Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain _REVIEW ARTICLE.pdf

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Development of the indirect-drive approach to inertial confinementfusion and the target physics basis for ignition and gainJohn LindiLawrence Livermore National Laboratory, Livermore, California 94551(Received 14 November 1994; accepted 14 June 1995)Inertial confinement fusion (ICF) is an approach to fusion that relies on the inertia of the fuel massto provide confinement. To achieve conditions under which inertial confinement is sufficient forefficient thermonuclear burn, a capsule (generally a spherical shell) containing thermonuclear fuelis compressed in an implosion process to conditions of high density and temperature. ICF capsulesrely on either electron conduction (direct drive) or x rays (indirect drive) for energy transport todrive an implosion. In direct drive, the laser beams [or charged particle beams) are aimed directlyat a target. The laser energy is transferred to electrons by means of inverse bremsstrahlung or avariety of plasma collective processes. In indirect drive, the driver energy (from laser beams or ionbeams) is first absorbed in a high-2 enclosure (a hohlraum), which surrounds the capsule. Thematerial heated by the driver emits x rays, which drive the capsule implosion. For optimallydesigned targets, 70%-80% of the driver energy can be converted to x rays. The optimal hohlraumgeometry depends on the driver. Because of relaxed requirements on laser beam uniformity, andreduced sensitivity to hydrodynamic instabilities, the U.S. ICF Program has concentrated most of itseffort since 1976 on the x-ray or indirect-drive approach to ICE As a result of years of experimentsand modeling, we are building an increasingly strong case for achieving ignition by indirect driveon the proposed National Ignition Facility (NIF). The ignition target requirements for hohlraumenergetics, radiation symmetry, hydrodynamic instabilities and mix, laser plasma interaction, pulseshaping, and ignition requirements are all consistent with experiments. The NIF laser design, at 1.8MJ and 500 TW, has the margin to cover uncertainties in the baseline ignition targets. In addition,data from the NIF will provide a solid database for ion-beam-driven hohlraums being considered forfuture energy applications. In this paper we analyze the requirements for indirect drive ICF andreview the theoretical and experimental basis for these requirements. Although significant parts ofthe discussion apply to both direct and indirect drive, the principal focus is on indirectdrive. 0 1995 American Institute of Physics.

TABLE OF CONTENTSI. ICF OVERVIEW .......................... 3933II. HISTORICAL DEVELOPMENT OF

INDIRECT DRIVE IN THE U.S. ICFPROGRAM .............................. 3940

III. IGNITION PHYSICS. ..................... 3952IV. PULSE SHAPING ......................... 3955V. IMPLOSION DYNAMICS. ................. 3958VI. HYDRODYNAMIC INSTABILITY ........... 3961VII. CAPSULE GAIN .......................... 3969VIII.Ix.X.XI.IXII.XIII.XIV.

HOHLRAUM COUPLING EFFICIENCY. . . . . 3969HOHLRAUM RADIATION UNIFORMITY.. . . 3979COMBINED TESTS OF SYMMETRY ANDHYDRODYNAMIC INSTABILITY. . . . . . . . . . 3992HOHLRAUM PLASMA CONDITIONS. . . . . . . 3994HOT ELECTRON PREHEAT. . . . . . . . . . . . . . . 4002NATIONAL IGNITION FACILITY ANDIGNITION TARGETS. . . . . . . . . . . . . . . . . . . . . 4004INERTIAL FUSION ENERGY. . . . . . . . . . . . . . 4015

I. ICF OVERVIEWInertial confinement fusion (ICF) is an approach to fu-sion that relies on the inertia of the fuel mass to provideconfinement. l-3To achieve conditions under which inertial confinementis sufficient for efficient thermonuclear burn, high-gain ICFtargets have features similar to those shown in Fig. 1. A

capsule generally is a spherica shell filled wi th low-densi tygas (s1.0 mg/cm3). The shell is composed of an outer re-gion, which forms the ablator, and an inner region of frozenor liquid deuterium-tritium (DT), which forms the mainfuel. As shown in Fig. 2, the cross section4 for DT fusionreactions is approximately two orders of magnitude largerthan that for the next largest reaction in the relevant tempera-ture range, up to about 40 keV. Hence, ignition and high-gaintargets planned for the near term use DT fuel. Many of thenear-term targets discussed later, which only use neutrons fordiagnostic purposes, contain deuterium-deuterium (DD)fuel. Energy from a driver is delivered rapidly to the ablator,which heats up and expands. As the ablator expands outward,Phys. Plasmas 2 (ll), November 1995 1070-664X/95/2(1 1)/3933/92/$6.00 Q 1995 American Institute of Physics 3933

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Drive L Capsule ablatornsrgy 3 i

r.;-..K MainK VI,,\ fuel layer

Driver-target coupling3 I, 51Oi5W/cm2 or 5300 eVTo control:l Absorption/preheat. X-ray conversionl Transport/drive

I ~~~~~~~ 2 =Conv;;rce = 20-35 j ,cI;~,9yoL IL I 18 Stability: _L = in-filght L 25-35 =+ $ Z 4 x 1OW/Cm* OrAR aspect ratfo 250eVsurface cl000 ii

ignition: l Ti = ltj kevl prHs - 0.3 gtcm * 4m,3-4x107cIn/sfor Eddvar 1-2 MJ

FIG. 1. The target physics specifications on current ICF igniti on targets include constraints on drive intensity, symmetry, stability, and ignition.

the rest of the shell is forced inward to conserve momentum.The capsule behaves as a spherical, ablation-driven rocket.The efficiency with which the fusion fuel is imploded typi-cally lies in the range of 5%-15%. The work that can bedone on the imploding fuel is the product of the pressuregenerated by the ablation process times the volume enclosedby the shell. Hence, for a given pressure, a larger, thinnershell that encloses more volume can be accelerated to ahigher velocity than can a thicker shell of the same mass.The peak achievable implosion velocity determines the mini-mum energy (and mass) required for ignition of the fusionfuel in the shell.In its final configuration, the fuel is nearly isobaric atpressures up to -200 Gbars but consists of two effectivelydistinct regions-a central hot spot. containing -2%-5% ofthe fuel and a dense main fuel region comprising the remain-ing mass. Fusion initiates in this central region, and a ther-monuclear burn front propagates radially outward into themain fuel, producing high gain. The efficient assembly of thefuel into this configuration places stringent requirements on

IO-= 100 IO 102 ldTempetature (keV)

FIG. 2. Thermonuclear reaction rates are strongly tempera ture dependent,and DT is by far the easiest fuel to ignite.3934 Phys. Plasmas, Vol. 2, No. 11, November 1995

the details of the driver coupling, including the time historyof the irradiance and the hydrodynamics of the implosionIn the implosion process, several features are important.The in-flight aspect ratio ( IFAR) is defined as the ratio of theshell radius R as it implodes to its thickness AR, which isless than the initial thickness because the shell is compressedas it implodes. Hydrodynamic instabilities,5 similar to theclassical Rayleigh-Taylor (RT) fluid instability, impose anupper limit on this ratio, which results in a minimum pres-sure or absorbed driver h-radiance. For 25


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TABLE I. Total energy released will determine energy output, but only charged-particle energy is available forself-ignition of ICF-size capsules.

E (MeV)E* (MeV)(chargedparticle) Energy/firam

D+T-+He4(3.52 MeV)+n(14.06 MeV)D+D-+He3(0.82)+n(2.45 MeV)D+D+T(l.Ol MeV)+p(3.03 MeV)D+He3-+He4(3.67 MeV)+p(14.67 MeV)T+TtHe4+n+n

17.58 3.52 3.39x 103.6 2.4 8.67X 1018.34 18.34 3.53x10

Il.32 1.82X 10

where u is the implosion velocity. Since 3OGC,440 is typi-cal, we require accelerations and velocities that are uniformto about 1%.The fuel conditions that must be achieved for efficientburn and a high yield relative to the driver energy can beobtained readily from an analysis of the bum of an inertiallyconfined fuel mass. The number of thermonuclear reactionsn per second is given by

where (au) is the reaction cross section averaged over aMaxwellian distribution of particles, and for an equimolarDT mixture,

where Nais the initial total number density. If we define theburn fraction by +=2nlNo, then we have4 No~=-+1-+)2(ou).

If we assume that the Maxwell averaged cross section isnearly constant over the burn duration, then we can integratethis equation to obtain-=--2C&),l-4 2 (6)

where G- s the confinement time. In inertial confinement,burn of an ignited fuel mass typically is quenched by hydro-dynamic expansion. (For a capsule below the ignition thresh-old, such as those on Nova, electron conduction usuallycools the fuel before hydroexpansion occurs, as discussed inSec. III.) From the outside of the fuel, a rarefaction movesinward at the speed of sound, C,. By the time this rarefac-tion has moved a fraction of the radius Y, the fuel density inmost of the fuel mass has dropped significantly, and the fuelno longer burns efficiently. If we chooser

7-- 3 (7)which would allow time for a rarefaction wave to propagateacross the dense main fuel layer in Fig. 1, we can write theburn efficiency as

&=,(m) &. sPhys. Plasmas, Vol. 2, No. 11, November 1995

For DT between 20 and 40 keV, which is typical of the burnof ICF capsules, the ratio of the cross section to the soundspeed is nearly constant, and we have approximately(p= pr NorPr+6(g/cm2) M N,~+5x10*5(s/cm3j (9)

where we have related number density No to the mass den-sity p by/Vo=6.02x1023 +2.4X10z3, for DT. (10)

Equation (9) compares well with detailed numerical simula-tions of most high-gain ICF targets.6Y7We need pr=3 g/cm2for a 33% burnup. As indicated in Eq. (9j, the pr require-ment for ICF is equivalent to the Nr requirement generallyquoted for magnetic fusion energy (MEE) plasmas. The fac-tor of 5 X 1Or5 n the Nr formula uses the DT cross section at20 keV. At 40 keV, the factor becomes 3X 1015.We can usethis burn efficiency formula to compare the fusion burn re-quirements of MFE with those of ICF.Both ICF and MFE refer to ignition of the plasma, butignition has different meanings for these two approaches tofusion.In MFE, which requires steady-state or near steady-stateoperation for most energy production approaches, ignition isdefined in terms of power balance. In this approach, ignitionoccurs when energy deposition from thermonuclear bumproducts during one energy confinement time equals the en-ergy required to heat the plasma to thermonuclear bum tem-peratures. When this occurs in steady state, the plasma cansustain itself indefinitely with no external heating.The energy per gram required to heat a DT plasma isgiven byE DT heating =0.1152X 109T (J/g)=2.3X10y (J/g),

at 20 keV. with T,=Ti, (11)where T, is electron temperature and Ti is ion temperature.The thermonuclear burn products and energy content of vari-ous thermonuclear fuels is given in Table I. In general, onlythe charged-particle reaction products are available to heatthe fuel since most of the neutrons escape the plasma withoutinteracting. For DT, the alpha particle energy (E,=3.5 meV)from the reaction is about 20% of the total energy produced.If we assume that all of the alphas are deposited, then theenergy per gram deposited in the fuel is given by

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6.68X 10OnrE hem~onuclear a particle= n T+ 5 x 10 I5 (Jk) tat 20 keV. ( 2)

If we set EDT heating=Ethermonuclear a particle in this simplemodel, ignition occurs for n7>1.7X lOI or pr=0.21 andcorresponds to a bum efficiency of about 3.4%.Ignition in this sense is adequate for a MFE plasma if theenergy required to maintain the magnetic confinement ismuch less than the energy to heat the plasma. Since themagnetic-field energy is much greater than the plasma en-ergy in magnetic confinement devices, it is generally as-sumed that superconducting magnets would be used to mini-mize the dissipation of magnetic field energy.As a measure of the fusion power performance for aMFE device, the fusion power gain is defined by Q = Pf/ Pi ,where Pf is the fusion power and Pi is the input power. Thefusion power is given by

and the input power is given bydV- f Pf,

where the integrals are over the plasma volume,E,=3.34X lOJ/g is the energy per gram produced by DTfusion reactions, and EDT heat& is the heat capacity of DTfrom Eq. (11). In Eq. (14), one-fifth of Pf , which is all of thea-particle energy, is assumed to be deposited in the plasma.The energy confinement time 7s characterizes the rate atwhich energy is lost from the plasma by cross-field transportand radiation. Ignition occurs when P,=O.O or when Q =m.An actual MFE reactor would run somewhat below the igni-tion limit, to maintain a stable operating regime, so that aQ-20 is desirable. Recent experiments with DT plasmashave achieved Q = a.In ICF, which is inherently pulsed, ignition occurs whenenergy production and LY eposition from the central hot spotare sufficient to initiate a self-sustaining bum wave thatpropagates into the surrounding main fuel. To compensatefor driver and implosion inefficiencies, ICF targets musthave a high bum efficiency, and most of the fuel must beheated by the burn wave propagating outward from the hotspot.Target gain, defined as the ratio of thermonuclear energyproduced to driver energy on target,is the closest equivalentto Q in MFR. A described in Sec. XIV, energy production inICF requires target gains high enough that the product ofgain times driver efficiency is -10. Depending on driverefficiency, target gains of 30-100 or more are required tosatisfy this condition.Compression of the DT fuel mass makes it feasible, inthe laboratory, to achieve the pr =3 g/cm2 necessary for aburn efficiency of 4, about a factor of 10 higher bum effi-ciency than for an ignited MFE plasma. For a sphere, wehave

Specific energy vs density for cold DT

Ideal Fermi fluid

Realistic quation f StateimplosionI I I

1 IO TO2 103 104Density (gkm3}

FIG. 3. For densities of interest to ICF, Fermi-degenerate compression fe-quires much less energy than does ignition.

(15)Hence, the mass (and also driver energy at fixed couplingefficiency) required for pr =3 g/cm2 scales as l/p. At a nor-mal liquid density of 0.21 g/cm3, more than 2.5 kg of DT isrequired. If this much mass were ignited, it would yieldabout 3X 10 J or 7Okt. On the other hand, at a density of400 g/cm3, a spherical shell with a thickness r/2 and radiusr would have pr=3 with a mass of 5 mg. This mass wouldhave a yield of about 6X IO8 J and is readily contained. Atfive to six pulses per second, such targets could drive a 1 GWreactor for power production.As shown in Fig. 3, if the DT remains nearly Fermidegenerate during compression, then compression is eco-nomical because the energy required for compression issmall compared to that required for ignition of the samemass of fuel, The Fermi compression energy can be obtainedfrom a simple estimate. Every Fermi particle occupies aphase space volume of h3. Then N particles in a volume Vmust occupy a phase space volume given by

4rrd3x d3p =(2s+ I) V 3 P;=Nh3. WIThe sum is over spin states that are 2 for spin s = f particles.The Fermi energy is defined by ef= Pf2/2m, where Pf is themomentum of the highest energy particle or

= 14p23(glcm3). (17)The average energy per particle is just 0,6ef, and the specificenergy per gram of DT, em, is given by

eor(J/g)=3 X 105p23(g/cm3). (1%When there is a finite temperature, Eq. (18) becomes

Eor=3X 105p23 1 -0.02 ( T$2)] (19)Equation (19) shows that the temperature of DT at a densityof 1 g/cm3 must remain below a few electron volts, or thefinite temperature corrections start becoming significant.Equations (18) and (19) ignore ion contributions and mo-

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lecular effects that affect the real equation of state for DT.Equation (18) is plotted in Fig. 3 for comparison with thespecific energy from a more accurate equation of state, suchas that given in the Sesame Tables.Although compression is energetically attractive and re-duces the driver size required for efficient burn, high gainalso requires hot-spot ignition. For example, it takes 6.5 X IO4J to compress 5 mg to 400 g/cm3. But to heat that mass to 5keV would require about 3 X IO6 J. If the implosion had anoverall efficiency of 5%, the driver size would have to beabout 6X lo7 J. This is near the upper limit of what could beconsidered for a laboratory driver, yet the target gain for aburn efficiency of f would be only 10. On the other hand, ifthe target can be ignited from a central hot spot containingabout 2% of the total mass, then the energy required to heatthis mass would be only about 6X 10 J. The total energyinvested in compression and ignition would be about1.25X 10 J (2.5X IO7 J/g), the driver size would be 2.5X lo6J, and the gain would be greater than 200. Depending on thedriver efficiency, target gains of 30-100 generally are re-quired for most ICF applications. The hot spot forms duringcompression from material at the center of the fuel, which ison a high isentrope. The hot-spot temperature will increaseas long as the energy gained due to the PdV work done bythe imploding main fuel material and charged-particle energydeposition exceed energy lost due to radiation and electronthermal conduction, as described in Sec. III. Once ignitionoccurs, heating of the surrounding main fuel layer from elec-tron conduction and a-particle deposition results in a ther-monuclear burn wave that propagates outward into the mainfuel layer. The typical configuration of the compressed fuelat ignition is shown in Fig. 1.For effective self-heating, the hot spot pr must exceedthe a-particle range. The range energy relationship for crparticlesi is approximated by Fraley14 as

where the first term is the interaction with electrons and thesecond term is the interaction with ions. Here V=EJ3.5MeV and po=0.25 g/cm3 is the density of solid DT. Figure4(a) is a plot of the a-particle range as a function of T, (keV)at various densities. At low temperature, most of thea-particle energy is deposited into the electrons, as shown inFig. 4(b). For solid-density DT, most of the energy goes intothe electrons below a temperature of about 32 keV Fraleyet al. find that the &-particle range pXo (g/cm2) in solid-density DT can be approximated by

p&&/cm)= 1.5x10-T,541+8.2x10-3T;4 (21)where the electron temperature T, is in keV. At 10 keV, fortypical hot-spot densities of IO-100 g/cm3, the a particleshave a range of about 0.3 g/cm. As discussed in Sec. III; a

10-z I IO 111rr , I,,,,,1 1$f!) 102

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.94 (fraction of CL nergy into ions)FIG. 4. Efficient alpha capture requires prwO.3 g/cm. (a) Alpha-particlerange pX, vs T, ; (b) alpha-energy absorption.

hot spot at a temperature of about 10 keV with a pr=0.3g/cm2 is required for ignition of a self-sustaining burn wavefor typical high-gain ICF capsules. Ignition and propagatingburn are discussed further in Sec. XIII for targets being de-signed for the NIF.The implosion of an ICF capsule can be described by arocket equation: l51

TypIcal rangeof efficienciesfor ablation-drivenspherical shell

10-20 0.2 0.4 0.6 0.6 1.0Remaining rocket mass fraction, mflmO ETLlG. 5. Subsonic ablation follows an isothermal rocket equation. Radiation-driven implosions typically have an efficiency of 1.5%~~20%.Direct-driveefficiency depends on laser wavelength and illumination geometry, but istypically 5%-10%; x=m/ mO is the ratio of the final shell mass mf to theinitial mass mn .

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In this equation, P, is the ablation pressure, ti is themass ablation rate per unit area, ma is the initial shell mass,and fnf is the fuel or payload mass. The rocket efficiencyversus mflmo is shown in Fig. 5 for both an ideal rocket andan ablation-driven rocket. The peak efficiency of an ablation-driven rocket is typically a factor of 4 or more smaller thanthat of an ideal rocket because the exhaust is continuallyheated by the incident flux driving the implosion. This isfurther discussed in Sec. V on implosion dynamics.ICF capsules rely on either electron conduction (directdrive) or x rays (indirect drive) for energy transport to drivean implosion.

LaMIarget

In direct drive, the laser beams (or charged particlebeams) are aimed directly at a target. The laser energy istransferred to electrons by means of inverse bremsstrahlungor a variety of plasma collective processes. This absorptionoccurs at a particle density equal to or less than the plasmacritical density nc(cmm3)= 102/h2, where X is the laserwavelength in ,um. Electron conduction must transport theenergy to the ablation front, which typically has an electrondensity of about 1024/cm3. Uniformity of the flux must beobtained by direct overlap of a large number of very uniformbeams, or by lateral electron conduction smoothing. Until itwas shut down in December 1992, the Omega laser16*17 t theUniversity of Rochester Laboratory for Laser Energetics(LLE) was the principal facility for direct-drive implosionexperiments in the United States. Omega was a 24-beam,glass laser facility capable of delivering 2-3 kJ of 0.35 ,umlight in a 0.6 ns pulse. Lawrence Livermore National Labo-ratory (LLNL), in collaboration with Rochester, is conduct-ing planar experiments on the Nova laser8*9 at LLNL toinvestigate hydrodynamic instabilities and beam smoothingin direct drive. These experiments use a single beam of Novadelivering 2-3 kJ of energy in about 3 ns. GEKKO XII atOsaka University in Japan is the principal facility outside theUnited States for conducting direct-drive experiments. The12-beam GEKKO laser2 can deliver about 10 kJ of energyin 1 ns at either 0.5 or 0.35 ,um. Rochester has completedconstruction of a 60-beam upgrade to Omega. The OmegaUpgrade21.22has achieved over 40 kJ of energy in a varietyof pulse shapes. The Naval Research Laboratory (NRL) isconstructing a KrF laser called NIKE,23,24 which is designedto deliver 2-3 kJ of energy in a 3-4 ns pulse. This laser isprimarily intended as a testbed for a NRL beam-smoothingtechnique called echelon-free ISI and as a technology devel-opment program for kilojoule-scale KrF lasers with the pre-cision needed for ICF applications. NIKE is scheduled tobegin target experiments in 1995.

FIG. 6. For indirect-drive targets, Nova and National Ignition Facility ex-periments are relevant to both laser and heavy-ion targets. Capsule implo-sion and bum physics, as well as hohlraum energetics and x-ray transport,are essentially driver independent.

optimally designed targets, 70%-80% of the driver energycan be converted to x rays. The optimal hohlraum geometrydepends on the driver.Schematic hohlraums for a laser and heavy-ion-beamdriver are shown in Fig. 6. The specific details of geometryare chosen to achieve flux uniformity on the capsule. Thesymmetry requirement will dictate driver beam placementand hohlraum geometry, including such issues as the ratio ofcapsule size to case size, hohlraum internal structure, andvarious other details, as discussed in Sec. IX.In general, laser-driven hohlraums designed to achieveradiation symmetry with two laser entrance holes (LEHs) areelongated with a length-to-diameter ratio greater than unity.Such a geometry arises from the need to balance the absenceof x-ray emission from the LEH by locating the laser beams,which have higher emission than the rest of the hohlraumwall, relatively close to the LEH. In a spherical geometry,proper placement of the beams would result in very highangles of incidence as the beam pass through the LEHs. Suchhigh angles can result in clipping of the beam on the LEH ora very large LEH. Alternatively, in a sphere, the beams canbe aimed past the capsule toward the opposite LEH. This canwork for short pulses, but capsule blowoff interferes withbeam propagation for longer pulses. There are some spheri-cal laser-driven hohlraums that have more than two holes.These designs must balance the increased LEH radiationlosses with a potentially smaller case.Ion-driven hohlraums, such as that shown in Fig. 6, areelongated because of the need to place internal shields forsymmetry control. Some spherical ion-driven hohlraums,discussed in Sec. XIV, use more than two radiators.Because of relaxed requirements on laser-beam unifor- The target physics specifications for laser-drivenmity and reduced sensitivity to hydrodynamic instabilities, indirect-drive ignition targets are shown in Fig. I. Driver-the U.S. ICF Program has concentrated most of its effort target coupling issues, which include laser absorption, x-raysince 1976 on the x-ray or indirect-drive approach to ICE In conversion, and transport, limit the x-ray temperature ofindirect drive, the driver energy, from laser beams or ion laser-dri ven hohlraums. This limitation is primarily the resultbeams, is first absorbed in a high-Z enclosure, a hohlraum, of laser-driven parametric instabilities,25 which result in scat-which surrounds the capsule. The material heated by the tering of laser light and production of high-energy electrons.driver emits x rays, which drive the capsule implosion. For Light scattering degrades symmetry, and high-energy elec-

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1.0Laser energy (MJ)

FIG. 7. The National Ignition Facility (NIF) is being designed to demon-strate ICF capsule ignition and propagating burn.

trons cause capsule preheat, which reduces the achievablecompression. For the typical ignition target designs describedin Sec. XIII, the hohlraum temperature is limited to about300 eV or an equivalent x-ray intensity of about 10 W/cm.As discussed in Sec. XI, Hohlraum Plasma Conditions,this temperature constraint limits the plasma density in thelaser propagation path to about 10% of the electron criticaldensity for 0.35 ,um laser light.Given the x-ray flux limitations and the implosion veloc-ity required for ignition, the flux onto the capsules must besufficiently uniform to allow the capsules to converge by afactor of 25-35, as discussed above. For a capsule to con-verge this far and remain nearly spherical, x-ray fluxes mustbe uniform to 1%-2%. To achieve this level of x-ray fluxuniformity requires a hohlraum that is large compared to thecapsule dimension. In current hohlraum designs, hohlraumareas are typically 15-25 times that of the initial capsulearea. Such a large-area hohlraum limits the coupling efficien-cies of driver energy to the capsule to lo%-15%, as dis-cussed in Sec. VIII. It should ultimately be possible toachieve a coupling efficiency of 20%-25% through the useof optimal driver and hohlraum geometries that minimizehohlraum and LEH area.The achievable implosion velocity, which is the primarydeterminant of the minimum-size driver for ignition, is de-termined by a combination of the allowable capsule IFARand the maximum achievable x-ray flux. Shown in Fig. 7 aregain curves at implosion velocities of 3 and 4X10? cm/s,under the assumption of a fixed hohlraum coupling effi-ciency of lo%-15%. If the capsule IFAR is limited to about30, an implosion velocity of 3 X lo7 cm/s requires a hohlraumtemperature of about 225 eV, whereas an implosion velocityof 4X lo7 cm/s requires a higher temperatur+about 300 eV.This near-linear relationship between radiation temperatureand implosion velocity is discussed in Sec. V. At any givenvelocity, capsules below a certain energy will fail to ignitebecause the hot spot will not achieve sufficient pr and tem-perature. The shaded bands correspond to a minimum cutoffenergy, which depends on hydrodynamic instability levelsand capsule surface quality. The left-hand edge of each bandcorresponds to the gain for perfectly uniform implosions.The right-hand edge of each band corresponds to the gain fortargets with surface finishes of 500-1000 A. As seen in Fig.

FIG. 8. Nova laser bay.7, capsules on the proposed NIF (described more completelyin Sec. XIII), which is being designed to deliver 1.8 MJ ofenergy, must reach implosion velocities approaching 4X lo7cm/s, and have hohlraum temperatures of approximately 300eV. The ICF program has used data from laboratory experi-ments and from underground nuclear experiments. A jointLos Alamos/LLNL program using underground nuclear ex-periments, called Halite at LLNL and Centurion at Los Ala-mos (collectively called H./C), demonstrated excellent perfor-mance, putting to rest fundamental questions about the basicfeasibility of achieving high gain.z6 It performed inertial fu-sion experiments using nuclear explosives at the Nevada TestSite at higher energies than those available in the laboratory.Since its completion in 1985, the Nova laser18~1g tLLNL has been the primary U.S. laboratory facility forradiation-driven experiments. Figure 8 is a picture of thelaser hall, showing some of Novas ten beams. Figure 9shows the Nova experimental area as it was before any di-agnostics were installed. The laser beams are arranged sothat five beams located along the rim of a 100 cone irradiateeach end of a hohlraum, such as that shown in Fig. 10. Novacan deliver about 30-40 kJ in 1 ns at an output wavelengthof 0.35 pm. This energy can also be delivered with a widevariety of pulse shapes. Figure 10 is a typical 1.6 mm diamhohlraum used on Nova for implosion experiments. For ease

FIG. 9. Nova target chamber.Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3939



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Implosion /-capsule-FormvarZ\PO

FIG. 10. Nova implosion target, illustrating beam geometry. Five Novabeams irradiate each side of the hohlraum. The beams are uniformly distrib-uted around the rim of a 100 cone.

of fabrication, the hohlraum wall for this target is made ofgold, but other high-2 materials such as tungsten and ura-nium are also used. The capsule shown inside is a plasticmicroballoon about 5 mm in diameter.Outside of the United States, GEKKO XII and the Phe-bus laser at Limeil have been the primary facilities for ex-periments on radiation-driven ICE Hohlraumsz7 used onGEKKO XII have been about half the scale of the Novahohlraums shown in Fig. 10. Experiments on Phebus2swhich is the equivalent of two beams of Nova, have used avariety of hohlraum geometries, including spheres ranging insize from 1 to 2 mm in diameter and targets with beamshields for implosions, as shown in Fig. 11. In Russia, theISKRA-5 laser29 at Arzamus-16 has been used for indirectdrive. ISKRA-5 is an iodine laser operating at a 1.3 15 pmlaser wavelength. In typical experiments, this facility can fo-cus lo-15 kJ in a 0.25 ns pulse into a spherical cavity withsix LEHs. Other facilities being used for indirect drive in-

& = 0.6 for all sizese200 I I I

lffO- iF 160 -3 ic 140 -

i-120 -

800 1200 1600 20002 4 (w)FIG. 11. Hohlraum drive on the Phebus laser;?has been measured at 0.35pm. Et,,,,= 6 kJ in 1.3 ns. as a function of cavity diameter.3940 Phys. Plasmas, Vol. 2, No. 11, November 1995

elude the Asterix III laser3 at Garching and the Shengguanglaser facility in Shanghai. The Shengguang facility is atwo-beam facility currently capable of delivering up to 800 Jin a 0.1 - 1.2 ns pulse at 1.06 ,um.The primary alternatives to laser drivers for indirectdrive are ion-beam machines. Sandia National Laboratorieshas developed a succession of pulsed-power, light-ion driv-ers. The pr imary challenge for ion beams has been, and con-tinues to be, achieving the required focused intensity. Com-pleted in 1985, the current Sandia facility is PBFA ILs2which can deliveG3 about 100 kJ of lithium ions at l-2TW/cm2. Sandia has begun conducting preliminary hohlraumand beam-coupling experiments,Heavy-ion drivers are also being developed for ICE Ofthe current ICF drivers, both the 1990 National Academy ofScience (NAS)26 and the Fusion Policy Advisory Committee(FPAC)34 reviews concluded that because of their potentialefficiency, durability, and rep rate, heavy-ion drivers have thegreatest potential as drivers for future inertial fusion powerplants. The heavy-ion driver work in the United States issupported primarily by the Office of Fusion Energy (OFE).The U.S. program in heavy-ion drivers focuses on inductionaccelerators. The experimental work has been carried outprimarily at Lawrence Berkeley Laboratory. Although induc-tion accelerator technology has had a variety of applications,primarily for electron beams, a heavy-ion driver using space-charge-dominated beams for ICF currently is the least matureof the major driver approaches. In contrast to the laser case,a typical ion-driven hohlraum, which requires a certain mini-mum intensity to achieve good x-ray conversion,35-37 con-centrates the driver into a few radiators, as shown schemati-cally in Fig. 6. This feature, which is attractive from areactor-design point of view,3s minimizes the solid angleover which beams must be distributed and allows for a widevariety of reactor designs, including liquid waterfall and ce-ramic granule designs, which protect the target chamber wailagainst the fluence of neutrons, x rays, and debris from thetarget.Although significant parts of the following discussionapply to both direct and indirect drive, the principal focuswill be on indirect drive.II. HISTORICAL DEVELOPMENT OF INDIRECT DRIVEIN THE U.S. ICF PROGRAM

We are nearing completion of a two-decade program todevelop the data and numerical modeling capabilities neededto accurately specify the requirements for ignition and high-gain, radiation-driven ICF targets. Although research on in-direct drive in the United States has been largely classifiedthroughout this period and some aspects remain classified, arecent DOE declassification decision39 goes a long way to-ward achieving a long-time goal of research scientists in thefield for more openness and international cooperation in ICEJohn NuckoIls seminal 1972 Nature paper was pub-lished at about the time when laser technology, diagnosticdevelopment, and numerical modeling were becoming ma-ture enough so that an expanded ICF program could begin toevaluate the limits and requirements for the success of ICF.This publication grew out of work, initiated by Nuckolls in

Review ArticleDownloaded 10 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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Capsule energy gain plotted vs compression

102 103 104 105Compression ( x liquid density)

FIG. 12. The initial capsule energy estimates for I CF could be met with afactor of 2.5 increase in the achievable implosion velocity compared tovelocities predicted for the NE The gains are plotted with the assumptionthat the fuel is near Fermi degenerate and that the yield is not degraded dueto hot electrons, asymmetry, or hydrodynamic instability. The thresholddriver energy and implosion1 velocity are obtained fromE,,,(MJ)~~(O.O5/~~~)p3'*(V/(3X 107))-, with aY,==3%.

the late 195Os, to address the challenge of creating the small-est possible fusion explosion. These early calculations werebased on radiation implosions and predated invention of thelaser. When the laser was invented in 1960, LLNL physicistsimmediately recognized its utility for inertial fusion. SterlingColgate, Ray Kidder, and Nuckolls independently calculatedvarious methods of using high-power lasers to implode andignite fusion target designs. Colgate and Nuckolls calcu-lated implosions in laser-driven hohlraums. Kidder applied aspherically symmetric pulse of laser light to the target with-out the use of a radiation implosion. Other early work inlaser-driven inertial fusion was proceeding around the world.In 1963 at the 3rd International Conference on QuantumElectronics (Paris), Basov and Krokhin evaluated the laserrequirements for using a laser to heat plasma to thermo-nuclear temperatures. This evaluation considered just directheating of a plasma by laser irradiation and did not use animplosion.Nuckolls 1972 paper was based on the direct-drive im-plosion of bare drops or shells of DT. But, as indicated,LLNL had shifted by 1975 to radiation-driven implosions forreasons described below.

Figure 12 shows Nuckolls original gain curves as func-tions of fuel compression. These curves predict that, if suf-ficient compression is achieved, targets driven by lasers assmall as 1 kJ could achieve target gains greater than unity.Drivers of about 1 MJ were predicted to be required for highgain. Although todays estimates of the driver size requiredfor high gain have not changed significantly, we now believethat a driver of about 1 MJ also will be required to achieveignition.Why has the ignition threshold increased by such a largefactor while the requirements for high gain have remainedfairly constant? This apparent disparity is explained by theextreme sensitivity of the ignition threshold to the implosionvelocity that can be achieved in near spherical implosions in

which the fuel remains nearly Fermi degenerate. A simplemodel for an isobaric implosion2Z43 would predict that therequired energy would scale as @V-lo, where V is the im-plosion velocity and p is the ratio of the pressure in the fuelto the Fermi pressure. Detailed numerical calculations44 pre-dict that this dependency is approximately reduced toE caps.leiMJ~=;E)P32( &1-. (23)

where rihy&, is the hydrodynamic efficiency and V is in unitsof cm/s. The reduction in the velocity dependence from anideal isobaric model is the result of several factors, includingan increase in the required hot-spot temperature as the targetsize decreases, and an increase in the fractional mass in thehot spot that self-consistently occurs during compression andresults in reduced compression and hot-spot coupling effi-ciency. The effects of hydrodynamic instability and asymme-try will result in an increase above the energy predicted byEq. (23). As discussed in Sec. VI, t hese deviations from auniform spherical implosion result in a factor of 2-3 increasein the minimum capsule energy required for ignition.The strong dependence of the minimum energy on theachievable implosion velocity means that only a factor ofabout 4 increase in the implosion velocity is required to gofrom a minimum energy of about 1 MJ to a minimum energyof 1 W, as shown in Fig. 12. The velocity indicated in Fig. 12depends on the ignition margin required to overcome theeffects of mix during the process of assembling the hot spot.The dependence of gain on implosion velocity is muchweaker. To lowest order, the reduction in gain with reductionin target size, or increase in implosion velocity, occurs pri-marily because less mass is imploded per Joule of energycoupled to the target. For equal burn efficiency, the gain

would scale as V- so that there would be about an order ofmagnitude less gain at 1 kJ than at 1 MJ, as shown in thecurves of Nuckolls. Once a target with a DT pusher ignites, itis expected to burn as calculated. In practice, compressionsachieved in self-consistent implosions are lower than the op-timal compression indicated in Fig. 12, and the gain is astronger function of energy as discussed in Sec. VII.We now believe that implosion velocities are limited tobetween about 3 and 4X lo7 cm/s because of two constraints:(1) the physics governing the hydrodynamic instability of anICF implosion; and (2) the maximum intensity allowed byefficient laser plasma coupling.Higher implosion velocities are possible in certain typesof high-entropy implosions, in which the high-density shellis heated rapidly to high temperature and then explodes. In aso-called exploding pusher target, the center of mass ofthe shell or pusher is almost stationary as it explodes. Theradius of the boundary between the inner edge of the shelland the fuel typically converges only a factor of 3 or 4. Suchtargets are quite insensitive to asymmetry. The direct-drive,electron-conduction-driven exploding pusher target45-49 wasthe most common early ICF target and was the first type oftarget to produce thermonuclear neutrons.7Y48However, itdoes not scale to high gain, because all of the mass of thetarget is on a high isentrope, which precludes high compres-sion.



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To obtain gain at laser sizes much smaller than about 1MJ, Nuckollsi used a very optimistic model for RT instabil-ity in the presence of ablation. As described in Sec. VI onhydrodynamic instabilities, this model, coupled with an as-sumption that implosions with absorbed laser intensities ap-proaching lOI W/cm2 would be feasible, was required toobtain ignition at laser energies approaching 1 kJ. In 1972,computers and numerical models were just becoming pow-erful enough to allow detailed evaluation of the effects ofhydrodynamic instability and the limits that laser plasma in-stabilities would place on the allowable intensity. Over thenext few years, experiments indicated that laser intensitieswould be limited to between 1014 and a few times lOIW/cm, depending on the laser wavelength. Numerical cal-culations provided most of the guidance for the growth of RTinstability until the quantitative data discussed in Sec. VIbecame available in the late 1980s and the early 1990s.By 1974, numerical calculation? using the LASNEXcode5 indicated that direct-drive capsules would have muchhigher instability growth rates than were assumed in Nuck-011s 1972 paper. In addition, new experiments using neody-mium glass lasers indicated that reduced absorption and hotelectron production would severely degrade direct-drive im-plosions at the high intensities required for ignition with la-sers in the I- 100 kJ range. The quality of the laser beam alsowas much worse than could be tolerated for the implosionuniformity required for direct drive. For direct-drive implo-sions, beam nonuniformities provide a source of small-spatial-scale perturbations (referred to as imprinting), whichare further amplified during the implosion.Much progress has been made since the 1970s towardsolving the irradiation-uniformity problem for direct drive. Aseries of clever optical inventions, both in the United Statesand Japan,52-54 raded off laser-beam coherence for laser-beam uniformity so that it is now possible to obtain beamsthat are uniform to a few percent. The overlap of a largenumber of beams, and further optical innovation should al-low nonuniformity to be reduced to less than l%, estimatedto be required for direct drive. With optimization of densitygradient stabilization effects, as discussed in Sec. VI, thedirect-drive ignition threshold is now estimated to be about 1MJ.s5 In the United States, the Omega Upgrade lase?s22 atthe University of Rochester is designed to answer these ques-tions, and the NIF conceptual design (see Sec. XIII) willpermit adding a direct-drive option. In Japan, the 300 kJKongoh laser project,56z57 n upgrade to GEKKO XII is be-ing proposed to study direct-drive ignition. Although thebeam-smoothing techniques that have been developedgreatly reduce the level of these effects, imprinting is still amajor concern for direct drive.Calculations carried out in 1975 showed that it is pos-sible, with proper design, to achieve high gain withradiation-driven targets5* such as those in Fig. 1. These tar-gets are very similar to direct-drive targets, except that thechoice of ablator material must be properly matched to thex-ray drive spectrum in order to control RT instability andensure that the fuel can be kept in a near-Fermi-degeneratestate. From one point of view, implosions driven by soft xrays could be considered as being driven by a laser with a

very short wavelength and a very broad frequency band-width.Compared to direct drive, these calculations for indirectdrive showed a dramatically reduced growth of perturbationsdue to RT instability. As discussed in Sec. VI, this reducedlevel of instability-one of the principal advantages ofradiation-driven implosions-occurs because radiation-driven implosions have much higher ablation rates and hencelower growth rates and thicker shells.In addition, because the laser beams are absorbed farfrom the capsule, as indicated schematically in Fig. 6,radiation-driven implosions are unaffected by small-scalenonuniformities in the laser beam.As discussed in Sec. XII, Hot Electron Preheat,indirect-drive targets are less sensitive to the effects of hotelectrons produced by laser-driven parametric instabilitiesbecause of solid-angle effects and because radiation-drivencapsules are thicker than directly driven capsules.A potential disadvantage of indirect drive for lasers,compared to direct drive, is the longer scale length of plasmatraversed by the laser as it propagates from the LEH to thehohlraum wall. Under some conditions, very large levels ofparametric instabilities can be generated in this plasma. Con-trolling the level of parametric instabilities places limits onlaser wavelength and intensity. In practice, both direct driveand indirect drive are optimized by using short-wavelengthlasers with XGO.5 pm, and intensities typically are limited toabout lOI W/cm2.For indirect drive, the capsules and such issues as radia-tion transport and hohlraum wall loss are essentially inde-pendent of the driver. This means that the ICF Program coulduse underground experiments driven by nuclear explosives totest aspects of ICF capsules at much higher energy thancould be tested by available laboratory sources. As men-tioned previously, the H/C program (from 1978 to 1988) laidto rest fundamental questions about the feasibility of high-gain ICF?6Because much of the physics of indirect drive is inde-pendent of the driver, many of the results learned with laserscarry over to other drivers such as heavy-ion beams. Thissynergism is particularly important for heavy-ion-beam driv-ers. Indirect-drive laser experiments provide a key elementof the database required to ensure that targets driven byheavy-ion beams will work when the accelerators areavailable.3459Because of the reduced level of hydrodynamic instabil-

ity, capsule energy requirements for ignition at a given x-rayintensity are very close to the projections in Nuckolls 1972paper. However, there is a substantial energy penalty in-curred in producing x rays and transporting them symmetri-cally to a capsule. Further, because of limits to the achiev-able x-ray intensity, the minimum driver energy for indirectdrive is about 0.5-I MJ, as shown in Fig. 7. The upper edgeof the band in Fig. 7 allows for the effects of asymmetry andthe mixing of hot and cold fuel while the hot spot is beingassembled.Hence, the currently projected minimum energy for ig-nition and burn propagation is quite similar for both directand indirect drive. However. because of relaxed beam-



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Forerunner argetA

lao+m goldscattering wire1Oy.mgold converterand radiation casel-pm Parylena ightand electron rhleld

I? \3aa,w

la&pm diagnostic holes 4 ball- 2 ma/cm3 DT ill- I mg/cms No ill

(a) W-pm tungsten-

250~pm-diamParylene light andelectron shield

A 520 ~III.c x

VO-urn-diem 10.7~pm-walifuel ball0.16~mg/cm3 DT fillO.i-mg/cm3 Ne fill

Hohlraum / / sf ./ \SO-pm diagnostic holes /

FIG. 13. The first indirect-drive, laser-driven implosion was achieved on theCyclops l aser at LLNL in 1976 using a target called a Forerunner.

quality requirements and reduced sensitivity to RT instabil-ity, it has been possible over the past two decades to makemore rapid progress toward obtaining the radiation-drive da-tabase required to quantitatively specify the driver require-ments for ignition. In the United States, a comparable data-base for direct drive will not be available until theexperiments planned for the Omega Upgrade are completed,sometime after the end of the 1990s.Between March and May 1976, LLNL carried out thefirst series of laser-driven radiation implosion experiments.Target designs for these experiments required about 100 J of1.06 ,um light. They were fielded on the Cyclops l aser6 atLLNL. Figures 13 and 14 show the two principal types oftargets fielded in these experiments. To simplify fabrica-tion, gold radiation cases were used for these targets and formost radiation-driven implosion targets since then. For thefirst few radiation implosions, leaded glass microballoonswere used as radiation cases, but gold was a far superiormaterial and could be shaped easily from available tubing orelectroplated onto mandrels of arbitrary shape. For these firstradiation-driven targets, with calculated radiation tempera-tures of about 100 eV, thin glass microballoons were used forcapsules. The radiation mean-free path in these capsules wascomparable to the shell thickness. The targets became nearlyisothermal and behaved as exploding pusher targets. The tar-gets shown in Fig. 13 had yields of about lo4 neutrons,whereas the target in Fig. 14, which was designed to coupleradiation to the capsule more efficiently, had a yield between

FIG. 14. Improved version of Forerunner target: (a) engineering drawing,(b) assembled target, and (c) fuel capsule and Parylene cover mounted onend cap prior to assembly.

1 and 2X105 neutrons. Yields for both types of targets werepredicted correctly. These results, which made us optimisticabout radiation drive, resulted in a shift of the 20 beam, 10kJ Shiva laser from a uniform-illumination scheme to a two-sided irradiation scheme for indirect drive and formed thebasis for the early optimism about the possibilities forachieving breakeven on a 200 kJ laser operating at 1.06 ,u,m.However, as we attempted the higher drive temperaturesneeded for high-density implosions and higher yields, laser-driven parametric instabilities in the hohlraum plasmas gen-erated high levels of energetic electrons. Also, coupling dif-ficulties hampered progress in the LLNL program on bothArgus62 (a two-beam laser capable of delivering l-2 kJ of1.06 pm light that served as a prototype for the laser hard-ware in Shiva) and Shiva as we worked to achieve a DTfuel density equal to 100X liquid DT fuel density (about 20g/cm3).In the initial Cyclops hohlraum experiments, the pres-ence of high-energy electrons, which we later determinedwere produced primarily by stimulated Raman scattering(SRS), showed up as noise in the neutron detectors.6 Be-sides the 500 pm diam target shown in Fig. 13, we tested300 and 400 ,zrn diam versions of this target. The smallertwo hohlraums generated such large signals (from high-energy electrons) in the neutron detectors that they could notbe used for implosions. Therefore, we did the implosion ex-periments in the larger, lower-temperature hohlraum, which



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j Gold hohlraum walland scattering cone

0 1 0 1prompt production region photon energy (keV) Prompt sink region photon energy (keV)FIG. 15. Time-resolved x-ray spectroscopy, showing energy loss and temperature gradient between production and sink regions of Cairn targets on the Arguslaser at LLNL (1978).

had low noise levels. As discussed in Sec. XI, HohlraumPlasma Conditions, laser plasma parametric instabilitiesstrongly limit the hohlraum temperature that can be achievedwith a laser of a given size and wavelength.Because we lacked adequate models for certain keypieces of the physics, including non-LTE (local thermody-namic equilibrium) or NLTE atomic physics for the high-Zhohlraum walls, and adequate understanding of the laser-plasma interactions below critical density inside the hohl-raum, we believed that absorption would be high in hohl-raums for 1 pm light and that conversion to x rays would bevery high. In addition, we had few measurements to quantifytarget performance: no quantitative measurement of x-raydrive, inadequate information about high-energy x rays fromenergetic electrons, and no measurements of the spectral dis-tribution of scattered light that could have identified Ramanscattering. We fully expected to achieve 100X liquid densityon Argus and go on to more aggressive implosions on Shiva.In 1977 and 1978, hohlraum experiments were performedwith increasingly sophisticated targets, as shown in Figs.15-17. Figures 15 and 16 show 1978 Argus laser targetsdesigned to measure radiation temperature and x-raypreheat.@ Figure 17 shows a hohlraum for capsules designedto achieve 10 to 100Xliquid density65*66 n Argus. Becauseof high-energy electron production, we were unsuccessful inall attempts to obtain measurable yields from capsules de-signed to achieve a density > loxliquid on Argus.3944 Phys. Plasmas, Vol. 2, No. 11, November 1995

Throughout 1978 and 1979, we tested a wide variety oftargets designed to achieve high density on Shiva. A sketchof the Cairn Mod-B hohlraum, which achieved the highestdensities, is shown in Fig. 18(a). The capsules were glassmicroballoons with diameters of -150 pm and wall thick-

L18Qllm~4420m ---J

'8%104 keVx raysT 5-Z shieldFIG. 16. Target setup for a coupling experiment on the Argus laser. Wemeasured the coupling of radiation (burnthrough) and superthermals tpre-heat) to a 12 pm slab of glass (100X-like target) in a 100X-like environ-ment (half-cairn).



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(W

Au!U/Nb conicaldeflector shield

f Argus laserCairn hlgh-density target

radiation casa(8-20 m thick)lastlc support/shield

, Laser entrance hole,

beamdArgus laser --tskewedinjactlonForerunner

Lassr beamfl2 opticsw/\/+-T Rilaflon case (Au)-//I Y \

TN fuil ballNOW

FIG. 17. By 1977, sophisticated hohlraum i mplosion targets were being fielded on the two-beam Argus laser: (a) Cairn high-density target; (b) Forerunnerexploding pusher target.

nesses of 5-10 pm. These capsules were coated with eitherTeflon (CF,,) or CHz. The illumination geometry for theCairn-B target is shown in Fig. 18(b). Shivas inner cone ofbeams was focused on the gold shine shields, while the outercone of beams was focused to pass beyond the capsule andilluminate the opposite hohlraum wall and endcap. Figure 19shows the variety of Cairn hohlraum types tested in the high-density campaigns on Shiva. Figure 20 is a plot of the den-sity, obtained by neutron activation68 of the glass pusher sur-rounding the fuel, and neutron yields obtained with thesedesigns. In general, the neutron yield anticorrelated withdensity. The more open geometries, which allowed more ef-ficient transport of energy to the capsule, also provided lesspreheat shielding against the large fluxes of hot electronsproduced in these experiments. Most of the Cairn implosionexperiments were designed to operate with radiation tem-peratures near 200 eV. Under these conditions, high-energyx-ray measurements indicated that up to 50% of the absorbedlaser light ended up in hot electrons. The presence of thesehigh-energy electrons, which generally had a temperature of50-60 keV, degraded the achievable density and neutronyield. In general, it proved quite difficult to calculate theperformance of these targets with large fractions of hot elec-trons, although the trends were understandable.On the basis of an examination of the plasma conditions

calculated for the Shiva hohlraums and an improved under-standing of SRS,25 a model was developed for the limitationson hohlraum temperatures based on filling hohlraums to den-sities near i critical density.69 At this density, the Ramaninstability-which couples an incident photon, a scatteredphoton, and a plasma wave-is an absolute instability withvery high gain. The plasma wave has a high phase velocityand produces energetic electrons when it undergoes Landaudamping. A series of scaling experimentsY7 which varied thehohlraum size and energy, gave hot-electron fractions thatscaled well with the fraction of energy remaining in the pulseafter the hohlraum filled to an average density of a critical, asshown in Fig. 21. In addition to measuring the hot-electronfraction, we also measured Raman-shifted backscatteredlight. The magnitude of this scattering, as well as the timedelay before large levels of scattering occurred, also wereconsistent with the model of hohhaum filling as the source ofplasma responsible for producing hot electrons. The time de-lay before the onset of hot-electron production is shown inFig.22 and is consistent with the calculated time delay forfilling to 4 critical densityF9 A Cairn scale 1, referenced tothe initial Argus experiments, was 500 pm in diameter and800 pm long. Most Shiva implosion experiments, such as theCairn-B shown in Fig. 18, were a scale 2. Because of the



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FlG.

5beamsfromeachside in inner c

18. (a) Cairn Mod-B, one of a series of targets that use radiation-driven. ablative compression of the fuel c20-beam Shiva laser.

relatively low critical density of 102 cmw3 for 1.06 pm laserlight, hohlraum experiments on Shiva at this wavelengthwere limited to between 130 and 140 eV before significantlevels of hot electrons were produced, with the 1 ns pulsesrequired for implosions.Low-preheat hohlraums are required for imploding cap-sules with fuel regions that remain nearly Fermi degenerate.To test our ability to predict the performance of ablativelydriven capsules in a low-preheat hohlraum, we designed theNova Precursor Implosion Research Experiments (NPIRE)?which were designed to implode capsules at 130- 140 eV andthat used the two types of hohlraums shown in Figs. 23(a)and 23(b) with the capsules shown in Fig. 23(c). The cap-sules performed as predicted, with a neutron yield of 107, asindicated in Fig. 23. This gave us confidence that capsulesdriven by radiation ablation in low-preheat hohlraums wouldbehave as predicted. With diagnostic and alignment shields,

apsule. (b) Mod-B in geometry for

these targets are quite complex to fabricate, as shown by theassembled targets in Fig. 24.From 1976 to 1981, we investigated both single- anddouble-shell targets as potential high-gain targets. Comparedto single-shell targets such as those in Fig. 1, double-shelltargets reach ignition conditions at lower implosion veloci-ties. Figure 25 shows a high-gain, double-shell target.72 In alldouble-shell targets, called Apollo targets, the main fuel ispart of the outer shell. During the implosion, the outer shellcollides with the much lighter inner shell and accelerates it toa higher velocity. In the limiting case of the inner shellsmass being negligible compared to that of the outer shell andthe collision being elastic, the inner shell can reach a velocitytwice that of the outer shell. Since compression to the highdensity required for high gain generally requi res a lower ve-locity than that required to ignite the hot spot, this velocitymultiplication can, in principle, result in a factor-of-4 higher3946 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article



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Mod BI 1I Y- lo-10np,AR-0.02405 g/cm*

Mod HI0 Y-lo8 np, AR-O.006 g/cm2

Mod II

Y-3xiOnppAR-0.01 g/cm*

3 > Y- lo8 nhTodK

0 Y-2xlOnFIG. 19. Radiation cases for five Cairn targets: the Mod-B, H, I, J, and K.When irradiated, they provided a variety of drive and preheat environmentsfor the Cairn capsules. most of which were SiO, microshells, 5 pm wallthickness, 150 pm diam, overcoated with 15 pm of Teflon, and filled withabout 10 mgkm- of DT.

gain for a double shell compared to a single shell. The innershell must be high Z for efficient high-density compressionof the fuel contained within it. Because this shell starts out ata density of nearly 20 g/cm3, it can tolerate the high-pressureshock generated during the collision and still achieve highdensity. Because it is high 2, such a shell also contains theradiation emission from the fuel as it compresses and furtherlowers the ignition threshold. Early projections of ignition ona 200 w, 20-beam Nova laser were based largely on103 I b fi~~~~~, b t 1 ~~*~~, 1 a b 3

Neutron yieldFIG. 20. Fuel density at burn time versus neutron yield for various Cairnhohum geometries.

Calm hohlraum scale sizef lo- - (scale 1 D soo-~ dlam x 8W wn long)

IIncident energy (kJ)

8p 10-Z -;

i lo4sJ IO4 I I , 1 , I I I, 1 I , , , , , ,, I , , I2X10-4 2xX+ 2x10-P 2x10-4 1f, = 1.0 4 r, dtU&,

FIG. 21. The experimental hot-electron fraction fhot in 1.06 pm hohlraumscales with the fraction of energy remaining in the pulse f, at time i, whenthe average hohlraum density reaches quarter-critical.

double-shell target designs7273such as those shown in Fig.26. The two capsules shown in Fig. 26 are labeled sub-sonic and transonic to characterize the velocity of theradiation f ront (Marshak wavej relative to the velocity of theshock generated by the ablation. In the subsonic capsule, theshock propagates ahead of the Marshak wave during most ofthe ablation process. In the transonic capsule, the Marshakwave and shock propagate through the LiH ablator at nearlythe same speed until the radiation wave is slowed by theTaCOH layer. In this transonic regime, the compressioncaused by the shock in the ablator depends on radiation tem-perature and decreases as the temperature increases. Thisnegative feedback results in a reduced sensitivity to radiationflux asymmetry because the pressure on the TaCOH shell isproportional to psT, where ps is the shocked ablator densi tyand T is the radiation temperature. These transonic capsulescould tolerate 5%-10% flux asymmetry, versus 1% for thesubsonic capsules.

However, the potential advantages of velocity multipli-cation ignore the effects of hydrodynamic instability duringthe collision of the two shells. When these types of targetswere proposed, little was known about the growth of theturbulent instability layer that is produced during the colli-sion and acceleration of the inner shell. More detailed analy-

0 X-ray streakcameral Onedlmenslonalcylindrical calculations4667

EWJ)FIG. 22. High-energy electron time delay versus energy for Shiva &O-scaleCairn target (1000 pm di am by 1600 ,um long) hohlraum (2 ns pulse).



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(a) Type I cylindrical hahlraum (5/E-4.0)Laser entrance holeT000 pm

14ClO+mdiamdiagnostic holes

(c) Capsules for NPIRE hohlraums (d) Perfonance summary

(b) Type II spherical hohlraum (2.5 8)b-900 umcl

10 I I .0=

~~~~~~~~

CH ablator 120 130 140 1505 W

FIG. 23. The NPIRE hohlraums on the Shiva laser were designed to operateat a low radiation temperature of C 30- 140 eV) in order to minimize hot-electron preheat problems.

sis of this instability, and experiments74 make it clear that theinner shell cannot be pushed the required distance beforebeing penetrated by this turbulent layer. We now believe thatthe minimum size for successful ignition of double-shell tar-gets makes it uninteresting for ICF applications.On Shiva,75-77we fielded a few double-shell targets suchas those shown in Fig. 27. The inner shell was a 180 pmdiam, 20 /*rn thick glass shell, and the outer shell was a 360,um diam, 50 ym thick CH shell formed from a pair of hem-ishells glued to the few-hundred-angstroms-thick film thatheld the inner shell in place. These Apollo targets had ahigher calculated density than did the single-shell Cairn tar-gets. However, the low neutron yields of < IO7 resulted inpoor statistics for the neutron activation measurement of theglass pusher area1 density, which was our only density diag-nostic.The model of hohlraum temperatures limited by plasmafilling predicted that we would be able to achieve the tem-perature required for high-gain, single-shell targets if theproposed Nova laser were built to produce the third har-monic of the neodymium glass laser. This became practicalbecause of efficient conversion schemes, using nonlinearconversion in potassium dihydrogen phosphate (KDP) crys-tals, initially devised by the University of Rochester.78 In198 1, the improved coupling in hohlraums was demonstratedat the 100 J level in a series of experiments at 0.53 and 0.35pm on the Argus laser.79 In these experiments, the hot-electron levels dropped to open-geometry levels, and thefraction of the incident light that was absorbed in the hohl-raum increased to nearly lOO%, as shown in Fig. 28(a).These results are consistent with those seen in 1988 experi-ments reported by Sakabe et c~l.,*~,~~as shown in Fig. 28(b).Hohlraum absorption greater than 90% also has been typical3948 Phys. Plasmas, Vol. 2, No. 11, November 1995

(WFIG. 24. The NPIRE targets: (a) cylindrical Cairn NPIRE after finalbly; (b) spherical NPIRE after final assembly. assem-

of most short-wavelength hohlraum experiments on largerlaser systems. The limitations to this high absorpti on are dis-cussed in Sec. XI on hohlraum plasma conditions.Using these estimates of the achievable radiation tem-peratures and an estimate of the hohhaum coupling effi-ciency that could be achieved consistent with the requiredimplosion symmetry, we estimated the single-shell targetgains shown in Fig. 29. These gains are very similar tothose now estimated for the proposed NIF.In 1979, when it became clear that ignition would not beachieved on Nova, we devised a strategy for obtaining thedatabase that would be required for ignition on a futurefacility. This strategy tests the physics of high-gain targetsby using a series of Nova experiments on targets that are asclose as possible to being hydrodynamically equivalent tar-gets (HETs), and by using a series of underground nuclearexperiments (Halite/Centurion) at much higher energy. Thiscombination of experiments and modeling was devised toprovide the basis for the facility that ultimately would berequired for ignition and high gain.Since 1979. the LLNL ICF program has focused on de-veloping the quantitative modeling tools, diagnostics, and

Review Article



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T8- 01

FIG. 25. High-gain Apollo double shell. This target had capsule absorbedenergy=0.8 MJ, yield=313 MJ, maximum gold pusher velocity= 1.9X lo7cm/s, peak spark-plug fuel p-0.68 g/cm2, peak Au pusher p-3.6 g/cm,peak main fuel DT prw0.96 g/cm, and peak TaCOH prwO.11 g/cm* (pre-heat shield).

experimental techniques required to provide this quantitativephysics basis. This strategy was endorsed by the FosterReviewg3 in October, 1979, along with the recommendationthat Nova be a smaller, ten-beam laser with 20.1 0.53 pmwavelength) and 30 (0.35 ,um) capability. These recom-mended changes were implemented, and Nova has proved tobe an extremely successtil facility.s4In 1983, the first two beams of Nova were constructed asa laser test bed in an experimental facility called Novette,which gave us our first multikilojoule experience with 2w

210

160

- 150Bii%

120iiLUJf9 60

30

0

F , I 1 I I

1CIl5~nsb I I I I 160 180 200 220Channel temperature (ev)

240FIG. 26. Calculati ons in 1979, which predict ed ignition for a 20-beam 200kl Nova, required high hohlraum coupling efficiency and near I-D perfor-mance of double-shell t argets. Both capsules had E,,=50 kJ,V(TaCOH)=2X107 cm/s, V(Au)=3X107 cm/s. Capsule yields were about100 kJ.

Gold case

CH light shield 1,\ \ I /CH second shellGlass fuelcapsule

Goldscatteringcone

II 1000~m---+/

FIG. 27. (a) Apollo version B constructed for laser experiment s on the Shivalaser during 1979. (b) Completed Apoll o target. Outer shell and inner fuelcapsule are visible through a diagnostic hole.

light. ICF experiments on this facility lasted only about threemonths, but indicated that we were very l ikely to achieve ourhohlraum temperature goals on Nova. Implosions onNovettex5@ used hohlraums such as those shown in Fig. 30.With 7-9 kJ of 20 laser light, these hohlraums reached tem-peratures of 150- 160 eV. For hohlraums that were four-fifthsthe size of those in Fig. 30 (scale 0.8), the temperatures wereabout 20 eV higher. The most accurate temperature measure-



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(a) Argus laser (LLNL) C3oo~m--i

1

0.8s-

E 0.6sZi+B 0.4s

0.2

0 1 .

(~~~~~~~~

1

8 0.6-sE::$ 0.4 PX 0.44 pm0 1.3Fm0.2 0.6 0.8 1

Cavity diameter (mm)FIG. 28. Small-target hohlraum experiments showed efficient coupling withshort-wavelength laser light. (a) Results from 1981 Argus laser experimentsat LLNL using 0.35, 0.53, and 1.06 pm light. (b) Aster-ix laser (Garching,1988) results using 0.44 and 1.3 pm light.

ment for these hohlraums was obtained by using an alumi-num witness plate on a reentrant tube in megaphonehohlraums8 such as shown in Fig. 31. The witness platesused on Novette had steps of two different thicknessesmounted on the end of a gold reentrant tube. By looking atoptical emission when the radiation-driven shock breaksthrough the aluminum step and recording the time differencebetween the two steps, we obtain a shock velocity that can berelated to x-ray drive. As indicated in Fig. 3 1 for a scale-O.8hohlraum with 7.2 k.J of laser light, the hohlraum tempera-ture reached 172 eV with only about 3% of the absorbedenergy in hot electrons. (These results are consistent with theresults achieved on the Phebus laser,** as shown in Fig. 11.)

Between 1986 and 1990, LLNL made rapid progress onindirect-drive target physics. Nova experiments and quanti-tative modeling demonstrated symmetry contro1,y~q2he firstquantitative RT instability expetiments,93*94 the expectedbenefits of pulse shaping,95*96 nd the radiation-drive tem-

Capsule: 200 x 6-p&glass + 24-p CH5 or i0-mg/cm DT fillbnes overfilled by200 cum o compensatefor beam-pointingerrors

We also carried out some 4w (0.265 pm) experiment$with greater than 1.5 k.J of energy in a 1 ns pulse. Witness-

FIG. 30. Laser-target configuration for the two-beam Novette laser implo-sion campaign in 1983. These dimensions define a scale- Novette target.

1.0Laser energy (MJ)

FIG. 29. By 1979. best estimate gains for single-shell, radiation-driventa@S were comparable to todays estimates.

plate measurements on the 4w experiments indicated a hohl-raum temperature of 210 eV with only 0.08% of the energyin hot electrons in a half-scale Novette hohlraum (Fig. 32)using 1.63 kJ of energy.Although we did not carry out 30 experiments onNovette (the appropriate KDP crystal arrays were not avail-able), these results gave us confidence that Nova could meetor exceed its temperature goals of 200-225 eV. In principle,Nova could have been configured to produce 40 light insteadof 30 , but we concluded that the decreased performancefrom optical damage would more than offset the benefits ofthe increased margin of safety in laser plasma interactioneffects.The NAS review** chaired by Dr. William Happer oc-curred just as Nova was becoming fully operational at theend of 1985. Soon after its activation, Nova achieved itsinitial temperature goals of 200-225 eV with low levels ofhot electrons.89 We had established this goal as the tempera-ture that would be required for high gain with a 5-10 MJlaser. The DOE labeled such a facility the Laboratory Micro-fusion Facility (LMF).% The NAS review continued to en-dorse the HET approach, but made the H/C program thehighest priority.



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(a) 1 Alumlnum witness plate

64Vlew of theCassegrafntelescope

1 2Time (ns)

FIG. 31. Novette Megaphone O.&scale Cairn target used to measure the shock velocity of the drive at the center of the secondary. Target: 2487 pm long, 1198/*m in diameter, with 696 pm LEH. Laser beam: 7.2 kJ, 5270 A, 1 ns pulse, ,f/4.3 diverging beam spot at cone. Aluminum witness plate for incident fluxtemperature: 43 pm step, 990 ps; 67 ,um step, 1590 ps; u,=~.OX 10 cm/s+P=32 Mbars, T H= 172 eV. Hot electrons: 200 J of 34 keV electrons+7P,,heat= 1.3eV for 43 pm step, 0.3 eV for 67 q step. X-ray diode reemission tlux temperature: T,=15.5 eV.

perature scaling of implosions.7 These experiments and theirmore recent equivalent are discussed later in this paper.Based on the Nova and H/C progress, it was recom-mended that DOE begin considering the LMF based onglass-laser technology. This recommendation initiated a se-ries of internal DOE reviews in 1988 and a request fromCongress for an external review of the ICF Program, whichwas carried out by the NAS in 1989-1990. In its January1990 interim report. the NAS committee, under the chair-manship of Professor Steven Koonin, commended the

Rear view

b L diagno&lc hole diameter Dank holeFIG. 32. Half-Cairn targets for Novette scaling experiments. Dimensions:d=outside diameter of cylinder=1500 pm for 1.0 scale; l=length ofcylinder=(5/6)& a=distance from back wall to center of Dante hole=(13/30)d; b=diameter of Dante hole=[4/15)d: c=LEH diameter=0.5d;t,=wall thickness; R =radius of front comer=OZid; g=back corner angle=90+2.Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article

progress that had been made in ICF, but concluded that theLMF, with proposed yields of 200-1000 MJ, was too largefor the next step and encouraged the laboratories to explore astep between Nova and the LMF.26 In addition, Kooninscommittee concluded that the H/C program had achieved itsprincipal objectives and recommended that the remaining is-sues regarding the feasibility of ICF be resolved on Nova.Analysis of the relationship between implosion velocity,hydrodynamic instability, and hohlraum temperature indi-cated that ignition and modest gain would be possible with al-2 MJ laser if hohlraum temperatures of 300 eV, and im-plosion velocities of aXlO cm/s could be achieved.98.99Atthis implosion velocity, the capsule has sufficient ignitionmargin to accommodate the expected level of degradationfrom hydrodynamic instability and asymmetry. At a laser en-ergy of 1.8 MJ, which is the NIF baseline, there also is asufficient margin to account for uncertainty in the achievablehohlraum coupling efficiency. Early in 1990, using the in-creased power and energy that had become available whenNovas laser glass was replaced with improved platinum-freematerial, we were able to demonstrate 300 eV hohlraumswith less than 1% of the absorbed energy in hot electrons.Based on experimental and modeling results, both theSeptember 1990 final report26 of Koonins NAS committeeand the DOE Fusion Policy Advisory Committee (FPAC)

3951Downloaded 10 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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report34 recommended construction of a l-2 MJ glass laserfor demonstrating ignition and modest gain within about adecade. The NAS noted that ignition demonstration is thenatural next step in the ICF program. This recommendationwas made contingent upon successful completion of a seriesof experiments to be carried out on Nova. These experimentsand modeling in hohlraum and laser plasma interaction phys-ics (HLP) and hydrodynamically equivalent physics (HEP)constitute the Nova Technical Contract (NTC).26The HLP experiments address the issues of the effects ofhohlraum plasma conditions on implosion symmetry, and thescaling of a variety of plasma collective effects (includingparametric instabilities) in hohlraums.The HEP experiments address the issues of hydrody-namic instability and mix, as well as the effects of flux asym-metry on capsules that are scaled as closely as possible toignition capsules (hydrodynamic equivalence). Several im-provements to the Nova laser, including improved power bal-ance and pointing accuracy, were required to carry out someof these experiments. These requirements resulted in thePrecision Nova Project, which was completed in 1993.Except for cryogenic implosions, which are not nowplanned for Nova, the experiments of the NTC will completethe goals established for Nova in 1981.As part of its conclusions, the Koonin committee recom-mended that Los Alamos become an integral part of theNova physics program. That work has been pursued jointlyby LLNL and LANL since the end of 1990.In early 1993, DOE endorsed the mission need for theNIF and authorized development of a conceptual design re-port (CDR) for the facility. Demonstrat ion of ignition andburn propagation would complete the physics basis for ICFand open the door for ICF applications, including fusionpower production.

The following sections review in more detail the theo-retical and experimental progress in ICF, with an emphasison Nova and the NTC, and summarize the expected perfor-mance of the proposed NIF. Included are a wide variety ofanalytic scaling laws that serve an important role in illumi-nating key physics issues.III. IGNITION PHYSICS

Figure 1 shows the typical configuration of the com-pressed fuel at ignition. As a capsule implodes, P dV workand a-particle deposition from thermonuclear bum of DT actto heat the central hot-spot region. Electron conduction fromthe hot spot to the cold surrounding fuel, as well as radiativelosses, act to cool the hot spot. As the shell of main fuelcompresses the hot spot, pressure increases, and densities ofboth the hot spot and the main fuel increase. If conductionand radiative losses from the hot spot are too large, ignitionnever occurs. To achieve ignition by the time the implosionprocess has stopped, the hot spot must have a pr equal toabout 0.3 g/cm2 and must achieve a central temperature ofabout 10 keV. Under these conditions, a-particle depositioncan overcome electron conduction losses from the hot spot,and a self-sustaining bum wave will be generated.A simple analytic model demonstrates theserequirements.2*0,02 To estimate the rate of mechanical

work per unit vohtme, P, , done on the hot spot, we assumethat the main fuel acts as a piston on a gas with uniformpressure:P,= P(dVldt) PAv 3Pv=-=-V v r

=2,3X 1015 prv~107 (W/cm),where p is the hot-spot density in g/cm3, P is the pressure, Ais the surface area of the hot spot, V is its volume, r is itsradius in cm, v is the implosion velocity in cm/s, and T is thematter temperature in keV. Electrons and ions are assumed tobe in equilibrium. The thermonuclear heating rate per unitvolume P, is obtained from the bum rate and the fractionalalpha particle deposition:

P,= p&J%,+= i( I- ~)no(av)- 1.2x lo*sp(av),~,=0.67XlO" (J/g), (25)P,=8X 1016p2

In this equation, 4 is the rate of change of the bumup frac-tion, E, is the cr-particle energy per gram of DT, no is thetotal number density of particles, (crv} (cm3/s) is theMaxwell-averaged cross section, and F, is the &-particledeposition fraction. Efficient a-particle capture requires a prgreater than the a-particle range shown in Fig. 4. The radia-tion loss, P, , is assumed to be bremsstrahlung emission thatescapes the fuel:P,=3.OX 106p2T*2 (W/cm3). (26)

Conduction losses P, are obtained assuming Spitzer03 con-ductivity with a steady-state temperature profile determinedby balancing volume heating and conduction losses:Q=-k VT= -9.4x10'2s(z)Z.ln A T52 VT ( W/cm2),4n-r2Q= F r3(Po,+P,-PR)-+Q=constXr,

2-+T=T, [Ol- 11. 217 and T512 4t-0 VT(r,)= 7-gt27 7,p 2?!!=~e V r

y-712=8X lOI 7 (W/cm3), for In A=2,Z=l. (27)Here S(Z)=S(Z)E(Z)/[S(Z=I)E(Z=~)] is from Spitzer. Inaddition, S(Z) varies from 1.0 at Z= 1 to about 4.0 at Z=m.Table II gives Sand E at several different values of Z. HereTo is the central temperature of the hot spot and r. is its outerradius. The subscripts are dropped in Eq. (27). In obtainingthe temperature, the implosion velocity within the hot spot isassumed to be proportional to the radius r at each point. Thisis necessary to maintain a constant densi ty, which is a typical

3952 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article



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TABLE II. We use Spitzer values of 6 and E for electron thermal conduc-tivity.z 1 2 3 4 a6 0.225 0.356 0.513 0.791 1E 0.419 0.410 0.401 0.396 0.4

characteristic of the hot spot, as seen in Fig. 1. The Coulomblogarithm In A is also assumed to be a constant, and thetemperature at the edge of the hot spot is taken to be zero forsimplicity. The temperature profile obtained under these as-sumptions is close to that seen in detailed numerical simula-tions at ignition for a typical high-gain target.Equations (24)-(27) provide a qualitative picture of thegain and loss terms in the hot spot, but detailed numericalsimulations are required for quantitative accuracy.Energy gain in the hot spot occurs forf= P,,,+ Pa- P,- P,>O. The f =0 boundary is a quadraticin pr:(prj2[ ( +)Fa- 2) +pr( T(~~07) - $-oa8)

This boundary separates regions in which the hot spot gainsenergy as it is compressed from those regions in which itloses energy. The regions of gain and loss are plotted in Fig.33 for a velocity of 3X IO7 cm/s. At this velocity, there areuninterrupted trajectories in the energy gain region, from lowtemperature and low pr to ignition conditions. Plotted in Fig.33 are the boundaries that specify the regions in which thevarious terms of the energy equation dominate. Above a linegiven byT= 15.5(pr)23 (keV), (29)

the electron conduction loss rate exceeds the radiative lossrate. Typical ICF capsule implosions proceed entirely abovethis line, for DT with no impurities. It is also clear that PdVwork is the dominant energy gain term below O.l


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FIG. 34. 1Thecalculated NIF capsule trajectory i n Ti vs pr space is qualitatively consistent with a simple model of fuel energy gain and loss,spot achieves a higher temperature at preignition values of pr.

(34)The T vs pr curve would have a slope of unity, which wouldapproach the stable attractor curve from below. The tra-jectory could not cross that of the stable attractor, sincethe slope from below asymptotically approaches the samevalue as the stable attractor. The same process occurs inreverse for a capsule that starts out with too high a tempera-ture for a given pr. Most ICF capsules start out on this lattertype of trajectory since the shock that sets the initial adiabatoften establishes a higher temperature than can be sustainedby the corresponding implosion velocity.Figure 34 is an implosion trajectory from a numericalsimulation of the NIF capsule (see Fig. 107, Sec. XIII). Timeis implicit in the trajectory and increases as the temperatureand pr change from left to right across the figure. The con-tours labeled with different velocities are the f=O boundariesat the indicated velocities. This capsule has an implosionvelocity of 4X lo7 cm/s at the time it started decelerating. Asseen in Fig. 34, the hot-spot temperature increases somewhatmore rapidly during compression than this simple modelwould predict. This is at least partly because electron con-duction losses are not into a surrounding cold heat sink butinto DT, which is at a finite temperature so that conductionlosses are reduced. Also, during the low-pr hot-spot assem-bly stage, In h-6, which results in smaller conduction losscompared to Eq. (27), which used In A=2. The line in Fig.34, with V=4X lo7 cm/s and In R=6, is close to the trajec-tory followed by the mass-averaged hot-spot temperature ofthe NIF capsule.Figure 35 shows the calculated fuel temperature anddensity versus pr for a 0.2 MJ capsule that could be drivenby the NIF and a larger 2 MJ capsule. Although the capsuleenergies differ by an order of magnitude, the fuel configura-tion in temperature and pr space, the variables that deter-

but the fuel hot

mine bum propagation are nearly identical. The smaller cap-sule has larger density to make up for the reduced mass andenergy in the fuel.A key to the predicted success of capsules that are beingdesigned to ignite on NIF is the use of a pure DT cryogenicfuel pusher. Of all possible materials that cou

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