ICF Ignition, the Lawson Criterion and Comparison with MCF FSC Deuterium–Tritium Plasmas 100 Ignition

E Q ~ 10 x

i OMEGA (2009) T i 10 Q ~ 1 Q = Tokamaks 1993–1999 WFusion/WInput Q ~ 0.1 1 W = energy Laser direct kev s ) kev Q ~ 0.01 drive (1996) – 3 0.1

m Q ~ 0.001 Laser direct 20 0.01 drive (1986) ( 10 Q ~ 0.0001 Laser indirect 0.001 drive (1986) Q ~ 0.00001 Lawson fusion parameter, n Lawson fusion parameter, 0.0001 0.1 1 10 100 “Review of Burning Plasma Physics,” Central ion temperature (keV) FESAC Report (September 2001).

51st Annual Meeting of the R. Betti American Physical Society University of Rochester Division of Plasma Physics Fusion Science Center and Atlanta, GA Laboratory for Laser Energetics 2–6 November 2009 Collaborators FSC

K. S. Anderson (UO5.00004) P. Chang (TO5.00004) R. Nora C. D. Zhou University of Rochester Laboratory for Laser Energetics

B. Spears (UO5.00013) J. Edwards S. Haan J. Lindl Lawrence Livermore National Laboratory Summary The measurable Lawson criterion and hydro-equivalent curves determine the requirements for an early hydro-equivalent demonstration of ignition on OMEGA and on the NIF (THD) FSC

• Cryogenic implosions on OMEGA have achieved a Lawson parameter PxE á 1 atm-s comparable to large tokamaks • Performance requirements for hydroequivalent ignition on OMEGA and NIF (THD)*

GtRH GT H YOC Px Hydro-equivalent ignition n i n E g/cm2 keV (atm s) 15% OMEGA (25 kJ) ~0.30 ~3.4 (~3 × 1013 2.6 neutrons) NIF (THD) ~1.8 ~4.7 ~40% 20

* NIF will begin the cryogenic implosion campaign using a surrogate Tritium– Hydrogen–Deuterium (THD) target. Only a very small fraction of Deuterium (<5%) is used to prevent fusion reactions from affecting the hydrodynamics. TC8563a See B. Spears (UO5.00013). Outline FSC

• A 1-D measurable Lawson criterion for ICF • Hydro-equivalent curves and hydro-equivalent ignition • The 3-D extension of the Lawson criterion • Comparison with magnetic confinement

TC8633 Outline FSC

• A 1-D measurable Lawson criterion for ICF • Hydro-equivalent curves and hydro-equivalent ignition • The 3-D extension of the Lawson criterion • Comparison with magnetic confinement

TC8633a “Classic” work on ICF ignition has focused on static models of the hot spot and has neglected the dense shell FSC

• Lawson criterion applied to the hot spot 15 –3 nTixE > 3 × 10 cm keV s n, x cannot be measured • Static models of the ignition condition use the hot-spot areal density and ion temperature 2 tRhot spot á 0.3 g/cm Ti á 5 to 10 keV

tRhot spot cannot be measured

• J. D. Lawson, Proc. Phys. Soc. London • R. Kishony et al., Phys. Plasmas 4, 1385 (1997). B70, 6 (1957). • J. D. Lindl, Inertial Confinement Fusion: The Quest • S. Yu. Gus’kov et al., Nucl. Fusion for Ignition and Energy Gain Using Indirect Drive 16, 957 (1976). (Springer-Verlag, New York, 1998). • S. Atzeni and A. Caruso, Phys. Lett. A • S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial 85, 345 (1981). Fusion: Beam Plasma Interaction, Hydrodynamics, Hot • S. Atzeni and A. Caruso, Nuovo Cimento B Dense Matter, International Series of Monographs on 80, 71 (1984). Physics (Clarendon Press, Oxford, 2004).

TC8532a Ion temperatures, areal densities, and neutron yields are parameters of the fuel assembly that can be measured with existing diagnostics FSC dNneutron • Neutron yields and neutron rates Nneutron are measured with scintillators dt

• Ion temperature (neutron averaged) is Ti measured with the neutron time-of-flight neutron detectors 3 tR / tdr • Total areal density (neutron averaged) neutron #0 is measured with magnetic recoil neutron spectrometer measuring the Shell downscattered neutron fraction.*

Hot spot Total tR . shell (tD)stagnation

Dstagnation

TC8533a See J. Frenje (NI2.00004). A dynamic model of ignition relates the hot-spot stagnation properties to those of the shell FSC Dynamic model of hot-spot formation and ignition

Alpha Deceleration deposition

Peak implosion Stagnation Ignition velocity V = Vi

The initial conditions are those at peak Thermal implosion velocity instability

• R. Betti et al., Phys. Plasmas 8, 5257 (2001). • R. Betti et al., Phys. Plasmas 9, 2277 (2002). • J. Sanz et al., Phys. Plasmas 12, 112702 (2005). • Y. Saillard, Nucl. Fusion 46, 1017 (2006). • J. Garnier and C. Cherfils-Clérouin, Phys. Plasmas 15, 102702 (2008). • C. D. Zhou and R. Betti, Phys. Plasmas 15, 102707 (2008). TC8534a The heat and radiation energy lost by the hot spot does not propagate through the dense cold shell; no heat or radiation flux at the hot-spot boundary FSC mo < Dshell 5 2 mo qheat =-l] Tg dTT lSp ] g .l0 T

T t shell 3 2 nm TeV hokeV 1000 m = c m o 200 5 etg/ cco Heat flux Rad. flux

Radiation flux . 0 Shell Shell Heat flux . 0 Hot spot R+ Hot spot R r R + + qheat ` r = Rj . 0 qrad `r= R j . 0

TC8536

Shell The hot-spot global energy balance determines the ignition condition FSC

d 3 P] tg Vol^th = compression/decompression work dt ;2 E

+ a_heating — (conduction + radiation losses)

dR Compression/decompression work =-S t P t ]]g g dt fa 2 vv Alpha heating = P # dV fa = 3.5 MeV 16 v T2 2 + SR=4r Conduction losses at R = #S qheat :ndS = 0 4r 3 Radiation losses at R+ = q : ndS = 0 Vol= R #S rad 3

TC8537 The dynamic ignition model requires an equation for the temperature evolution FSC

3 3 Use a T approximation of GvvH & GvvH . CaT

• Hot-spot energy equation d 3 2 dR 2R 2 P]] tgR t g =-2P]] tgR t g +C P] tg # Tr dr dt 8 B dt a 0

• Shell’s momentum equation (simple “thin-shell” approximation, Msh / shell mass) 2 d R 2 Needs T(r,t) Msh =4rP]] tgR t g dt2

More realistic compressible “thick shell model” see:

TC8538 R. Betti et al., Phys. Plasmas 9, 2277 (2002). The heat lost by the hot spot is deposited on the shell inner surface driving an ablative mass flow into the hot spot (ignore radiation losses*) FSC 5 2 Enthalpy flux lsp ]TT g = l0

Mass T t 5 ablation Pv = -l TTd 2 a sp ] g 2tT T : Pva =va =2 ma mi mi Heat flux : m l Shell i 0 dT m = - T3 2 a 5 dr Hot spot 2/ 5 r2 useTT= 0 ^th f 1Z p R2 R r 5/ 2 : 4mi l0T 0 ma = 25 R^ t h *Radiation losses are ignored in this talk for simplicity. TC8539 They are included in C. D. Zhou and R. Betti, Phys. Plasmas 15, 102707 (2008). Mass conservation in the hot spot determines the temperature evolution FSC

5 2 • Ablation rate from shell : 4mi l0 T0] tg ma = to hot spot 25 R] tg

• Hot-spot-mass dM : =4rR2 m conservation dt a

3 m P t 4m P]]tg R t g • Mass–Temp relation M=##t dV = i ] g dV. i 2 T r,t T t v v ^ h 0] g

3 • Temperature equation d PR 4r 5 2 f p . l0 RT0 dt T0 25

TC8541 Hot-spot-ignition model: three ODE’s for pressure, radius, and central temperature FSC

• Hot-spot energy or pressure equation

d dR P t R t 3 =-2P t R t 2 +CP t2 T t R t 3 dt 7 ]]g g A ]]g g dt a ]]g0 g ] g

• Shell momentum or hot-spot-radius equation

2 d R 2 Msh =4rP]] tgR t g dt2

• Hot-spot-mass or temperature equation*

3 d P]] tgR t g 4r 5 2 . l0 R]] tgT0 t g dt > T0] tg H 25

TC8542 *Radiation losses are neglected in this talk for simplicity The initial conditions are related to the time when the imploding shell reaches the maximum implosion velocity FSC

t = 0 " Maximum implosion velocity Vi Vi Dense shell R(0) Stagnating core P(0) T(0) Hot spot

0 : PP^0h=0TT 0 ^ 0 h = 0 RR^0h=0 RV ^ 0 h =- i

• Expansion parameter d % 1

3 Hot- spot thermal energy ^t=0h 2rPR^0h ^ 0 h ! / = % 1 Shell kinetic energy t=0 2 ^ h ^1 2hMVsh i

TC8543 The model has an analytic solution in the absence of a-particle energy deposition FSC

• Stagnation pressure PPno-a .!-5 2 (without alphas) st 0

• Stagnation radius no-a 1 2 Rst .! R0 (without alphas)

R 3 V2 7 • Stagnation temperature no-a S0. 1 MVsh i W Tst = S W (without alphas) l0 no-a 2 S _Rst i W T X

3 2rPR^0h ^ 0 h ! / %1 Expansion parameter 2 ^1 2hMVsh i

TC8544 The no-a stagnation values are used in the derivation of the dimensionless ignition model (with a’s); ignition depends on the one dimensionless parameter ca FSC Dimensionless variables

ˆ no-a ˆ no-a ˆ no-a no-a PP= PRst = RRst TT= Tst x= tVRi st

Energy Mass Momentum ˆ ˆ 3 2 ˆ d ˆ ˆ 5 ˆ ˆ 5 ˆ d PR 5 2 d R ˆ ˆ 2 _PR i = ca PR T d n =RT =PR dx dx Tˆ dx2

Initial conditions Critical parameter—determines ignition t 5 2 P]0g = ! t -1 2 no--ano a no-a R]0g = ! PRst st Tst d"0 ca= C a to 8Vi R]0g = - 1 t 1 2 T]0g = ! TC8545a Ignition condition for the model equations: find the critical value of ca leading to an explosive solution FSC

Singularity P ( t )

Time

Condition for singular Singularity ca > 1.2 explosive solution caused by 3 GvoH ~ CaT

no--ano a no-a PRst st Tst ca~ C a 8 Vi

Cannot be measured TC8546a The ignition parameter ca can be written in terms of the measurable parameters tRtotal and Ti FSC

Energy conservation Ignition condition: ca > 1.2 1 2rPR3 = MV2 no --ano a no - a st st 2 sh i PRst st Tst ca~ C a 8Vi Shell mass at stagnation 2 Msh .4rtstDst Rst Rst Temperature-velocity relation 2 7 Dst no-a 0. 4r no-a 3 Tst = ^tD h Vi Shell < l0 st F

Measurable ignition condition

no-a 2 3 no-a 13 6 c~ C ^ tDh aTst k > 1. 2 ^tD h . tRtotal a a : st D st

TC8547 Verify that the theory is right. Simulate many marginally igniting targets and plot the total areal density versus the ion temperature FSC 6 • Simulation database Fit of simulations

) 5 – marginal ignited targets 2 (Gain = 1) 4 Ignition 1-D simulations – laser energy ( g / cm 35 kJ to 10 MJ 3 – implosion velocity n no- a 2 170 to 530 km/s R H t G tR no-a = neutron-averaged 1 n total areal density 0 no-a 2 3 4 5 6 Ti = neutron-averaged n no-a ion temperature GTHn (keV)

1-D simulations show that all marginally ignited targets no--ano a lie on a single curve in the tRT, i plane.

TC8234a C. D. Zhou and R. Betti, Phys. Plasmas 15, 102707 (2008). The 1-D Lawson criterion can be written in terms of the measurable parameters tRtotal, Ti FSC • Simple model (this talk)

39/12 RTno-a no-a > const C3/ 2 ^t hst a st k a

• Include more physics: finite shell thickness

5/ 2 RTno-a no-a > 40 g/ cm2keV 5/2 ^t hst a st k

• Include radiation transport (analytic model)* no-a no-a 5 4 2. 5 T in keV ^tRTh a st k . st no-a 5 2 tR in g/cm2 1- b3 Tst l 14444 2 44443 Bremmsstrahlung pole

TC8549a C. D. Zhou and R. Betti, Phys. Plasmas 15, 102707 (2008). The analytic model agrees reasonably well with the simulations; the latter can be accurately fit by a simple power law tR × T2 > 20 for 3.5 < T < 7 keV FSC 4 2.0 Ignition Ignition ) ) 2 3 2 1.5 Best simple 1-D simulations fit for 3.5 < T < 7 keV

( g / cm ( g / cm 2

tR = 20/T

a 2 1-D analytic model 1.0 no- no- a n n H H

1 0.5 G t R G t R

0 0.0 2 3 4 5 6 7 8 4 5 6 7 no-a no-a GTHn (keV) GTHn (keV) Ignition condition 2 no-a 1-D ignition no-a TkeV no-a / R 2 > 1 3.5 < T < 7 parameter |1-D t g cm f np keV n 4. 6 TC8634 When can Tno-a, tRno-a be measured and the Lawson criterion be assessed? FSC 1 • Surrogate D2 implosions • Surrogate THD implosions2 • DT implosions on OMEGA3,4 • DT implosions on the NIF with Gain < 0.1

For all of the above T . Tno-a, tR . tRno-a. Use the measurable Lawson criterion.

• DT implosions on the NIF with 0.1 < Gain < 1.0: T > Tno-a • DT implosions on the NIF with Gain > 1: T > Tno-a and tR < tRno-a For those, no need for a Lawson criterion. Just look at the neutron detector.

1T. C. Sangster et al., Phys. Rev. Lett. 100, 185006 (2008). 2B. Spears (UO5.00013). 3V. N. Goncharov (UO5.00002). TC8550a 4T. C. Sangster (NI2.00002). Outline FSC

• A 1-D measurable Lawson criterion for ICF • Hydro-equivalent curves and hydro-equivalent ignition • The 3-D extension of the Lawson criterion • Comparison with magnetic confinement

TC8633b Hydro-equivalent implosions have the same implosion velocity, in-flight adiabat, and laser intensity leading to equal stagnation density and pressure FSC

Vi Vi a

a P a = shell adiabat/ & measure the entropy PF

2 350 Vi ^km sh max 780 Vi ^km sh 0. 13 Pst ]Gbarg . tst ^g cch . I15 a0. 9= 300 G a = 300 G

• In hydro-equivalent targets, mass and size depend on laser energy 1 3 1 3 Mass ~ EL Radius = RE~ L Thickness = D ~ EL

TC8635 Hydro-equivalent implosions have similar Rayleigh–Taylor growth factors and nonlinear bubble-front penetration FSC • Hydro-equivalent implosions have the I15 same in-flight aspect ratio( IFAR)* 1 2 R0 R0 40 Vi ^km s h -1 4 / IFAR . I D 0. 6= 300 G 15 if a t t p Dif • Hydro-equivalent implosions have a similar linear growth factor ct 2 RR h= h0 ec t ~k gt ~ kDif ~ ~ IFAR DDif if ~R ~1

• Hydro-equivalent implosions have a similar nonlinear growth h bgt2 bR bubble ~ ~ ~ b : IFAR DDif if Dif 0.05

*J. D. Lindl, “Inertial Confinement Fusion: The Quest for Ignition and Energy TC8636 Gain Using Indirect Drive (Springer-Verlag, New York, 1998), Chap 6, p. 61. Total areal densities and ion temperatures increase as hydro-equivalent implosions are scaled up in energy FSC

0. 06 Vi 1 3 Marginal Ignition tRtot ~ EL ignition a0. 6 NIF Hydro-equivalent

tot curve V1. 25 i 0. 07 Vi = constant E Ti ~ EL t R L a0.15 a = constant EL varies OMEGA C. D. Zhou and R. Betti, Phys. Plasmas 14, 072703 (2007).

Ti

Hydro-equivalent curves show how OMEGA implosions would perform (in 1-D) when scaled up in energy.

TC8637 The progress in direct-drive ICF can be assessed on the tR, Ti plane through hydro-equivalent curves; OMEGA’s goal is to achieve hydro-equivalent ignition FSC Ignition †

) 2.0 1.5 MJ 2 1.5 MJ 1.5 MJ‡ 1.0 0.5 MJ Marginal ignition OMEGA 0.45 MJ ( g / cm 0.5 23 kJ** no- a n OMEGA 2009 23 kJ† 17 kJ 0.2 2007* 23 kJ

7 7 7

Total G t R H Total V = 2.2 × 10 V = 3.5 × 10 V = 4.3 × 10 0.1 a = 2.5 a = 2.0 a = 3 CH ablator CH ablator All DT point design 2001

0 1 2 3 4 5 6 7 8 no-a GTiHn (keV) This diagram measures progress in 1-D compression; it does not include a good measure of implosion uniformity.

* T. C. Sangster et al., Phys. Rev. Lett. 100, 185006 (2008). † V. N. Goncharov (UO5.00002). ** T. C. Sangster (NI2.00002). ‡ P. W. McKenty et al., Phys. Plasmas 8, 2315 (2001). TC8638 Outline FSC

• A 1-D measurable Lawson criterion for ICF • Hydro-equivalent curves and hydro-equivalent ignition • The 3-D extension of the Lawson criterion • Comparison with magnetic confinement

TC8633c In 3-D the fusion yield is reduced by the Rayleigh–Taylor instability that cools down parts of the hot spot FSC 3 3 VR3- D ~ 3- D

3- D 2 1-D V3- D Shell Nneutron ~ ni vv V3- D xburn ~ Nneutron V1D-

Hot spot • The yield-over-clean YOC = 3-D fusion Cold R yield; 1-D yield is approximately equal 3-D to the ratio unmixed volume/1-D volume R GvvH 1-D ≈ 0

Can be measured

N3- D V YOC without YOC/.neutron 3- D a-deposition 1D- V no-a Nneutron 1D- YOC

TC8551 *R. Kishony and D. Shvarts, Phys. Plasmas 8, 4925 (2001). The YOC is used to extend the measurable Lawson criterion to three dimensions FSC

Back to the 1-D Lawson criterion

39 12 RTno-a no-a > const C3 2 ^t hst a st k a

Ca ~ #v v v dV

V 3- D ..1D- 3- D 1D- no-a Ca ~ #V vv dV Ca Ca : YOC 3- D V1D-

3-D measurable Lawson criterion

39 12 3 2 tRTno-a no-a _YOCno-ai > const ^ hst a st k

TC8552a An analytic model based on the free-fall lines provides a quantitative estimate of the 3-D Lawson criterion* FSC

The RT becomes nonlinear The spikes free fall

R = shell trajectory Shell R Hot spot 1-D rebound

R3-D RT spikes

Time

• Analytic 3-D measurable Lawson criterion 5 2 Tno-a |analytic / tR no-a f st p YOCno-a > 1 3- D ^ hst 4. 6

TC8639 *P. Chang (TO5.00004). The clean volume analysis is validated by comparing 2-D simulations with inner-surface roughness and 1-D simulations no-a having reduced GvvH→GvvHV3-D/V1-D ≈ GvvHYOC FSC • In the 1-D simulations, GvvH is reduced by the YOC (or clean volume fraction) until the hot-spot temperature reaches 10 keV. Direct-drive surrogate of NIF Direct-drive 1.5-MJ 1.0-MJ indirect drive all-DT target design 45 25 40 35 20 30 25 15

Gain Gain 20 10 15 10 5 1-D code 1-D code 2-D code 5 2-D code 0 0 0 20 40 60 80 100 0 20 40 60 80 100 YOCno-a (%) YOCno-a (%) TC8553 K. S. Anderson (UO5.00004). Results from a 2-D + pseudo 2-D simulation database are in reasonable agreement with the ignition model FSC

1-D 1.0

0.8

0.6 Minimized spread 0.4

0.2 Normalized gain G / Normalized 0.0 0.0 0.5 1.0 1.5 2.0 no-a 2 T 0.7 |= tR no-a e st o YOCno-a ^ hst 4. 7 ^ h

• 3-D measurable Lawson criterion (fit from simulations) no-a 2 T 0. 7 |fit = tR no-a f st p YOCno-a > 1 3- D ^ hst 4. 7 ` j TC8640 Hydrodynamic scaling laws provide the requirements for an hydro-equivalent demonstration (1:60) of ignition on OMEGA FSC

• Areal density: OMEGA needs to demonstrate GtRH á 0.3 g/cm2

• Ion temperature: OMEGA needs to demonstrate Ti .3.4 keV • Yield-over-clean (YOC): the required YOC on OMEGA is difficult to estimate. Use simple clean volume analysis: NIF X R3--DD= R1 – DRRT DRGRT ~ v0 RT GGRT . RT RT spike amplitude Initial seed Growth factor Hydro-equivalency

R 1/ 3V3 S X NIF W X v0 EL YOC . S1– ^1– YOCNIFh W S NIF f X p W S v0 EL W T X

TC8660 A simple estimate indicates that OMEGA must achieve YOC’s around 15% (weakest point of the theory) FSC • Seeds for the RT come from the ice roughness and the 2 2 laser nonuniformities: v0 . vice+v laser X NIF • Beta layering makes NIF targets as smooth as OMEGA’s: vice. v ice 1/3 • Laser nonuniformities grow with size (EL ) and are reduced by a larger number 1// 3 Z1 2 of overlapping beams (Nb) vlaser ~ ENL b

X 2 v 1+vˆ X 0 . X v NIF L v NIF 2/ 3 X vˆ X / 0 E Nb X 1+ L vˆ 2 vice f X p f NIF p X EL Nb 0.3 Ice roughness is dominant Upper bound . 20% YOC on OMEGA 0.2 that extrapolates X 0.15 to a YOC á 50%

YOC 0.1 on the NIF Laser nonuniformities (very approximate!) are dominant 0.0 0 1 2 3 TC8661 vˆ X OMEGA (DT) and NIF (THD) campaigns aim to achieve an early hydro-equivalent demonstration of ignition (on different scales) FSC • Where does OMEGA currently stand? tR . 0.2 g/cm2 T .2.1 keV YOC á 10% n i n T 2 Igniton parameter | = 0.008 |/ tR YOC0. 7 b4. 7 l

• A scale 1:60 (25 kJ:1.5 MJ) hydro-equivalent demonstration of ignition on OMEGA requires tR .0.3 g/cm2 T .3.4 keV YOC á 15% n i n Ignition parameter | = 0.04

• An early scale 1:1 demonstration of ignition on the NIF-THD* requires tR .1.8 g/cm2 T .4.8 keV YOC á 40% n i n Ignition parameter | = 1

TC8662 *THD = Tritium–Hydrogen–Deuterium targets, see B. Spears (UO5.00013). Outline FSC

• A 1-D measurable Lawson criterion for ICF • Hydro-equivalent curves and hydro-equivalent ignition • The 3-D extension of the Lawson criterion • Comparison with magnetic confinement

TC8633d A confinement time for ICF can be derived from the ignition condition FSC

• Start from the analytic measurable Lawson criterion 4 5 c YOC T 15 8 a = tR 3 4 YOC4 5 / |3 4 >1 1. 2 ^ h c4. 6m

• Rewrite ca and define a 1-D confinement time Energy conservation fa vv Rst 1-D Rst 1 2 3 c / P x / MVsh i =2r PRst st a 2 st f V p E f V p 2 24 Tst i i • The 1-D confinement time is the time required to displace the shell by a distance of the order of the hot-spot radius

1-D Rst Msh xE / = Vi 4rPRst st • The 3-D confinement time is reduced by the RT instability. Its degradation is measured through the YOC

3--D 1 D 4 5 xE = xE : YOC

TC8721 Simulations show a confinement time for OMEGA of about 10 ps and a pressure of about 100 Gbar, leading to PxE ~ 1 atm × s FSC • Cryogenic DT implosions: simulation/experimental results sim sim 7 exp Rst . 22 nm Vi . 3 # 10 cm s YOC . 0.1

Simulation of shot 52729 100 160 Rst x / YOC4 5 . 12 ps ) t 80 E 3 Vi

120 Shell P 60 80 40 Pst . 80 Gbar Hot spot Density ( g / cm 40 20 ( Gbar ) Pressure Pst xE . 1 atm × s 0 0 0 10 20 30 40 Radius (nm) TC8722 An effective PxE for ICF can be constructed using the ignition model and compared with PxE in MCF FSC

• Define ax E from the ignition model 2 3/ 4 24 T 3/ 4 ca ~ PstagxE ~ | Pstag xE . | fa vo

3 • Use GvvH ~ CaT consistent with the analytic model |3/ 4 Px . 98 atm# s ^ EhICF T keV n ^ h

& • OMEGA: |..0.008,T 2.1 keV PxE . 1.2 atm # s

• JET: PxE ~ 1.2 atm × s*

TC8663 * “Review of Burning Plasma Physics,” FESAC Report DOE/SC-0041 (September 2001). The Lawson plots show the current performance and the future directions for OMEGA FSC Deuterium–Tritium Plasmas

103 * E 100 Ignition x i Q ~ 10 T OMEGA H. E. I. 2 OMEGA i 10 OMEGA (2009) hydro-equivalent ITER 10 Q ~ 1 ignition Q = 1 W /W 10 Fusion Input Tokamaks Q = 2 Q ~ 0.1 OMEGA (2009) Jet 1 W = 100 Ignition energy TFTR CTF C-mod s ) kev FRC Q ~ 0.01

–1 DIIID – 3 10 Spheromak 0.1 ( atm × s ) LHD E RFP m Q ~ 0.001 –2 NSTX ST 20

H x 10 Stellarator 0.01 P

G LSX –3 Tokamak ( 10 Q ~ 0.0001 10 Tokamak MST Tokamak 0.001 10–4 Tokamak Q ~ 0.00001 SSPX ITER

Lawson fusion parameter, n Lawson fusion parameter, 0.0001 10–1 100 10–1 102 0.1 1 10 100 GTH (keV) Central ion temperature (keV)

OMEGA hydro-equivalent ignition:** How to resolve the discrepancy | á 0.04, GTH á 3.4 keV, pxE á 2.6 atm × s with the thermonuclear Q = Pfus/Pinput?

* Figure courtesy of J. P. Freidberg (MIT) TC8678 ** Assuming the YOC prediction is correct The discrepancy on Q is resolved by defining a physics-based thermonuclear Q FSC • “Conventional” hot-spot energy balance 3 p 5Win 5 3 p WWa +in =Wlosses = Wa f1+ p =Wa c1+ m = 2 xE Wfus Q 2 xE

• Fine pxE from the energy balance 24 T2 Q pxE = fa vo 5+Q

• Define a physical thermonuclearQ for ICF WOMEGA = 24 kJ physics Wfusion physics Wfusion laser QICF ! QICF = Wlaser Whot spot WOMEGA . 440 J From 1-D hot spot simulations

12 physics Measured neutron yield: 6 × 10 QOMEGA . 3.% 8

For a measured T = 2.1 keV, 24 T2 Q pxE = .1 atm # s the previous result is recovered fa vo 5+Q

TC8679 Hydro-equivalent ignition on OMEGA requires Q ~ 20% to 25% and a neutron yield ~ 3 × 1013 FSC

• Hydro-equivalent ignition requires pxE á 2.5 atm/s with T á 3.4 keV • Determine Q from energy balance 24 T2 Q pxE = Q á 0.25 fa vo 5+Q

• Determine neutron yield from Q 13 Wfusion .0.25 Whot spot .110 J& 3.8 # 10 neutrons

• Check with 1-D simulation of hydro-equivalent design 1-D – neutron-yieldsim á 2 × 1014, YOC á 15% & 3 × 1013 neutrons

• Summary for hydro-equivalent ignition requirements on OMEGA 2 13 GtRH á 0.3 g/cm GTiHn á 3.4 keV neutron-yield á 3 × 10

TC8680 Summary/Conclusions The measurable Lawson criterion and hydro-equivalent curves determine the requirements for an early hydro-equivalent demonstration of ignition on OMEGA and on the NIF (THD) FSC

• Cryogenic implosions on OMEGA have achieved a Lawson parameter PxE á 1 atm-s comparable to large tokamaks • Performance requirements for hydroequivalent ignition on OMEGA and NIF (THD)*

GtRH GT H YOC Px Hydro-equivalent ignition n i n E g/cm2 keV (atm s) 15% OMEGA (25 kJ) ~0.30 ~3.4 (~3 × 1013 2.6 neutrons) NIF (THD) ~1.8 ~4.7 ~40% 20

* NIF will begin the cryogenic implosion campaign using a surrogate Tritium– Hydrogen–Deuterium (THD) target. Only a very small fraction of Deuterium (<5%) is used to prevent fusion reactions from affecting the hydrodynamics. TC8563a See B. Spears (UO5.00013).