IFE THICK LIQUID WALL CHAMBER DYNAMICS: GOVERNING MECHANISMS AND MODELING AND EXPERIMENTAL...

IFE THICK LIQUID WALL CHAMBER DYNAMICS:GOVERNING MECHANISMS AND MODELING ANDEXPERIMENTAL CAPABILITIESA. R. RAFFRAY,*† W. MEIER,‡ S. ABDEL-KHALIK,§ R. BONAZZA,7 P. CALDERONI,#C. S. DEBONNEL,** Z. DRAGOJLOVIC,†† L. EL-GUEBALY,7 D. HAYNES,7 J. LATKOWSKI,‡C. OLSON,‡‡ P. F. PETERSON,** S. REYES,‡ P. SHARPE,§§ M. S. TILLACK,††and M. ZAGHLOUL77##

†University of California, San Diego, Mechanical and Aerospace Engineering Department,and Center for Energy Research, 458 EBU-II, La Jolla, California 92093-0438

‡Lawrence Livermore National Laboratory, Livermore, California 94550§Georgia Institute of Technology, School of Mechanical Engineering, Atlanta, Georgia 30332-04057University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53706-1687#University of California, Los Angeles, Los Angeles, California

**University of California, Berkeley, Department of Nuclear Engineering, Berkeley, California 94720-1730††University of California, San Diego, Center for Energy Research, La Jolla, California 92093-0417‡‡Sandia National Laboratories, Albuquerque, New Mexico 87185§§Idaho National Engineering and Environmental Laboratory, Fusion Safety Program, EROB E-3 MS 3815,

Idaho Falls, Idaho 83415-381577United Arab Emirates University, College of Sciences, Department of Physics, P.O.B. 17551, Al-Ain,

United Arab Emirates

Received December 16, 2004Accepted for Publication March 21, 2005

For thick liquid wall concepts, it is important tounderstand the different mechanisms affecting the cham-ber dynamics and the state of the chamber prior toeach shot as compared with requirements from the driverand target. These include ablation mechanisms, vaportransport and control, and possible aerosol formation,as well as protective jet behavior. This paper focuseson these research topics and aims at identifying the

major issues, assessing the latest results, reviewing thecapabilities of existing modeling and experimental fa-cilities with respect to addressing remaining issues, andhelping guide future analysis and research and devel-opment efforts.

KEYWORDS: inertial fusion energy, liquid wall, chamberdynamics

I. INTRODUCTION

The thick liquid wall ~TLW! concept for an inertialfusion energy ~IFE! chamber consists of a neutronicallythick region of flowing liquid between the fusion targetand the chamber first wall and structures. This not only

provides a renewable wall to accommodate the photonand ion threat spectra from the fusion microexplosion butalso provides significant moderation and attenuation ofthe high-energy neutron flux from the target, therebyreducing the radiation damage rate and leading to longerlifetimes for the first wall and blanket structures. Byutilizing a lithium-containing liquid, such as the moltensalts flibe ~Li2BeF4! or flinabe ~LiNaBeF4!, the TLWalso serves as the tritium-breeding blanket and the pri-mary coolant since it directly absorbs all of the short-range target emissions ~X-rays and target debris! and themajority of the neutron energy.

*E-mail: [email protected]##Permanent address: Zagazig University, Department of Phys-

ics and Engineering Mathematics, College of Engineering,Zagazig, Egypt

FUSION SCIENCE AND TECHNOLOGY VOL. 49 JAN. 2006 1

Early TLW concepts date to the 1970s ~Refs. 1, 2,and 3!. The first detailed conceptual design work wascarried out at Lawrence Livermore National Laboratory~LLNL! leading to the High Yield Lithium Injection Fu-sion Energy ~HYLIFE! chamber design.4,5,6 Subsequentdesign modifications ~including use of flibe instead of Lias the working fluid! led to the HYLIFE-II design.7 Themost recent integrated design based on a TLW chamber,a heavy ion driver, and indirect-drive targets, known asthe Robust Point Design ~RPD!, was completed in 2002~Ref. 8!. A variety of flow configurations have been pro-posed over the years including vortices, single and seg-mented annular curtains, and various combinations ofrectangular and cylindrical liquid jets to make up themain TLW and create liquid beam ports.

Key issues for TLW concepts include the liquid wallbehavior under the IFE threat spectra and the ensuingclearing process dictating the chamber environment priorto the next shot. This chamber environment must accom-modate the target injection and driver propagation re-quirements. These issues were the focus of the 2003ARIES Town Meeting on Liquid Wall Chamber Dynam-ics, whose major objective was to bring together expertsin these areas to identify the major issues; share the latestresults; understand better the accuracy of various mod-eling predictions; and, through discussions, help focusfuture analysis and experimental research and develop-ment ~R&D! efforts.9 This paper is inspired by the infor-mative presentations and discussions at the meeting andaims to provide a comprehensive summary of the statusof the present understanding of these issues and of thetools available to further this understanding.

First, an example TLW chamber concept, HYLIFE-II, is presented, and the driver and target constraints aresummarized. Next, the mechanisms affecting chamber0liquid wall dynamics and chamber clearing are dis-cussed. The models and experimental facilities that canbe used to shed light on these mechanisms are then de-scribed. Finally, the R&D needs are summarized, andconcluding remarks are drawn.

II. TLW CHAMBER CONCEPT AND OPERATION

II.A. Example HYLIFE-II Design with Heavy Ion Driver

and Indirect-Drive Target

Figure 1 shows a computer-aided design ~CAD!modelof the HYLIFE-II chamber as modified to be consistentwith the driver and target specifications of the RPD. Inparticular, this latest version accommodates 120 ion beams~60 from each side! that are needed to drive the indirect-drive target with the correct pulse shape. Figure 2 illus-trates the current liquid wall configuration for the RPD ina more schematic manner. Several types of flow are re-quired including oscillating jets to make up the centralpocket, steady flow, crossing cylindrical jets in the re-

gion of beam entry, and vortices in the chamber penetra-tions and beam tubes leading to the final-focus magnetsection.

Oscillating nozzles at the top of the chamber repet-itively ~6 Hz for the RPD! form a pocket of flibe ~orflinabe for the RPD! around the point of the fusion targetexplosion at the center of the chamber. The purpose ofthis oscillating flow is to physically sweep any dropsfrom the previous shot out of the central region of thechamber and provide an essentially clear inner cavity.The liquid blanket surrounding the central cavity is made

Fig. 1. CAD model of HYLIFE-II chamber for the RPD.

Fig. 2. Schematic of liquid jets that make up TLW protection.

Raffray et al. IFE THICK LIQUID WALL CHAMBER DYNAMICS

2 FUSION SCIENCE AND TECHNOLOGY VOL. 49 JAN. 2006

up of many individual jets with an overall packing frac-tion of ;50%. This functions as a shock absorber toreduce or even eliminate large impact stress on the firststructural wall. The inner radius of the central pocket is;0.5 m, and the liquid wall thickness is 0.56 m ~1.12 mat 50% effective density!. Beams enter the central cavityfrom two sides as shown in Fig. 1. To shield chamberstructures ~and focusing magnets! in the beam entry re-gion, an array of crossing jets is used to form thick-liquidbeam ports. These jets should be as smooth as possible sothat they can be positioned close to the beams and thusprovide better shielding. The injection velocity of boththe central pocket jets and beam-port crossing jets is highenough ~;12 m0s! to reestablish the configuration in theinterpulse time. Vortex flow protects the beam tubes inthe region between the chamber and final-focus magnets.This flow can be at a lower temperature than the bulkflow to assist in vapor condensation and minimize flowup the beamlines.

From the standpoint of chamber dynamics, the keyissues for the TLW design are ~a! whether the protectiveliquid configuration can be established to the requiredprecision, ~b! whether the liquid jet structures protect thefirst wall effectively, and ~c!whether chamber conditionscan be reestablished at ;6 Hz to allow for beam andtarget injection. This includes return of chamber pressureto a level that allows beam propagation and pathwaysessentially clear of droplet aerosols for the beams andtarget.

II.B. Driver and Target Considerations

The chamber conditions prior to each shot canimpact target injection and survival as well as driverpropagation. Constraints based on driver and target con-siderations are discussed in detail in Ref. 10 for bothdirect- and indirect-drive targets and for laser and ionbeam drivers. Here, the key points are summarized.

The temperature of the frozen DT is ;18 K whenthe target leaves the injector. As the target travels to thechamber center, it is exposed to heating from energy-exchange with the chamber vapor. Direct-drive targetsare very fragile, and their thermal behavior during in-jection through the vapor is of particular concern sinceit could lead to unacceptable target deformation and0ordensity variations ~when compared to target physics re-quirements!. Indirect-drive targets include a massivehohlraum surrounding the DT-containing capsule andeffectively insulating it from the heat load during theshort transit to the center of the chamber. The hohlraumis illuminated from two sides by arrays of beams in arelatively narrow cone angle. These features make indi-rect drive targets compatible with the TLW chamber.

There are also requirements from the driver limitingthe chamber gas density. For a laser driver, laser break-down considerations limit the vapor0gas density in thechamber.10 For a heavy ion driver, which is the preferred

option in combination with an indirect-drive target, therequirements posed on the chamber gas depend on themode of transport and focusing.10 Neutralized ballistictransport sets the most stringent limit based on strippingwith integrated line gas density equivalent to ;1 mtorr.Channel transport sets the least demanding limits basedon scattering with integrated line density equivalent to;1 torr. Self-pinched transport is somewhere betweensetting limits based on self-pinch resulting in integratedline density equivalent to 100 mtorr.

The example target considered for the analysis pre-sented in this paper is a 458-MJ heavy ion indirect-drive target11 whose energy partition is summarized inTable I ~based on LASNEX calculations12!. The cham-ber liquid wall is mainly affected by X-rays and ions.Neutrons penetrate much more deeply into the structureand blanket and, as such, are much less of a threat tothe chamber wall. For the indirect-drive target, X-rayscarry a large portion of energy ~25%! with a relativelysoft spectrum dominated by soft ~,1 keV!, shallowlypenetrating photons, as shown in Fig. 3. The photonenergy deposition time is very small ~,10 ns!, whichresults in extremely large heat fluxes on the liquid wallgiving rise to a number of ablation mechanisms, dis-cussed in Sec. III. The ions carry less energy ~2% forthe fast ions and 4% for the debris ions!, have a longertime of flight ~up to ;ms! than the photons, and aremuch attenuated by the ablated material from the pho-ton energy deposition.

III. CHAMBER AND LIQUID WALL DYNAMICS

A number of processes affect the chamber and liquidwall dynamics at different times following the fusionmicroexplosion. These are summarized in the followingsubsections.

TABLE I

Energy Partitioning for 458-MJ Heavy IonIndirect-Drive Target*

Heavy IonIndirect-Drive

Target~MJ!

X-rays 115 ~25%!Neutrons 316 ~69%!Gamma rays 0.36 ~0.1%!Burn product fast ions 8.43 ~2%!Debris ion kinetic energy 18.1 ~4%!Total 458

*References 11 and 12.



III.A. Short-Term (;1 ms) Chamber Dynamics

III.A.1. Ablation Mechanisms

As discussed in Sec. II.B, the X-rays carry muchmore energy than the ions ~;25% compared to;6% forall ions for the example indirect-drive target!, and their

very short energy deposition time ~approximately nano-seconds or less! results in large heat fluxes and liquidwall ablation. The ions carry less energy, and their longertime of flight ~up to approximately microseconds!meansthat they will be significantly attenuated by the ablatedmaterial from the photon energy deposition before reach-ing the liquid wall. As such, the ions contribute muchmore to raising the energy level of the already ablatedmaterial than to causing ablation itself. Consequently,the discussion of ablation mechanisms in this sectionfocuses on the impact of the photon energy deposition onthe liquid wall.

Figure 4 is a schematic diagram of the basic physicalprocesses and material removal mechanisms involved inthe X-ray ablation of the liquid wall. The energy depo-sition from the X-ray heats the skin layer of the liquidwall and produces a thermal spike. The rapid increase ofthe internal energy during this thermal spike leads tophase change and ablation. The resulting ablation pres-sure pulse propagates through the liquid bulk. Reflectionof the pressure pulse at a free surface or at the interfacewith a back wall of lower acoustic impedance than that ofthe liquid produces a rarefaction wave ~tensile stress!. Ifthe tensile stress is greater than the strength of the ma-terial, rupture or spall occurs, establishing a new surface;this process continues until the wave is sufficiently at-tenuated. These processes can be illustrated through sim-ple example computations that help to determine theirrelative importance for the given energy deposition re-gime and heating rate conditions. They are summarized

Fig. 3. Photon spectrum from LLNL 458-MJ HIB indirect-drive target.11,12

Fig. 4. Physical processes in X-ray ablation.13



below. A detailed investigation of these physical pro-cesses and material removal mechanisms due to photonenergy deposition is presented in Ref. 13.

The major phase change ~boiling! processes for aliquid subject to high-energy deposition are surface va-porization, heterogeneous nucleation, and homogeneousnucleation. In the case of the photon energy deposition,the heating rates are so high ~;1013 K0s, analogous tolaser material ablation! that the surface evaporation pro-cess does not have sufficient time to occur and plays aminor role.13–15 However, it would play a major role forheating rates corresponding to the ion energy deposition~;109 to 1010 K0s!. Similarly, results reported in Refs. 13and 15 indicate that heterogeneous nucleation would alsoplay a minor role under the extremely high photon heat-ing rates. Instead, for such extremely high heating rates,the boiling process is dominated by homogeneous nucle-ation, which leads to “explosive boiling.” This involvesrapid superheating to a metastable liquid state with alarge excess free energy, which decomposes explosivelyinto liquid and vapor phases. Under these conditions, asthe temperature approaches;90% of the critical temper-ature, an avalanche-like explosive growth in the homo-geneous nucleation rate ~by 20 to 30 orders of magnitude!leads to this explosive boiling.15 A discussion of moredetailed estimates of explosive boiling is given in Ref. 13.Here, for simplicity the 90% critical-temperature crite-rion ~0.9Tc! is used to provide an example of the amountof a flibe liquid wall ablated by the photon energy depo-sition, as illustrated in Fig. 5.

Figure 5 shows the spatial profile of the photonenergy deposition within a flibe liquid wall at a 0.5-mradius from the microexplosion. A line representing thecohesion energy ~the total evaporation energy Et ! is

shown, illustrating the thickness of flibe that would beevaporated ~;103 mm!. There would be a two-phaseflibe region below this threshold ~the lower limitingline representing the sensible energy is not shown inFig. 5 as it is off-scale!. It is not clear to what extentthis two-phase region will ablate or remain on the sur-face. However, it seems clear that at least the part ofthis region experiencing explosive boiling will ablate.Superimposing a line corresponding to 90% of the crit-ical temperature ~as suggested by Ref. 15! shows thatthe explosive boiling region is ;127 mm in this case,resulting in a total ejected mass of ;0.8 kg for an as-sumed spherical chamber. The radius of the liquid wallfrom the microexplosion center is an important param-eter as it determines the wall surface area seen by thephotons. Increasing the liquid wall radius would resultin a thinner explosive boiling region but because of thelarger surface area would result in an increase in thetotal mass of ejected flibe. For example, the explosiveboiling region thickness decreases to ;10.9 mm whenthe liquid wall radius is increased to 3.5 m, but the totalmass of ejected flibe increases to ;6.2 kg ~assuming aspherical liquid wall configuration!.13,14

The liquid wall ablation due to explosive boilingwould generate an impulse creating a shock wave. Uponreaching the liquid boundary at the back of the liquidwall, this shock wave would give rise to a rarefactionwave moving inward. If the net tensile stress in the liquiddue to the rarefaction wave is higher than the spall strengthof the liquid, spalling would occur, establishing a newliquid surface and potentially providing an additionalsource of ablated material. A detailed discussion of thispotential ablation mechanism is given in Ref. 13 for thecase of a liquid film on a solid wall where the rarefactionwave formation would depend on the liquid and reflect-ing wall acoustic impedances. Reference 13 also pro-vides a derivation of the theoretical spall strength of flibe,which is summarized in Table II.

The exact shape of the pressure pulse is important inestimating the local stresses in the liquid and the possi-bility of spalling. Such calculations can be quite com-plex. Simple example estimates of spalling can be made

Fig. 5. Volumetric heat deposition in a flibe wall ~or curtain! at0.5 m from the microexplosion for the 458-MJ indirect-drive photon spectra, illustrating the region where ex-plosive boiling is likely to occur.

TABLE II

Theoretical Spall Strength of Flibe*

T~K!

Spall Strength~GPa!

750 �2.49141450 �1.42122250 �0.68482999 �0.28143749 �0.0657

*Reference 13.



based on the ablation pressure wave profile computedfrom a previous IFE study @OSIRIS ~Ref. 16!# with com-parable X-ray yield and scaled to the case being ana-lyzed.13 The scaling is based on the magnitude of therelative reactive impulses ~see Table III!, and the pres-sure profile is assumed to be steady ~no change in shapeaccording to the acoustic approximation!. Figure 6shows the pressure profile from the OSIRIS study andthe corresponding scaled profiles in a flibe liquid wall forthe photon energy deposition from the 458-MJ indirect-drive target. Cases with a 3.5-m liquid wall radius ~sim-

ilar to OSIRIS! and with a 0.5-m liquid wall radius ~thecase of interest here! are both shown; for the latter case,the pressure pulse shown has been arbitrarily scaled downby a factor of 1

5_ so that it can be represented within the

scale of the graph.According to Jantzen and Peterson,17 the peak pres-

sure in the shock wave would decay rapidly over the firstfew millimeters of depth; thus, for thick liquid jets, onlya small fraction of the total thickness would experiencehigh stresses. However, the theoretical spall strength offlibe is about two orders of magnitude lower than themagnitude of the initial shock for this case, and even a“dampened” shock could result in spalling. As an illus-tration, a conservative estimate of spalling was madeunder a worst-case scenario of a steady pressure wave~i.e., no change in shape as shown in Fig. 6!. The resultsare illustrated in Fig. 7. In this case, the shock wave uponreaching the rear of the liquid wall ~or curtain! gives riseto a rarefaction wave, and the net tensile stress exceedsthe theoretical spall strength of flibe at;28 mm from therear of the jet, forming a new liquid surface.

From these simple analyses, the ablation mecha-nisms ~such as the ejecta from explosive boiling and,possibly, the fractured liquid layer from spalling! wouldprovide a source for aerosol formation, discussed inSec. III.A.3. The behavior of the aerosol if not sweptout ~e.g., by the reformation of the liquid jets! couldaffect the heavy ion driver focusing. Clearly, furtherefforts are required to better understand the complexdynamic processes associated with these ablation mech-anisms through a combination of modeling and scaledexperiments ~simulating prototypical conditions!.

III.A.2. Isochoric Nuclear Heating

Over the past three decades, numerous heavy ionbeam ~HIB! designs have been developed, employingthin liquid walls and TLWs to protect the solid structureagainst the target X-rays and debris and therefore extendthe service lifetime and improve the reliability of thestructural components. The thin liquid walls tend to pro-tect the first wall but do not appreciably change the levelof radiation damage or the lifetime of the structure. Theintent of the thick liquid metal or molten salt systemswould be to protect the chamber structure such that itwould last for the life of the plant.18

To understand the isochoric heating problem, it isessential to identify the sequence of events as well as theevolution of the liquid wall with time following the targetimplosion. The target threat to the liquid surface is in theform of highly energetic X-rays, neutrons, and debrisions. At the liquid surface, the neutron heating is approx-imately five orders of magnitude lower than the X-rayand ion heating, which means the surface effect of theneutrons can be neglected.

The geometry of the bulk liquid hardly changes be-fore the arrival of the neutrons. The neutrons deposit

TABLE III

Comparison of Parameters from OSIRIS and fromthe Assumed 458-MJ Heavy Ion Indirect-Drive Target*

Parameters OSIRISPresentStudy

Liquid0structure Flibe0C FlibeX-ray yield ~MJ! 129a 115Closest distance from target ~m! 3.5 0.5Vaporized mass ~kg0m2 ! 0.0278 0.251Reactive impulse ~Pa{s!b 59.0 525.6

*Reference 16.aX-ray and debris.bAblated material velocity ; sonic velocity ; 2094 m0s forflibe at Tcrit ; 4500 K ~Ref. 13!.

Fig. 6. Scaled pressure pulse profile from OSIRIS ~Ref. 16!for flibe liquid wall at radii of 0.5 and 3.5 m for the458-MJ heavy ion indirect-drive target. For the 0.5-mcase, the peak pressure ~;280 MPa! has been scaleddown to 1

5_ of its value so that it can be represented

within the scale of the graph.



their energy volumetrically in the remaining liquid bulk~and any underlying structure!. The neutron heating causespressurization of the liquid. If the energy density is highenough, the liquid jets can break up. The disassembly ofthe liquid wall0jets is allowed in free-jet systems, likethe HYLIFE-II TLW design.7 In the HIBALL thin liquidwall design,19 the pressure is lower because of the muchlarger surface radius ~;5 m!, and the liquid is containedin thin porous tubes.

The physical geometry of the two representative de-signs ~HYLIFE-II and HIBALL! and the flow of theprotecting liquids are quite different. Although the totalenergy assumed in both studies is ;400 MJ, HYLIFE-IIhas a much smaller radius ~0.5 m! from the target to theliquid wall as compared to 5 m for HIBALL. The time-integrated power density deposited in the wall is muchlarger for the HYLIFE-type designs ~;150 W0cm3! ascompared to 2 W0cm3 for HIBALL. The time-integratedpower density in both designs decreases by ;2% withinthe first 1 cm of the liquid, unlike the X-ray and ionenergy deposition that diminishes in a few microns.

Because of the pulsed nature of IFE systems, it isinstructive to examine the results of time-dependent nu-clear analyses. The IFE fusion reactions occur during avery short burn time ~10 to 100 ps!. Most of the high-energy neutrons reach the liquid surface in 10 to 150 ns,depending on the surface radius. The lower-energy neu-trons arrive over a longer period of time. The neutronsspend tens of nanoseconds slowing down within the liq-uid blanket. The HIBALL study performed rigorous time-dependent heating analysis for both liquid and structureof an IFE power plant.20 A more recent time-dependentstudy21 has focused on the neutron flux within Fe and

SiC structures and the neutron-induced radiation damagefor thick flibe and Pb-17Li liquid wall systems with noevaluation for the isochoric nuclear heating.

The variation of power density with time at the liq-uid surface of HIBALL is shown in Fig. 8 ~Ref. 20!.From Fig. 8, the following broad trends emerge:

Fig. 7. Illustration of spalling in a TLW at a 0.5-m radius from the microexplosion under the scaled initial pressure pulse shownin Fig. 6 ~the shock is assumed to move at the speed of sound, C!. The right-side figures occur at a later time than theleft-side figures. The ordinate scales on the right-side figures have been magnified for clarity. ~Note that these results areonly dependent on the distance from the back of the jet and not on the actual thickness of the jet.!

Fig. 8. Instantaneous nuclear energy deposition at the surfaceand middle of the 2-m-thick Pb-17Li wall of theHIBALL design.



1. The peak is approximately 107 times the averagebased on the chamber repetition rate.

2. The temporal distribution has a narrow width of;20 ns.

3. The heating diminishes in microseconds.

Results such as these provide input to calculations ofliquid response to neutron heating.

III.A.3. Shock Propagation Through Chamber

Because of the arrangement of the numerous liquidjets, shock propagation through HYLIFE-II-type cham-bers is far more complex than in dry-wall or thin-liquidIFE chambers. In a thick-liquid chamber, indirect-drive-target X-rays ablate a thin layer off the surface of theinner pocket, fast ions quickly deposit their energies inthe ablated gas, and slow target debris interact with theexpanding ablated layer. A complex pattern of reflectedand transmitted waves is then generated in which wavescan be transmitted through the jet structures or reflectedoff the inner liquid pocket or other waves. The gas willultimately vent through the various thick-liquid jets, fill-ing in the volume of the target chamber.

In the HYLIFE study, it was realized early on that aclosed pocket ~besides leaving no room for target or driverpropagation! would result in an excessive pressurizationof the inside pocket and in the liquid curtain beingslammed into the structural first wall. Both HYLIFE-IIand the RPD rely on oscillating slab jets with ventingopenings to avoid pocket overpressurization. HYLIFE-IImakes use of a “slot pocket,” made of a row of distinctoscillating slab jets and ablated flibe vents through theslots. The RPD uses a “hybrid” configuration with large

voided slab jets for better shock abatement and a largeventing opening to favor rapid target and ablated debrisventing toward the liquid droplet spray on the sides of thechamber. The propagation of the blast wave inside thejets, over longer timescales, is described in Sec. III.B.3.Assessment of the efficiency of the venting process isessential and has been carried out with the TSUNAMIgas dynamics code,22,23 to be described in Sec. IV.I.3.Results from gas dynamics simulations set the initial con-ditions for the pocket response to the ablation and pocketpressurization impulse load. The pressure exerted on thestructural first wall by the gas can also be investigated.24,25

Another crucial issue is the propagation of target andablated gas up the beamlines where it could deposit andcause arcing between the still unneutralized beamand the tube wall. Although pockets can be designed tomaximize gas venting in directions opposite to the beam-lines, TSUNAMI helped recognize that this approachwould not be effective enough. As mechanical shuttersare too slow to close off the beamlines quickly enough, acold flinabe liquid vortex layer was suggested to coat andprotect the beamline near the target chamber.22 However,it was realized that this layer could not be long enoughfor all the debris and ablated gas to condense.26 Thecombination of an ionizing plasma and a weak magneticdipole was proposed to effectively stop the debris andprevent their ingression past the vortex.26 The dipolewould also prevent the neutralizing electrons from stream-ing up the beamline, hence limiting beam emittancegrowth. However, further work is required to fine-tunethese “magnetic shutters.” Figure 9 shows the RPD beam-line schematic.

State-of-the-art two-dimensional ~2-D! gas dynam-ics simulations of the RPD chamber are presented in

Fig. 9. RPD beamline schematic.23,26



Sec. IV.A.3. Advancement in simulating gas dynamics inthick-liquid IFE systems is currently underway with thedevelopment of multidimensional, multispecies, multi-phase gas transport models ~see, for instance, Ref. 27!.

III.A.4. In-Flight Aerosol Formation

Material vaporized from the thick protective wallfollowing an IFE microexplosion could at some time bein a state suitable for particulate condensation in additionto film condensation onto the TLWs or droplet spray.Aerosol nucleation and growth likely occur as sufficientmaterial cools during expansion from the ablated region~as understood from gas dynamics simulations discussedin Sec. IV.A.5!, leading to what is termed in-flight aero-sol formation within the chamber. Particulate growth andbehavior are described by the aerosol dynamic equa-tion,28 which is coupled to the gas dynamic equations bysource0sink terms in mass, energy, and momentum. Theaerosol dynamic equation balances the contribution ofvarious mechanisms in the change of the aerosol popu-lation. Transport mechanisms such as convection, diffu-sion, and external forcing ~e.g., gravitational andelectrodynamic forces! are part of the equation, as areterms representing rates of change in the aerosol sizedistribution due to coagulation and particulate growth~homogeneous nucleation and condensation growth!. Insimulating IFE-relevant conditions, one generally doesnot consider diffusion and deposition since they impactan aerosol population on timescales larger than the typ-ical IFE intershot frequency. Other phenomena that areimportant in IFE chamber dynamics, for example, ion-induced nucleation, splashing of melt at the surface, andaerosol impact deposition and reflection, are being mod-eled to extend the usefulness of the simulations. It is

important to note that although flibe is a leading candi-date material for the TLW protection scheme, presentmodeling capabilities for gas and aerosol behavior areincomplete for the simulation of this material. Exampleresults illustrating these mechanisms presented here aretherefore provided for a single-component material,namely, liquid lead.

In-flight aerosol formation is possible since very highnucleation and growth rates are found at chamber loca-tions with significant supersaturation caused by rapidexpansion cooling of vaporized wall material. Scopingstudies for possible wall materials in IFE systems haveshown that aerosol particles may be formed by homo-geneous nucleation for time periods shortly after the va-porized material begins to cool. Figure 10 illustrates theresults for liquid lead. Figure 10a shows the homo-geneous nucleation rates and the droplet critical radii ~thesize at which nucleated particles have a stable growthrate! as the saturation ratios increase for various vaportemperatures. A vapor that cools to 1500 K ~from an es-timated 7000 to 8000 K ablative layer! forms 0.8-nmparticles at a rate of 1020 particles0m3{s�1 at a saturationratio of 5. Particles of this size are composed of aboutfive atoms of neutral lead. Nucleation rates are a strongfunction of saturation ratio; doubling the saturation ratiofrom 5 to 10 increases the rate by 6 orders for a vapor at1500 K. Figure 10b gives the time required to nucleate1015 particles0m3, a concentration at which coagulationbecomes increasingly important in the IFE chamber. Forthe conditions mentioned above, the time required tonucleate particles to this concentration is ;80 ms, dem-onstrating that in-flight aerosol formation is a relevantmechanism for early-time chamber dynamics.

Aerosol particles that are formed from homogeneousnucleation may continue to grow because of surface vapor

Fig. 10. ~a! Homogeneous nucleation rate ~solid lines! and critical particle radii ~dashed lines! for nucleation of Pb aerosolparticles. Note the highly nonlinear behavior at moderate saturation ratios. ~b! Illustration of the time required to nucleate1015 particles0m3.



deposition in the presence of vapor that is not depleted bynucleation alone. This mechanism, termed condensationgrowth, is also a function of vapor saturation ratio, albeitto a much lesser extent than homogeneous nucleation.Figure 11 shows the time needed for a 10% increase involume of a 1-nm lead particle as a result of condensa-tion growth. This volume increase reflects a significantchange in the aerosol population size distribution, whichin turn impacts aerosol growth and transport behavior.With the particle and vapor temperature at 1500 K, therequired time for 10% volume growth is ,1 ms for allsaturation ratios.5. Condensation growth rapidly slowswhen less vapor is available; i.e., the saturation ratioapproaches unity. In a real condensing system, both ho-mogeneous nucleation and condensation growth mayoccur to varying degrees during the same time periodonce some population of particles have formed, and theircompeting rates are coupled through the amount and stateof available vapor.

III.B. Intermediate-Term (;100 ms) Chamber Dynamics

III.B.1. Film Condensation on Cold Surfaces

The net film condensation may be expressed by thedifference between the condensation flux to the liquidsurface and the evaporation flux from the liquid surface.In Ref. 14, a characteristic condensation time based oncondensation rate and corresponding vapor mass in thechamber is used to estimate the time required for filmcondensation to clear the chamber as a function of vaporpressure and temperature for both Pb and flibe. The re-sults for an example 5-m chamber indicate that for agiven vapor temperature, the characteristic condensationtime is virtually independent of the vapor pressure untilit decreases to within about one order of magnitude of

the saturation pressure corresponding to the liquid filmtemperature. This characteristic time ~,0.04 s! is sig-nificantly smaller than the time between shots ~0.1 to1 s!, showing that condensation itself is fast. The overallfilm condensation process in a chamber would proba-bly be more limited by vapor transport to the liquid sur-face. However, the vapor pressure prior to each shot willbe higher than the liquid saturation pressure by up toa factor of ;10 ~as reference, for Pb at 1000 K, the sat-uration pressure is ;1.1 Pa, and for flibe at 800 K, thesaturation pressure is;0.0063 Pa!. To alleviate this con-cern, a spray of droplets colder than the liquid jet struc-tures can be employed. The combination of surfacerenewal ~by the continuous introduction of fresh drop-lets! and low temperature of the injected droplets en-hances condensation and helps in a faster attainment ofvapor pressure equilibrium.

III.B.2. Aerosol Coagulation and Evolution

Coagulation describes the process of two aerosol par-ticles ~or droplets! colliding to become one particle witha volume equal to the sum of the volumes of the initialparticles without affecting general particle shape. Aero-sols produced by in-flight nucleation and growth withinthe chamber will experience collisions and coagulationat time periods beyond that of formation. Unlike nucle-ation and growth mechanisms, coagulation is compara-tively less dependent on fluid state properties but is itselfdependent on the size distribution. Figure 12 illustratesthe time characteristics of coagulation by examining thetime required for changing a given number density of1-mm aerosol particles. The closeness of the curves rep-resenting different temperatures illustrates the weak de-pendence on the fluid state. An initial concentration of

Fig. 11. Time needed for a 10% increase in volume of a 1-nmlead particle as a result of condensation growth.

Fig. 12. Time required for a 10% change in a given numberdensity of 1-mm aerosol particles due to coagulation.



1015 particles0m3 at 1mm in size requires 100 ms to alterthe size distribution by increasing average particle sizewhile reducing the total number ~in a unit volume! by10%. This simplified analysis shows that coagulationshould be considered as a longer-term chamber dynamicstransport mechanism. It also gives some credibility to theassumption that gravitational settling and removal of theaerosol particles is unlikely during the intershot period.Large particles ~greater than ;50 mm! are necessary forgravitational settling to become important, and the analy-sis shows that 1-mm particles cannot grow to an averagesize of 50 mm within 100 ms ~Ref. 28!. In the case ofHYLIFE-II, estimates of aerosol population shortly be-fore the next shot should take into account the effect ofthe “larger” droplet spray, which would substantially en-hance surface vapor condensation and reduce the cham-ber vapor pressure, thereby mitigating the aerosol concern.

III.B.3. Jet Reformation

III.B.3.a. Jet Structures. In the original HYLIFE-IIdesign, the protection of the first wall and final-focusmagnets was provided by an array of slab jets and anoscillating liquid pocket. The main ideas have beenretained for the RPD target chamber, with a few modifi-cations.29 “Voided” slab jets are used for the pocket, asthey provide a better abatement of shocks. Voided slabjets are made of a sheet jet and an array of packed cylin-drical jets.

The use of cylindrical jets is recommended to protectthe beam ports. A “vortex” is used to coat the last fewmeters of the beam tube; it serves as a buffer between thetarget chamber and final-focus magnet region where therequirements on background gas and cleanliness are dif-ferent. The background gas blowing from the target cham-ber is expected to condense on the cold vortex beforereaching the final-focus magnet region. Oscillating voidedslab jets, cylindrical jets, and vortex flows have beendemonstrated to have the required geometric precision inscaled experiments.29

The corrosion-induced wear of the nozzles and theirpossible obstruction by target debris still need furtheranalysis. Molten salt corrosion and purity can be con-trolled effectively to limit corrosion and debris concen-tration through careful control of redox potential andconstant purification of the coolant. Purification tech-niques depend on the choice of the target and hohlraummaterials; work on this issue will require a flibe recircu-lation loop.

III.B.3.b. Pocket Disruption. Studies of disruption ofvoided slab jets have been conducted at the Universityof California at Berkeley ~UCB!. The snowplow modelof shock propagation through a voided jet structure hasbeen successfully developed and benchmarked againstexperimental data. As the shock propagates through thevoided jet, the effective liquid density increases, as if a“molten-salt-plow” were crushing the cylindrical jets.

The process is illustrated in Fig. 13. Use of jet structureswith a 50% packing fraction ensures that the pocket hasalready reached the bottom of the chamber before theshock wave has time to reach the back of the pocket; thisis essential to prove that no high-speed droplets are ejectedfrom the back of the liquid pocket toward the structuralfirst wall.

Timely recovery of the oscillating pocket has beendemonstrated experimentally.29 Shock waves travelingupward could disrupt the jets before they form the nextpocket at the center of the chamber, or might even dam-age the nozzles. This restricts the range of pocket shapesthat can be employed.30 Studies of the disruption of thearray of cylindrical jets have yet to be performed, but asimilar disruption model is expected to apply.

III.B.3.c. Hydrodynamic Droplet Source Term. The“hydrodynamic droplet source term” refers to dropletproduction by primary turbulent breakup of liquid jets.Recent publications in this area suggest that liquid jets inthe regimes of interest to thick-liquid protection conceptsmay be inherently unstable and susceptible to primaryturbulent breakup,31,32 whereby droplets are continu-ously ejected from the surface of the jets and spread

Fig. 13. Schematic of voided slab jet compression. Note thatthe actual slab jets are each made of one sheet jet andan array of cylindrical jets.30



about the chamber, possibly interfering with driver prop-agation and target delivery. Empirical correlations havebeen reported for the onset of primary breakup, the Sau-ter mean diameter of the ejected droplets, and the dropletmass flux for turbulent, unconditioned, annular, and roundjets with exit conditions corresponding to fully devel-oped channel flow.32 Application of such correlations tounconditioned round jets with dimensions like the jetsused in the stationary protective lattice of the RPD-2002design predicted a large hydrodynamic source term.29,33

Based on these results, an experimental investiga-tion has been undertaken to determine whether flow con-ditioning and0or boundary layer cutting can reduce thehydrodynamic source term to a sufficiently low levelcompatible with beam propagation requirements.33 Ver-tical turbulent sheets of water at near-prototypical Reyn-olds number ~1.3�105! flowing downward from nozzleswith exit cross sections of ~1 cm � 10 cm! were exam-ined. A simple mass collection technique was used tomeasure the rate of droplet ejection from the jet surfaceat different locations along the flow direction. Severalflow-conditioning schemes were examined to establishthe relative importance of traditional flow-straighteningelements. The effect of boundary layer cutting on thehydrodynamic source term was also quantified.33 Theresults indicate that standard flow-conditioning schemesin combination with contracting nozzle designs can re-duce the droplet mass flux from turbulent breakup bythree to five orders of magnitude and that boundary layercutting in conjunction with standard flow conditioningcan eliminate the hydrodynamic droplet source term, pro-vided that fine-mesh screens are included in the flow-conditioning elements.33 For these reasons, conditioningand boundary layer trimming are used in the RPD-2002.

IV. MODELS AND EXPERIMENTS

Understanding and characterizing the different mech-anisms affecting the liquid wall chamber dynamics ~de-scribed in Sec. III! are very important in designing thechamber and in being able to estimate key parameterssuch as the aerosol concentrations in beamlines prior toeach shot ~which must be compatible with the driverrequirements!. Models and experimental capabilities thatcan simulate IFE conditions are key tools in succeedingin this endeavor. Many such models and experimentalfacilities already exist and might only need specific mod-ifications to address these issues. An example list ~non-inclusive! of the known models and experimental facilitiesavailable in the United States is shown in Table IV interms of their applicability to addressing issues linkedwith liquid wall chamber mechanisms occurring at dif-ferent times following the fusion microexplosion. Theyare described in the following subsections with a view ofhelping to better recognize where there are gaps in cur-rent understanding and capabilities and where future R&D

effort should be directed. This represents just a startingpoint for a process that must be much more thorough~such as considering the possibility and cost of addingnew capabilities to experiments and of running the ex-periments! to arrive at a clearer vision of a future R&Dplan based on a given budget.

IV.A. Models

The example numerical models described here are:BUCKY, developed at the University of Wisconsin~UW!, Madison; Ablation By LAgrangian Transient One-dimensional Response ~ABLATOR!, developed at LLNLand UCB; TSUNAMI, developed at UCB; SPARTAN,developed at the University of California, San Diego~UCSD!; and TOPGUN, developed at the Idaho Na-tional Laboratory ~INL!. In addition, hydrodynamicsmodels @e.g., the Flow3D code at the University of Cal-ifornia, Los Angeles34,35 ~UCLA!#, although not de-scribed in detail here, can be useful tools for simulatingjet reformation as well as jet flow instabilities andbreakup ~which could lead to additional aerosol sourceterms!. This list is not inclusive as there may be othermodels that could be adapted to help address some ofthe specific issues associated with liquid wall chamberdynamics ~e.g., the FronTier code,36 which could beapplied potentially to simulate isochoric heating in jets!.However, the models described here provide a goodsnapshot of the capabilities of current modeling toolsand of their possible application to help solve thoseissues.

IV.A.1. BUCKY

BUCKY, a one-dimensional ~1-D! Lagrangianradiative-hydrodynamics code,37 is used to simulate theresponse of the chamber gas and wall to target X-rayand ion threat spectra. Prompt X-ray deposition is mod-eled using cold opacities from Biggs and Lighthill. De-position of ion energy is approximated by the theory ofMelhorn,38 and the free electron contribution inter-polates between the low-energy Lindhard-Scharff limitand the high-energy Bethe limit. Radiation transport39

is calculated in the flux-limited multigroup diffusionapproximation. Energy that reaches the wall is treatedas a source term in a thermal diffusion equation. As thetemperature in a wall cell approaches the vaporizationtemperature, the zone begins to vaporize at a rate deter-mined by the relative rates of vaporization and conden-sation, as determined by the kinetic theory of Labuntsovand Kryukov.40

BUCKY was originally developed to analyze drywall chambers with minimal wall ablation. For a liquidwall, the relevance of a 1-D simulation of chamber re-sponse past the time when the vapor ejected from thewall meets the shock of the chamber vapor pushed out-ward from the target chamber center is questionable. The



TABLE IV

Summary of Simulation Capabilities of Different Models and of Simulation and Measurement Capabilities of DifferentExperimental Facilities in Addressing IFE Liquid Wall Mechanisms

Time Less than ;10 ns ;10 to 100 ns ;0.1 to 1 ms ;1 to 30 ms 30 ms to 3 ms 3 to 100’s ms

Energy deposition Photon energy depositionin liquid wall

Neutron energy deposition Ion energy deposition

Model simulation ABLATORBUCKYTSUNAMI

BUCKY BUCKY

Experimental simulation UCSDXAPPERZ

UCLA

Liquid wall Explosive boiling Shock propagationthrough liquid wall

Surface evaporation Spallation Jet reformation

Model simulation ABLATORBUCKYTSUNAMI

ABLATORBUCKY

ABLATORBUCKYTOPGUNTSUNAMI

ABLATOR Hydrodynamic Models


UCLAUCSDXAPPERZ

UCLAUCSD

UCSDXAPPER

Georgia TechUCB

Experimental measurement UCSDa Georgia TechUCBa

Impulse generationin liquid wall

Liquid jet breakup dueto isochoric heating

Film condensation

Model simulation ABLATORBUCKY

TOPGUNTSUNAMI

Experimental simulation UCLAUCSDXAPPERZ

UCLAUCSD

Experimental measurement UCLA

Surface evaporation Aerosol coagulationModel simulation ABLATOR

BUCKYTOPGUNTSUNAMI

TOPGUN

Experimental simulation UCLAUCSD

UCLAUCSD

Experimental measurement UCSD UCLAa

UCSDa

Hydrodynamic dropletsource term

Model simulation Hydrodynamic modelsExperimental simulation Georgia Tech

UCBExperimental measurement Georgia Tech

UCBa

Chamber Ionization ofablated material

Expansion of ablatedmass in chamber

Further ionizationof ablated mass

Ablated vapor propagationthrough chamber

Shock wave traversethrough chamber

Aerosol evolution

Model simulation BUCKYTSUNAMI

ABLATORBUCKYSPARTANTSUNAMI

BUCKY BUCKYSPARTANTSUNAMI

BUCKYTOPGUNSPARTANTSUNAMI

TOPGUN


UCLAUCSDXAPPERZ

UCLAUCSDXAPPER

UCBUCLAUCSDUW~shock!

UCLAUCSDGeorgia Techa

Experimental measurement UCSD UCSD UCLAUCSD

UCBUCSD

UCLAa

UCSDa

High re-radiationto liquid wall

Radiation cooling Expansion and compression~cooling down throughradiation!

Cooling throughcondensation

Model simulation BUCKYTSUNAMI

BUCKYTSUNAMI

BUCKYTSUNAMI

TOPGUNTSUNAMI

Experimental simulation UCLAUCSDXAPPER

UCLA UCLAUCSDGeorgia Techa

Experimental measurement UCLAUCSDa

In-flight condensation andaerosol formation

Vacuum pumpingdynamics

Model simulation TOPGUNExperimental simulation UCLAExperimental measurement UCLAa

aIn progress.



code simulations would also lead to an optimistic cham-ber response scenario since the code does not include theeffects of aerosolization and possible liquid injection intothe chamber ~for example, due to explosive boiling orscattered droplet formation from jet instabilities!. BUCKYhas been used to simulate the response of a thin Pb liquidwall chamber to the threat from a 458-MJ heavy ionindirect-drive target. The results indicate that the denseionized vapor formed by the interaction of the early partof the X-ray pulse shields the surface from later X-raysand ions, reradiating the absorbed energy in timescaleslong compared to the pulse from the target.14 These re-sults tend to be conservative given the code’s limitationswhen applied to a liquid wall, but they provided a lower-bound estimate of ablated material for aerosol calcula-tions. BUCKY would need to be substantially upgradedto correctly simulate the response of a TLW chamberconfiguration such as HYLIFE-II, including more com-prehensive modeling of the shock wave in the chamber,inclusion of the effect of different ablation source termsand of in-flight condensation and aerosolization, and bet-ter simulation of a multidimensional geometry.

IV.A.2. ABL ATOR

ABLATOR is a 1-D finite difference code for thecalculation of material response to X-rays that was de-veloped at LLNL and UCB ~Ref. 41!. The code uses anexplicit scheme for advancing in time ~conditions at thenext time step are calculated directly from the state at thecurrent time step plus any incremental energy input!.Four processes are modeled: energy deposition from theX-rays, transient thermal conduction, thermal expansion~which raises pressures and causes hydrodynamic mo-tion!, and removal of material through surface vaporiza-tion and various spall processes.

LLNL has recently updated and debugged the AB-LATOR code in order to generate an enhanced versionfor use in IFE. The most relevant modifications include

1. implementation of direct- and indirect-drive X-rayspectra

2. ability to account for attenuation through a back-ground gas

3. introduction of a restart capability

4. generation of a multi-material version of the code

5. addition of new materials ~tungsten and flibe! tothe code’s material database.

In order to assess the use of ABLATOR for thespecial case of IFE liquid walls, a series of runs wascarried out to compare the ABLATOR results againstthose from the TSUNAMI code described in Sec. IV.A.3.For this purpose, a 40-ns pulse from a single energyline of 113 eV was assumed ~based on XAPPER param-eters!, and results were obtained on flibe ablation depthfor a series of different X-ray fluences. The results of

these calculations showed very good agreement be-tween the two codes ~see Table V!. It was found thatABLATOR’s vaporized depths were slightly smaller thanthose calculated with TSUNAMI. This result is consis-tent with the fact that ABLATOR considers heat con-duction during the pulse, whereas the energy depositionis instantaneous in TSUNAMI.

LLNLalso estimated the flibe ablation thickness underthe real HIF spectrum for a flibe pocket 0.5 m from thetarget and for a thin film at different distances from thetarget. The results yielded a total initial ablated thicknessof 150 mm in the case of the thick-liquid pocket. Fig-ure 14 shows the results for the case of a thin flibe film asa function of distance from the target. It can be observedthat in the case of a wetted wall at 6.5 m, the estimatedinitial ablated thickness is 2.2 mm.

Finally, it must be pointed out that the ABLATORcode was originally developed to model ablation of the

TABLE V

Comparison of ABLATOR and TSUNAMI Results onVaporized Flibe Thickness During a 40-ns Pulse

of a Single 113-eV Line

Thickness Vaporized

Fluence~J0cm2 !

Tsunami~mm!

Ablator~mm!

1 0.19 0.152 0.24 0.205 0.30 0.27

10 0.35 0.3220 0.40 0.3730 0.43 0.40

Fig. 14. Vaporized flibe thickness for a thin film as a functionof standoff distance from the target.



National Ignition Facility ~NIF! dry wall under low flu-ences where in the absence of plasma formation, theassumption of cold opacities is adequate to model photon-matter interaction. The main limitations of the use ofABLATOR for IFE liquid chambers are based on the lackof models for hot opacities, re-radiation, and condensa-tion. The use of cold opacities in the code assumes thatthe attenuation of photons at a given energy level staysconstant throughout the run. However, if a plasma isgenerated during X-ray deposition, this cold-opacity as-sumption would no longer be valid. The results presentedhere are a mere estimation of initial ablated mass causedby the arrival of the X-rays. For a more realistic simula-tion of the ablation of flibe under IFE X-ray irradiation,it is recommended that models be considered that ac-count for additional phenomena such as re-radiation fromhot vapor, surface condensation and evaporation of theablated material, and use of hot opacities.

IV.A.3. TSUNAMI

TSUNAMI refers to a series of hydrodynamics codesdeveloped and maintained since the early 1990s at UCB.The first two versions of the code were developed tomodel the gas dynamics inside the original HYLIFE-IItarget chamber.6 Chen42 developed the first 1-D version

to assess X-ray ablation and hydrodynamics expansionof target debris and ablated molten salt in the interior ofthe thick-liquid pocket. Concurrently, Liu24,25 wrotethe first 2-D version of TSUNAMI to model hydro-dynamics venting through the “slot” array of slab jets.In addition, Liu24 developed a 1-D version that in-cluded a condensation0evaporation model. TSUNAMIwas later modified and employed to model ablation andgas dynamics phenomena in the NIF target cham-ber.43,44 Later, Scott’s version was expanded to includesome radiation transport45 and assess its effects on thegas dynamics in the HYLIFE-II chamber. Simulationsencompassing both the inside of the target chamber andthe array of jets are presented in Ref. 45.

TSUNAMI was then upgraded with a user-friendlyinput file builder and output file processor. This version,TSUNAMI 2.8, was used to predict the mass and energyfluxes at the beam ports of a HYLIFE-II-like chamber.22

TSUNAMI 2.8 was then employed to model the gas dy-namics inside a beam tube,26 and the first “integrated”simulation was presented in Ref. 23. This simulation cov-ered the whole domain of early-time gas dynamics,namely, from the target explosion location to the site ofthe magnetic shutters. Figure 15 shows snapshots ofthe gas density at various times in the RPD chamber.23

The simulation shows how the target and ablated debris

Fig. 15. TSUNAMI density contour plots at various times ~the density of the liquid and solid structures is arbitrarily low!.



pressurize the pocket and then vent through the thick-liquid structures.

The TSUNAMI physical models and assumptionsused for the RPD simulations are summarized as follows:

1. The compressible Euler equations are solvedthrough a Godunov’s scheme.

2. Viscous and dissipative effects are neglected sinceviscous and dissipative timescales are much longer thanthe typical run time of the order of a millisecond.

3. A real gas equation of state is used.

4. Mass transfer is neglected, and the composi-tion of the ablated molten salt is assumed to remainstoichiometric.

5. Radiation transport is neglected since earlier sim-ulations including radiation transport showed that radi-ation plays a secondary role.

6. Initial conditions are given by considering therelevant phenomena in the very short term ~such as pho-ton and ion energy deposition!.

7. Neutrons are neglected since the background gasand ablated molten salt are virtually transparent to theneutrons. The neutron energy will be deposited muchmore deeply into liquid structures. This would cause iso-choric heating and could induce disruption of some jets.Assuming that proper design of the target chamber wouldavoid generation of high-speed slugs ~.1 m0s!, neutronisochoric heating can be neglected for sub-millisecondsimulations.

8. A fairly efficient model computes the ablationthickness and the energy profile of the X-ray ablatedlayer.

9. Fast ions will be stopped in the expanding ab-lated molten salt. The mass of fast ions is small comparedto that of ablated molten salt, and their energy is smallcompared to the target energy converted into X-rays ~2versus 25%!. Their effect is neglected in the RPD simu-lation. Slow target-debris ions are modeled as a sphere ofmolten salt.

10. Two different boundary conditions are imposed:open and reflective. An open boundary is used wheneverpossible to limit the size of the computational domain. Areflective boundary simulates a solid surface or an axis0plane of symmetry. Most versions of TSUNAMI assumethat a liquid boundary could be modeled as a reflective,stationary boundary.

11. Convective transport is assumed to dominate heatand mass transfer in the vicinity of the jets, heated to hightemperatures by the target X-rays.

12. The liquid vortex surface is assumed to be per-fectly condensing because of its low temperature. This

assumption was useful to show the necessity of usingmagnetic shutters to supplement the annular vortex. Thedroplet spray is assumed to be perfectly condensing aswell.

TSUNAMI 2.8 was recently employed to model avariant of the thick-liquid RPD chamber that accommo-dates the assisted-pinch final transport scheme.46 TSU-NAMI 2.8 also showed good simulation of the gasdynamics phase from LLNL’s Condensation Debris Ex-periment.47 UCLA, in collaboration with UCB, has im-plemented Liu’s model into an early version of TSUNAMI2.8 and used the code to model the UCLA flibe conden-sation experiment, described in Sec. IV.B.2 ~Ref. 48!.Agreement between simulation and experimental resultswas satisfactory.

The next version of TSUNAMI, “Visual Tsunami,”makes use of modern programming languages and soft-ware and includes a user-friendly input file builder andoutput file processor.27 It includes a three-dimensional,multispecies, ablation and hydrodynamics code with con-densation boundaries based on Schrage’s model.49 VisualTsunami is being benchmarked. Models for radiation andaerosol transport have been developed and may be im-plemented into future versions of Visual Tsunami.47

IV.A.4. SPARTAN

SPARTAN is being developed at UCSD as a fullyintegrated computer code for modeling and studyingdry-wall chamber dynamic behavior in the hydrodynam-ics timescale, including: the dynamic gas response totarget implosion; the effects of various heat sourcesand transfer mechanisms such as photon and ion heatdeposition, and chamber gas conduction, convection andradiation; the chamber wall response and lifetime; and thecavity clearing.At present, SPARTAN solves the 2-D tran-sient compressible Navier-Stokes equations. The code iswritten in a modular fashion so that extrapolation to three-dimensional geometry is straightforward. The behavior ofstrong shocks born out of the target blast is captured ac-curately by a second-order Godunov algorithm. Diffusiveterms ~viscosity and thermal conductivity! are includedand can depend on state variables ~e.g., local tempera-ture!. The uniform accuracy throughout the fluid domainis obtained through adaptive mesh refinement. This is es-sential as the width of the shock region is usually severalorders of magnitude smaller than the chamber dimen-sions. The arbitrary chamber geometry is incorporated intoa Cartesian grid and resolved by an embedded boundarymethod. The details of numerical methods utilized inSPARTAN and the convergence tests are given in Ref. 50.Example results are shown in Fig. 16 for a 154-MJ direct-drive target case in a 6.5-m-radius chamber filled withxenon ~with an atom density of 1.6�1021 m�3!. The sim-ulation results demonstrate the robustness of SPARTANnumerical algorithms in studying the highly nonlinearchamber dynamics with fast moving discontinuities.



SPARTAN has been developed to model the cham-ber dynamics of dry wall concepts. It could be a usefultool if applied to the liquid wall concept also; however,the capability to model liquid wall specific mechanismssuch as ablation, condensation, and aerosol formationand behavior would need to be included.

IV.A.5. TOPGUN

A useful model that integrates the coupled transportbehavior of gases and aerosols is the TOPGUN codedeveloped at INL ~Ref. 51!. The code was originallydeveloped to simulate plasma-gun experiments used togenerate and characterize aerosols representative of thoseproduced in the disruption of a tokamak fusion reactor. Ithas recently been modified to study the generation andbehavior of aerosols in the context of IFE chamber clear-ing.28 TOPGUN includes a 1-D gas dynamics model fora multiple-charge species, single-component gas, and zero-dimensional aerosol dynamics model coupled to the gasdynamics model by source0sink terms in mass, energy,and momentum, in addition to cell-convection terms foraerosol transport. The solution algorithm incorporatessemi-implicit differencing and subcycling of the aerosolmodel within the gas dynamics solution. Although thegas dynamics model is not as suitable for IFE postshotchamber conditions as other codes ~e.g., SPARTAN andBUCKY!, the essential features are present that providea reasonable estimate of conditions for aerosol formationand growth. The solution technique of TOPGUN does

permit modifications and extension of the aerosol model,allowing exploration of mechanisms relevant to chamberdynamics and clearing. Studies performed to date haveincorporated aerosol transport mechanisms discussed inSecs. III.A.4 and III.B.2. Results of an example TOP-GUN simulation for aerosol formation are shown in Fig. 17~Ref. 28!. Aerosol size distributions at various times are

Fig. 16. Example simulation of an IFE dry-wall chamber with xenon as background gas. ~a! Geometry of the chamber with theinitial conditions imposed from a 1-D solution obtained by the BUCKY code. The temperature field, as shown in ~b!, ~c!,and ~d!, is given 100 ms after the target implosion. Solution ~b! is obtained by setting diffusive terms to zero. Atemperature-dependent viscosity is estimated by an empirical law in ~c!, while the conductivity is neglected. Case ~d!features a similar empirical law for conductivity while the viscosity is set to zero. In all the cases the protective gas isxenon.

Fig. 17. TOPGUN simulation results for aerosol production ina 6.5-m spherical chamber with a liquid lead wallindicate a significant population of moderately sizedaerosol particles existing in the central region of theIFE chamber.



shown for the central region of an example 6.5-m spher-ical chamber protected by a thick wall of liquid lead. Thesimulation showed that material vaporized from the wallexpands, cools, condenses, grows, and is convectedthrough the chamber, giving the size distributions shownin Fig. 17. Benchmarking of TOPGUN was performedusing aerosol size data from the plasma-gun experi-ment,51 with TOPGUN reasonably matching the mea-sured size distributions of particles less than ;50 mm.Components of the TOPGUN aerosol model would bevery useful in a more comprehensive IFE chamber dy-namics simulation code, and implementation of similarmodels into the next version of TSUNAMI is beingconsidered.

Key R&D needs to help in better modeling and un-derstanding of aerosol formation and behavior in a TLWchamber should include

1. Extending models to include conditions more rel-evant to TLW chamber conditions ~and choices offluid, i.e., flibe!, such as ionization and coolingplasma effects for gas dynamic and aerosol nu-cleation, multiple-component materials, and im-pact deposition and reflection of aerosols.

2. Performing experiments to verify simulations ofaerosol dynamics, and studying the relevancy ofother proposed condensation mechanisms, such aslaser ablation in background plasma for ion-inducednucleation studies ~with extension to multiple com-ponents!, high velocity aerosol impact on liquidsurfaces, and condensation behavior of pure flibe.

IV.B. Experiments

Table IV shows the capabilities of various existingexperimental facilities in simulating and measuring TLWchamber dynamic mechanisms. They include: the laser0material interaction laboratory ~UCSD!; the X-ray facil-ity ~XAPPER at LLNL!; the Z facility at the SandiaNational Laboratories ~SNL!; the plasma-gun facility~UCLA!; and the shock tube facility ~UW!. In addition,hydraulic facilities can provide valuable data on jet ref-ormation and aerosol source terms from jet [email protected]., the facilities at UCB and the Georgia Institute ofTechnology ~Georgia Tech!#. Again, this list is not inclu-sive as there may be other facilities that could be adaptedto help address some of the key issues associated withliquid wall chamber dynamics. However, they provide agood snapshot of current experimental capabilities thatcould be utilized to help understand and solve those issues.

IV.B.1. Laser Simulation Experiments (UCSD)

Short-pulse lasers can provide heat fluxes with pro-totypical energy density and timescale to simulate thethermal, mechanical, and phase-change response of liq-uid wall IFE chambers. Their advantages include ease of

operation, low cost, and flexibility. Typically, a laser willbe directed at a planar sample that represents only a por-tion of the wall of a chamber. Some of the light will beabsorbed very close to the surface ~the remainder is re-flected!; typical absorption depths for metals are of theorder of several nanometers. The intensities needed toreach IFE-relevant temperatures are quite modest, suchthat laser-induced breakdown is usually avoidable.

The small absorption depth of a laser is one of the keyconcerns with the fidelity of the simulation, and as such,laser simulation would be better suited to IFE cases withshorter ablation depth ~e.g., for larger chambers, R; 5 mor larger, more relevant to a wetted-wall case!. Figure 18shows a thermal analysis of a Pb wall following a laserpulse as compared with a burst of X-rays. The laserenergy has been scaled in order to match the late-stagethermal response of the X-ray case. The X-ray spectrumwas obtained from a 458-MJ indirect-drive target spec-trum.52 Figure 18 shows that during the pulse the surfacetemperature rises a factor of;2 higher in the case of thelaser irradiation, but only in a very thin region ~;100 nm!.After the pulse terminates at;2 ns, the near-surface tem-perature equilibrates very quickly, and the resulting ther-mal diffusion wave is nearly identical in the two cases.

In an evaporating system, it is perhaps more impor-tant to maintain similarity in the mass that is evaporatedor explosively ejected. Since the laser is absorbed moreclosely to the surface, less mass will evaporate for agiven fluence ~J0cm2!, but that mass will absorb moreenergy. It will come off hotter and be more prone toexplosive boiling. A qualitative comparison can be madebetween the conditions predicted to occur following anIFE explosion and the conditions often observed in laserablation plumes. Laser ablation plumes with initial tem-perature of the order of 1 to 20 eV and density of the orderof 1021 cm�3 are easily obtained.53 These temperaturesand densities are very similar to those expected follow-ing an ablation plume resulting from IFE X-rays, as sum-marized in Table VI.Ablation plumes are highly dynamic;as the plume expands, the temperature rapidly falls below1 eV ~after 50 to 100 ns!, the density falls, and the vaporinterpenetrates the surrounding medium.

When using a simulated energy source, the most im-portant criterion is to clearly understand the physics in-volved so that the results can be properly scaled. Oneneeds to exercise caution when simulating X-rays with alaser, but roughly similar material conditions can beachieved such that meaningful experiments are possible.

IV.B.2. X-Ray Facility (XAPPER)

The XAPPER X-ray damage experiment, which islocated at LLNL, is capable of providing high-flux burstsof soft X-rays at repetition rates of up to 10 Hz. Fluencescan be as high as ;5 J0cm2 in a 40-ns pulse with anaverage X-ray energy of ;120 eV. The high repetition



Fig. 18. Thermal response of the surface of Pb exposed to a 2-ns laser pulse and a 2-ns soft-X-ray pulse. The time followinginitiation of the energy source is 2, 5, 10, and 50 ns.

TABLE VI

Comparison of Laser-Induced Ablation Plume Parameters to IFE Liquid Wall Parameters Under X-Ray Energy DepositionSpectrum from 458-MJ Indirect-Drive Target

Parameter X-Rays from Heavy-Ion Target ExplosionLaser Simulation~107 to 1010 W0cm2 !

Pulse length ;2 ns 8 nsAttenuation length 1 to 5 mm ~Pb0flibe! 10 nmAblation depth ;1 to 10 mm at R; 5 m ~wetted wall concept!

;100 mm at R; 0.5 m ~TLW concept!1 to 2 mm ~thermal!

Initial plumeTemperature ,30 eVa 1 to 20 eVDensity ,nc ; 10210cm3 ;10210cm3

Zeff Not available 0 to 3

Plume at 1 msTemperature 0.5 to 1.5 eVPlasma density 3 � 1018 cm�3

Zeff 0 to 1

Background gas density 0 to 50 mtorr ~at 300 K! 0 to 1 atm ~at 300 K!Background gas temperature .10008C ~wetted wall concept! Room temperature

;5008C ~TLW concept!Spot size 1000 m2 1 mm2

Geometry Quasi–1-D Quasi–1-D

aRough estimate from ABLATOR.



rates offer shots on demand as well as the possibility ofobtaining favorable statistics by performing a large num-ber of shots. XAPPER has demonstrated continuous 10-Hzoperation for 2 � 105 pulses and can be operated for;107 pulses prior to requiring minor maintenance. Ad-ditional details on the XAPPER experiment can be foundin Refs. 54 and 55.

To a somewhat lesser extent than for the laser, thesoft-X-ray energy is absorbed close to the material sur-face. For example, the mean free path of 120-eV X-raysis ;75 nm in flibe. This longer deposition lengthmay enable the experiment to more closely follow thetime-temperature history expected from an actual IFEexposure.

XAPPER would be well suited for study of liquidwall ablation and condensation. Implementation of liq-uid wall experiments would require several relativelyinexpensive modifications. First, a small, custom opticwould be designed and fabricated. Such an optic woulddeliver a larger, flat-topped X-ray pulse as opposed to thesmall, highly peaked pulse currently available. Second, asmall target chamber ~15- to 20-cm diameter! would bedesigned and built. Instrumentation might include resid-ual gas analysis ~already available on XAPPER! and otherdiagnostics similar to those described below in Sec. IV.B.4.Early experiments would begin with frozen materials,but later experiments could take advantage of currentlyavailable heaters to provide a liquid target.

One concern in the testing of liquid wall vaporiza-tion and condensation is the initial state of the liquid.Some argue that a flowing or continuously renewed sur-face is required in order to obtain results that are trulyrelevant to TLW systems.56 It is possible to design a verymodest ~small! flow loop that could meet this require-ment. Clearly, such experiments would be more compli-cated and, thus, more expensive to conduct.

IV.B.3. Z Facility

The Z machine at SNL is the world’s most powerfulX-ray machine.57 A multiwire fast Z-pinch load on Zroutinely produces up to 1.8 MJ of X-rays at a powerlevel of ;230 TW and at fluences that can exceed 3000J0cm2 on a single-shot basis. Testing of materials on Z isdone on an add-on basis, when available on scheduledshots. By varying the sample location, and using aper-tures and filters, an extremely uniform X-ray fluence canbe obtained. At distances of the order of 50 cm from theZ-pinch source, fluences can be produced in the range of1 to 50 J0cm2 over a sample area of several square cen-timeters or more. With appropriate X-ray filters, an X-rayspectrum above 1 keV is routinely attainable at IFE-relevant fluences. Through use of apertures, filters, andpossibly shutters, the effects of debris from the Z-pinchcan be minimized. Postshot diagnostics include surfaceprofilometry measurements, scanning electron micros-copy, and ion milling.

Recently, Z has been used to examine solid materialablation at relatively high fluences ~tens of J0cm2! toexamine solid-surface roughening with no net ablation atsmaller fluences ~a few J0cm2! and to establish the thresh-old for solid-surface roughening ~which is of the order of1 J0cm2 or less!. In this role, Z has been very useful intesting many candidate first wall solid materials ~C, W,W0Re, etc.!. For liquid wall material testing, Z is uniquelyqualified to produce fluences at all of the levels thatwould occur in a liquid wall power plant—from fluencelevels of 1 J0cm2 to model the effects of wetted walls atseveral meters from the target all the way up to fluencelevels of 2000 J0cm2 to model the closest TLWs ~at;50 cm from the target! envisioned for IFE power plants.The capability for producing, testing, and diagnosing liq-uid targets on Z could presumably be done when supportbecomes available.

Currently, the capability for testing heated samples~on add-on shots on Z! at temperatures up to 12008C isavailable. A sample test area diameter of 1 cm2 can beshared by four samples on each shot. The X-ray fluenceis adjustable by varying the distance from the Z-pinch,and the X-ray spectrum can be manipulated through theuse of X-ray filters.

IV.B.4. Plasma-Gun Facility (UCL A)

The objective of the UCLA plasma-gun experimen-tal facility is to study vapor condensation and chamberclearing rates in IFE-relevant conditions using prototyp-ical materials. The main attractiveness of the facility isthe capability of generating a large amount of excitedvapors in relatively short periods ~10�4 s!, allowing thedecoupling of the generation, injection, and expansion ofthe vapors from the chamber clearing process ~10�1 s!~Ref. 58!. With the electrothermal source typically oper-ating at 30% of its full capability, ;0.4 g of the materialof interest can be ablated. This allows one to produce thesame initial vapor density in a 5-� test chamber as ex-pected in the HYLIFE-II chamber from the vaporizationof the liquid pocket surfaces.6 Another fundamental char-acteristic of the facility is the capability of testing IFEprototypical materials, in particular, flibe. Although thefacility has been mainly operated using only the nontoxiccomponent of the molten salt ~LiF!, preliminary runshave demonstrated the possibility of using flibe in thesource.59

The facility has been mainly designed and scaled tosimulate the IFE chamber clearing process. For this pur-pose, the condensation chamber is equipped with sen-sors that are capable of measuring the pressure at differentlocations over a wide range that characterize the clear-ing process. A steady-state residual gas analyzer is thenused to evaluate the presence of noncondensable impu-rities. Typical results for LiF vapor and CH4 vapors arepresented in Fig. 19. Time-resolved spectroscopic analy-sis of light emission from the excited gas coupled with



Langmuir probes is currently tested to better character-ize the local gas thermodynamic properties ~density andtemperature!. The condensation chamber is also equippedwith a photodiode system to measure the velocity of theshock front as it first enters the chamber. This is donemainly to compare gas velocity measurements with theTSUNAMI code simulations of vapor propagationthrough the chamber. Another inherent capability of thecondensation chamber regards the investigation of in-flight condensation and aerosol formation, which wouldjust require additional diagnostics for the time-resolveddetection of droplet formation. Currently, only passivediagnostics are employed, such as collecting buttons forsurface postanalysis.

IV.B.5. UW Shock Tube Facility

The UW shock tube ~shown in Figs. 20 and 21! isvertical, with an outer round and inner square cross sec-tion ~25.4 cm � 25.4 cm! so as to have parallel walls toperform flow visualization anywhere along the tube ~e.g.,Ref. 60!. The facility’s structural capability allows forthe production of Mach-5 shock waves in air at atmo-spheric pressure. The driver section is 2.0 m long; thedriven section is;7.6 m long and composed of modularsegments of different lengths that can be arranged at will.Special sections are available to contain one or morewater layers and one or more metal cylinders and toperform flow visualization. These sections can be mountedanywhere along the length of the tube. Available instru-mentation includes piezoelectric pressure transducers, sev-

eral high-speed data-acquisition channels, continuouswave ~cw! and pulsed lasers, several charge-coupled de-vice ~CCD! cameras ~both scientific grade and high speed!,and a large variety of optical components.

The facility is very well suited to study the effect ofa shock wave upon one or more stationary liquid layerswith either circular or rectangular cross section. Experi-ments so far have concentrated on the measurements ofthe x-t trajectories of the shock and of a single, initiallystationary, water layer and on the changes in the spatialand temporal distributions of pressure around a solid cyl-inder with and without a stationary water layer placedabout four diameters above the cylinder.

Experiments in the near to midterm future will con-centrate on two main areas: ~a! the behavior of multiple,stationary water layers subjected to impulsive accelera-tion and their ability to reduce the peak pressure load ona single cylinder or bank of cylinders and ~b! the mech-anisms that lead to the fragmentation and disruption ofthe water layer and possible formation of aerosols. Longer-term plans include experimental campaigns to study theinteraction of a shock with single or multiple liquid jetswith both circular and rectangular cross sections ~simu-lating, for example, liquid impact on HIBALL flow tubesor HYLIFE jets!.

IV.B.6. Hydraulic Facilities

Hydraulic facilities such as those at UCB and at Geor-gia Tech can be utilized to help understand the dynamics

Fig. 19. Pressure history of Teflon and LiF shots from UCLA’splasma-gun experimental facility.

Fig. 20. UW shock tube schematic.



of the liquid jet formation for a TLW chamber such asHYLIFE-II that utilizes oscillating jets to form a pocketprior to each shot as well as an array of crossing jets infront of beam ports ~see Fig. 2!. A key issue is linked tothe quality of the jets to avoid droplet formation in par-ticular if the nozzle starts to wear out ~because of erosionand0or corrosion! or if small-scale impurities or depositscause local nozzle obstruction.

IV.B.6.a. UCB Hydraulic Test Facilities. Several hy-draulic facilities at UCB are used to help understand thedynamics of thick-liquid jet formation, disruption, andrecovery. These are described below. In addition, UCB’sexperimental activities include the investigation of theproperties of both flibe and flinabe and, in particular, oftheir vapor pressures as a function of temperature. Theattractiveness of flinabe stems from its lower meltingpoint and its low vapor pressure at temperatures belowthe melting point of flibe, which makes it compatible foruse in neutralized ballistic transport beam tubes.7,22,26

Target Chamber Liquid Jet Structures. As presentedin Secs. II.A and III.B.3, the RPD thick-liquid structuresconsist of an oscillating voided pocket, cylindrical jets,and beamline vortices. All three kinds of jet structures~see Fig. 22! have been demonstrated experimentally inscaled experiments at UCB. Of particular interest forFig. 21. Image of UW shock tube facility’s bottom third.

Fig. 22. Three of UCB jet experiments: high-Reynolds-number cylindrical jets, beamline vortex flow, and oscillating voidedjets.29



fusion systems are the vortex flow surface roughness,surface renewal, and droplet ejection rate that remain tobe characterized. Particle image velocimetry will pro-vide detailed velocity and turbulence information on thevortex flow.61

As an alternative to HYLIFE-II-like chambers, whichis the main focus of this paper, another thick-liquid cham-ber, the newly introduced “vortex chamber,” is beinginvestigated.46,61 The vortex chamber would consist of aneutronically thick swirling layer that runs over the struc-tural first wall. A thick-liquid IFE chamber, in whichbeam final focus and transport in the chamber would beperformed by a set of solenoids, is depicted schemati-cally in Fig. 23.

UCB demonstrated the feasibility of establishing andcontrolling the thick-liquid layer in a cylindrical cham-ber, as shown in Fig. 24. This work is still at an early stage,and further effort is required to adapt this work to curvedgeometries for use in IFE and, potentially, MFE chambers.

Liquid Jet Response to Ablation and Pocket Pressur-ization Impulse Load. The Vacuum Hydraulic EXperi-ment ~VHEX!, shown on the right side of Fig. 22, wasdesigned to study thick-liquid jet structure formation,disruption, and recovery. Past work focused on the dis-ruption and recovery of the thick-liquid pocket.29 Exper-iments conducted on VHEX demonstrated the firstoscillating pocket and the timeliness of the pocket refor-mation following the disruption caused by the ablationand pocket pressurization impulse. The validity of thesnowplow model of jet disruption was confirmed, asshown in Fig. 25.

Current work includes upgrading the firing mecha-nism of VHEX for higher-fidelity experimental simula-tions of scaled pocket disruption and reformation. TheVHEX used blank shotguns to simulate the IFE im-pulse. High explosives are now being used for a betterrepeatability and quality of the impulse delivered to thejets.61 New disruption experiments will use a scaledpocket that includes oscillating voided slab jets and apartial array of cylindrical jets. This work aims at prov-ing that the pocket and cylindrical jets can be restoredbefore the next shot and assessing how the jets break upinto droplets. Use of a different nozzle and other minormodifications to the facility will allow simulation of aZ-IFE thick-liquid curtain as well.

Fig. 23. Schematic of the vortex chamber.46 The first wall isnot depicted.

Fig. 24. UCB large-vortex experimental setup.61

Fig. 25. Comparison of snowplow compression model withexperimental data ~the position of the target-facingsurface of the slab that makes up part of the oscillat-ing voided jet is shown as a function of time!.30



IV.B.6.b. Georgia Tech Hydraulic Test Facilities.

Three IFE-relevant hydraulic test facilities are avail-able at Georgia Tech; two of them, the Forced Film TestFacility and the Porous Wetted-Wall Test Facility, areapplicable to a wetted-wall concept; the third one, theLarge-Scale Hydraulic Test Facility, is applicable to aTLW concept and is described in this section.

The Georgia Tech Large-Scale Hydraulic Test Fa-cility is a recirculating flow loop for the study of turbu-lent water jets issuing into ambient air ~see Fig. 26!.Rectangular jets with Reynolds numbers Re � 1.0 �104 to 1.5 � 105 and Weber numbers We � 5.0 � 102 to2.4 � 104 can be examined. The jets can be either sta-tionary or oscillated at prescribed frequencies ~up to10 Hz! and amplitudes, with Strouhal number St � 6.0 �10�3 to 6.0 � 10�2. An external chiller allows the sys-tem to operate isothermally for an indefinite period oftime. The end flow elements, flow conditioner ~E! andnozzle ~G!, are removable for replacement or modifica-tion. Initial conditions may also be modified using anexternal boundary layer cutter ~I!.

Several experimental setups for the study of differ-ent flow phenomena are available at this facility. Initialconditions are evaluated by measuring velocity and tur-bulence intensity profiles just upstream of the nozzle exitusing laser-Doppler velocimetry ~LDV!. Planar-laser–induced fluorescence is used to examine the free surface

of the jet at different downstream locations. The water inthe test loop is dyed with a fluorescing salt and illumi-nated by a laser sheet ~L!. A CCD camera ~M! images thefree surface as the interface between fluorescing water~bright! and nonfluorescing air ~dark!. Jet cross section,free-surface fluctuations, and average free-surface posi-tion are all quantifiable by this technique. The primaryturbulent breakup of the jet is estimated with a masscollection apparatus ~K!. Cuvettes of known mass arepositioned at a given distance away from the free surfacefor a specified period of time. The mass collected in thecuvettes then gives a measure of mass of droplets ejectedat the free surface.

V. CONCLUSIONS AND FUTURE R&D

Thick liquid wall chambers offer the advantage ofmoderating the high-energy neutron output from the tar-get, thereby reducing the radiation damage rate and lead-ing to longer lifetimes for the first wall and blanketstructures. By utilizing a lithium-containing liquid, suchas the molten salts flibe or flinabe, the TLW also servesas the tritium-breeding blanket and the primary coolantsince it directly absorbs all of the short-range target emis-sions ~X-rays and target debris! and most of the neutronenergy. The key issues to be addressed to realize thepotential of TLW chambers can be summarized in threeprimary categories: ~a! issues related to the repetitivenature of IFE, including liquid wall response to the pulsedenergy release and recovery of chamber conditions be-tween pulses ~reformation of the protective liquid con-figuration, clearing of drops, and vapor that could interferewith the next shot!; ~b! issues related to shock mitigation,including the ability of multilayer TLW configurations toattenuate shocks and thus protect the structural wall frompossible damaging effects of shocks; and ~c! issues re-lated to the use of molten salt ~the preferred liquid! orliquid metal, including material compatibility ~corro-sion!, target debris transport and removal, tritium recov-ery, heat transport, and power conversion.

This paper has focused on the first category. Thechamber dynamics in a TLW concept such as HYLIFE-IIare governed by a number of different mechanisms oc-curring at different times in the liquid wall and chamberfollowing the target microexplosion. The photon energydeposition at very short times dictates the ablation mech-anisms, including explosive boiling and, possibly, spall-ing created by the resulting impulse on the wall. Isochoricheating from neutrons could create additional jet breakupdepending on the target yield and jet location. The be-havior of the ablated material in terms of aerosol forma-tion and then transport is an important issue as any aerosolremnant after the pocket reformation or at the axial openends of the pocket might affect the driver performance.The liquid jet quality is also important as any spray couldprovide additional aerosol material and the behavior ofFig. 26. The Georgia Tech Large-Scale Hydraulic Test Facility.



the oscillating jets in forming the pocket prior to eachshot must be also highly reliable. Typical capabilities ofexisting models and experiments in addressing these is-sues have been described with a view of helping to betterrecognize where there are gaps in current understandingand capabilities and where future R&D effort should bedirected.

The information from this paper is intended to helpin the assessment of R&D needs for TLW chambers, suchas the recent one carried out by IFE researchers as part ofa Virtual Laboratory for Technology ~VLT! exercise.62

The list of the R&D required to address and resolve keyissues for TLW chambers included the following itemsrelated to the TLW chamber dynamics, which in generalreflects well the observations from this paper:

1. The need for fundamental science research onvarious aspects of TLWs: For example, turbulence ef-fects on free surfaces, shock propagation and mitigation,aerosol formation and evolution, etc. These are typicallyuniversity-scale tests and research, which have provenvaluable in advancing TLW chambers to their currentstate.

2. Hydraulics Test Facility: To demonstrate the typeof flow configurations needed for TLW chambers at ; 1

4_

scale. A simulant fluid ~e.g., mineral oil or water! wouldbe used to minimize costs. The facility would simulate~e.g., by using high-explosive detonations! the disruptionof the flow by fusion energy pulses to study the ability toclear the chamber of drops in time for the next shot. Thefacility would also be used to study and validate scaledshock mitigation techniques.

3. Chamber Dynamics Test Facility: To study thedynamics of vaporization and condensation of moltensalt or liquid metal in the chamber with a focus on as-pects that are unique to the working fluid and cannot besimulated in the hydraulic test facility.

Other R&D items included liquid test loops and heattransfer component facilities. While much more work isneeded to define experiments, design the test facilities,and estimate construction and operating costs, prelimi-nary estimates from the VLT assessment indicate thatthis type of R&D could be conducted at the approxi-mately $10 million0yr level.

ACKNOWLEDGMENTS

This paper was motivated by the informative presentationsand discussion at the 2003ARIES Town Meeting on Liquid WallChamber Dynamics. The authors are grateful to all participantsof the Town Meeting and to the ARIES-IFE Team for their in-spiring contributions to the discussion. This paper was sup-ported in major part by grants from the U.S. Department ofEnergy, in particular under contract DE-FC03-95ER54299.

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IFE THICK LIQUID WALL CHAMBER DYNAMICS: GOVERNING MECHANISMS AND MODELING AND EXPERIMENTAL...

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