Yaakobi, B.,Bradley, D. K., Bahr, R., Millecchia, M.,Meyerhofer, D. D., and Seka, W.,Spectroscopic Analysis of Electron Temperaturein Laser Driven Burnthrough Experiments,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137875-ABS.Prepared for 12th Topical Conf on AtomicProcesses in Plasmas, Reno, NV,Mar 19–23, 2000.

Remington, B. A., Drake, R. P., Takabe, H.,and Arnett, D., Review of AstrophysicsExperiments on Intense Lasers, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-134961-REV-1.Prepared for 41st Annual Mtg of theDivision of Plasma Physics, Seattle, WA, Nov 15–19, 1999.

Remington, B. A., Kalantar, D. H., Weber,S. V., and Colvin, J. D., Experimental Path toDeep Earth Interior Physics and HypervelocityMicro-Flier Plates, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138109-ABS. Prepared for 3rdIntl Workshop on Laboratory Astrophysics onIntense Lasers, Houston, TX, Mar 31–Apr 2, 2000.

Remington, B. A., Overview of AstrophysicsExperiments on Intense Lasers, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-137570-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics on Intense Lasers, Houston, TX,Mar 29–Apr 1, 2000.

Richard, A. L., Jadaud, J. P., Dague, N.,Monteil, M. C., Turner, R. E., Bradley, D.,Wallace, R. J., Landen, O. L., Pien, G.,Morse, S., and Soures, J. M., SymmetryExperiments on OMEGA with LMJ likeMultiple Beam Cones Irradiation, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-137873-ABS.Prepared for 26th European Conf on LaserInteraction with Matter, Prague, CzechRepublic, Jun 12–16, 2000.

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Roberts, C. C., Orthion, P. J., Hassel, A. E.,Parrish, B. K., Buck ley, S. R., Fearon, E.,Letts, S. A., and Cook, R. C., Developmentof Polyimide Ablators for NIF: DefectAnalysis, Novel Smoothing Technique andUpilex Coatings, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137737. Submitted to FusionTechnol.

Robey, H. F., Kane, J., Remington, B. A.,Hurricane, O., Drake, R. P., and Knauer, J.,Astrophysics Experiments on the OMEGALaser: Interface Coupling in SupernovaeCaused by Rippled Shock Imprinting,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137443-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics with Intense Lasers, Houston,TX, Mar 30–Apr 1, 2000.

Roth, M., Cowan, T. E., Brown, C., Christl,M., Fountain, W., Hatchett, S., Johnson, J.,Key, M. H., Pennington, D. M., and Perry,M. D., Intense Ion Beams Accelerated byPetawatt-Class Lasers, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136218-ABS. Prepared for 13thIntl Symp on Heavy Ion Inertial Fusion, San Diego, CA, Mar 13, 2000.

Ryutov, D. D., and Remington, B. A.,Destabilizing Effect of Thermal Conductivityon the Rayleigh–Taylor Instability, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-137568-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics with Intense Lasers, Houston,TX, Mar 30–Apr 1, 2000.

Ryutov, D., Ditmire, T., Edwards, J.,Glendinning, G., Remington, B., andShigemori, K., Simple Description of theBlast Wave in the Medium with Y Close to 1,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137567-ABS.Prepared for 3rd Intl Conf on LaboratoryAstrophysics with Intense Lasers, Houston,TX, Mar 30–Apr 1, 2000.

SSangster, T. C., Ahle, L. A., Halaxa, E. F.,Karpenko, V. P., Olddaker, M. E.,Thompson, J., Beck, D. N., Bieniosek, F. M.,Henestroza, E., and Kwan, J. W., New 500-keV Ion Source Test Stand for HIF,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-136744-ABS.Prepared for 13th Intl Symp on Heavy Ion Inertial Fusion, San Diego, CA, Mar 13, 2000.

Sangster, T. C., Glebov, V., Lerche, R. A.,Phillips, T. W., Stoekl, C., Padalino, S. J.,Olliver, H., and Thompson, S., Calibrationof the Medusa Neutron Spectrometer at theOMEGA Laser, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-137923-ABS. Prepared for 13thTopical Conf on High-Temperature PlasmaDiagnostics, Tucson, AZ, Jun 18–22, 2000.

Sharp, R., and Runkel, M., AutomatedDamage Onset Analysis Techniques Applied toKDP Damage and the Zeus Small AreaDamage Test Facility, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-134765. Prepared for 31st BoulderDamage Symposium: Annual Symposium onOptical Materials for High Power Lasers,Boulder, CO, Oct 4–7, 1999.

Still, C. H., Berger, R. L., and Langdon, A.B., pF3D, version 2.0, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-CODE-2000-019.

Still, C. H., Berger, R. L., Langdon, A. B.,Hinkel, D. E., and Williams, E. A.,Filamentation and Forward Brillouin Scatterof Entire Smoothed and Aberrated LaserBeams, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-135006. Prepared for 41st Annual Mtg ofthe Div of Plasma Physics, Seattle, WA, Nov 15, 1999.

Still, C. H., Berger, R. L., Langdon, A. B.,Hinkel, D. E., and Williams, E. A., LaserPlasma Simulations Using Entire Smoothedand Aberrated Laser Beams, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-138283-ABS.Prepared for 30th Annual AnomalousAbsorption Conf, Ocean City, MD, May 21–26, 2000.

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Strobel, G. L., M Dependence of SurfaceExpansion Coefficients, Lawrence LivermoreNational Laboratory, Livermore, CA, UCRL-JC-137516-ABS. Prepared for Sherwood 2000,Los Angeles, CA, Mar 27–29, 2000.

Suratwala, T. I., Steele, R. A., Wilke, G. D.,Campbell, J. H., and Takeuchi, K., Effects ofOH Content, Water Vapor Pressure, andTemperature on Sub-Critical Crack Growth inPhosphate Glass, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-132912; also in J. Non-Cryst.Solids 263(1-4), 213–227 (2000).

Suter, L., Rothenberg, J., Munro, D., VanWonterghem, B., Haan, S., and Lindl, J.,Feasibility of High Yield/High Gain NIFCapsules, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-136784. Prepared for 1st Intl Conf on InertialFusion Sciences and Applications, Bordeaux,France, Sep 18, 1999.

Suter, L., Rothenberg, J., Munro, D., VanWonterghem, B., and Haan, S., Exploringthe Limits of the National Ignition Facility’sCapsule Coupling, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-136319-REV-1; also in Phys.Plasmas 7(5), 2092–2098 (2000).

TTakagi, M., Cook, R., Stephens, R., Gibson,J., and Paguio, S., Decreasing Out-of-Roundin PaMS Mandrels by Increasing InterfacialTension, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-135539. Submitted to Fusion Technol.

Takagi, M., Cook, R., Stephens, R., Gibson,J., and Paguio, S., Effects of ControllingOsmotic Pressure on a PaMSMicroencapsulated Shell during Curing,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-135540.Submitted to Fusion Technol.

Takagi, M., Cook, R., Stephens, R., Gibson,J., and Paguio, S., Stiffening of PaMSMandrels during Curing, LawrenceLivermore National Laboratory,Livermore, CA, UCRL-JC-135545.Submitted to Fusion Technol.

Turner, R. E., Landen, O. L., Bradley, D. K.,Bell, P. M., Costa, R., Moody, J. D., and Lee,D., Comparison of CCD vs Film Readouts forGated MCP Cameras, Lawrence LivermoreNational Laboratory, Livermore, CA,UCRL-JC-138003-ABS. Prepared for High-Temperature Diagnostics Mtg, Tucson, AZ,Jun 18–22, 2000.

WWarwick, P. J., Demir, A., Kalantar, D. H.,Key, M. H., Kim, N. S., Lewis, C. L. S.,Lin, J., MacPhee, A. G., Neely, D., and Remington, B. A., RadiographyMeasurements of Direct Drive Imprint inThin Al Foils Using a Bright XUV Laser,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-136395.Prepared for 5th Intl Conf on X-Ray Lasers,Lund, Sweden, Jun 10, 1996.

Williams, W., NIF Large Optics MetrologySoftware; Description and Algorithms,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-MA-137950.

Wolfrum, E., Allen, A., Barbee, T. W., Jr.,Burnett, P., Djaoui, A., Kalantar, D., Keenan,R., Key, M. H., Lewis, C. L. S., Machacek,A., Remington, B., Rose, S. J., O’Rourke, R.,and Wark, J. S., Measurements of the XUVOpacity of a Strongly-Coupled AluminumPlasma, Lawrence Livermore NationalLaboratory, Livermore, CA, UCRL-JC-137262. Submitted to Phys. Rev. Lett.

Wu, Z. L., Stolz, C. J., Weakley, S. C.,Hughes, J. D., and Zhao, Q., DamageThreshold Prediction of Hafnia/SilicaMultilayer Coatings by NondestructiveEvaluation of Fluence-Limiting Defects,Lawrence Livermore National Laboratory,Livermore, CA, UCRL-JC-137089.Submitted to Appl. Opt.

YYatsenko, L. P., Shore, B. W., Halfmann, T.,Bergmann, K., and Vardi, A., “Source ofMetastable H(2s) Atoms Using the StarkChirped Rapid-Adiabatic-PassageTechnique,” Phys. Rev. A 60(6), R4237–4240(1999).

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ICF/NIF and HEDES ProgramLawrence Livermore National LaboratoryP.O. Box 808, L-475Livermore, California 94551

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INERTIAL CONFINEMENT - Lasers, Photonics, and Fusion ... · Inertial Confinement Fusion Plasmas (S. H. Glenzer) 35 This article reports on a test of non-local thermodynamic equilibrium