Ignition, the Lawson Criterion, and Perfomance … the Lawson Criterion, and Perfomance Assessment for ICF implosions FSC Review of the National Ignition Campaign Livermore, CA 9–11

Ignition, the Lawson Criterion, and Perfomance Assessment for ICF implosions

FSC

Review of the National Ignition Campaign

Livermore, CA 9–11 December 2009

R. BettiUniversity of RochesterFusion Science Center andLaboratory for Laser Energetics

“Review of Burning Plasma Physics,” FESAC Report (September 2001).

GTH (keV)

GPHx

E (

atm

× s

)

10–1

10–4

10–3

10–2

10–1

100

101

102

103

100 10–1 102

Jet

ITER

TFTRDIIID

C-mod

LHD

NSTX

LSX

MST

SSPX

OMEGA (2009)Q = 2

IgnitionCTFFRCSpheromakRFPSTStellaratorTokamakTokamakTokamakTokamakITER

NIFThe National Ignition Campaign

Collaborators

K. S. AndersonP. Chang

R. L. McCroryR. Nora

C. D. Zhou

University of Rochester Laboratory for Laser Energetics

B. SpearsJ. Edwards

S. HaanJ. Lindl

Lawrence Livermore National Laboratory

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)

TC8563b

FSC

Summary

* 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.

• CryogenicimplosionsonOMEGAhaveachievedaLawsonparameter PxE á 1 atm-s comparable to large tokamaks

• Performancerequirementsforhydroequivalentignition on OMEGA and NIF (THD)*

Hydro-equivalent ignitionGtRHng/cm2

GTiHnkeV

YOC PxE(atm s)

OMEGA (25 kJ)1:60 ~0.30 ~3.4

15%(~3 × 1013 neutrons)

2.5

NIF (THD) (1 MJ) 1:1 ~1.8 ~4.8 ~37% 21

Outline

TC8633a

• A1-DmeasurableLawsoncriterionforICF

• Hydro-equivalentcurvesandhydro-equivalentignition

• The3-DextensionoftheLawsoncriterion

• Comparisonwithmagneticconfinement

FSC

A dynamic model of ignition relates the hot-spot stagnation properties to those of the shell

TC8534a

• R.Bettiet al., Phys. Plasmas 8, 5257 (2001).• R.Bettiet al., Phys. Plasmas 9, 2277 (2002).• J.Sanzet al., Phys. Plasmas 12, 112702 (2005).• Y.Saillard,Nucl.Fusion46, 1017 (2006).• J.GarnierandC.Cherfils-Clérouin,Phys.Plasmas15, 102702 (2008).• C.D.ZhouandR.Betti,Phys.Plasmas15, 102707 (2008).

Deceleration Alphadeposition

Dynamic model of hot-spot formation and ignition

Stagnation

Thermalinstability

IgnitionPeak implosionvelocity V = Vi

The initial conditionsare those at peakimplosion velocity

FSC

Hotspot

Dstagnation

Shell

Ion temperatures, areal densities, and neutron yields are parameters of the fuel assembly that can be measuredwithexistingdiagnostics

TC8533a

• Neutronyieldsandneutronrates Ndt

dNneutron

neutron

are measured with scintillators

• Iontemperature(neutron averaged) is Ti neutronmeasured with the neutron time-of-flight detectors

• Totalarealdensity(neutron averaged) R dr0neutron neutron/t t3#

is measured with magnetic recoil spectrometer measuring the downscattered neutron fraction.

FSC

Total tR . shell (tD)stagnation

Hot spot

R r

T t

mo

Sh

ell

Shell

R

R+

Hotspot

Shell

Heat fluxRad. flux

Radiation flux . 0Heat flux . 0

mo < Dshell

The heat and radiation energy lost by the hot spot does not propagate through the dense cold shell; no heat orradiationfluxatthehot-spotboundary

TC8536

FSC

q T T T T

T h200 5

1000/

shelleV keV

g cc

02

3

heat Sp

m 2

- d .l l l

mo

t

=

=on

5] ]

c e

g g

m o

q r R q r R0 0heat rad. .= =+ +` `j j

Heat conduction losses do not affect the hot-spot pressure. They reduce the hot-spot temperature and raise the hot-spot density

TC5778b

• Heat-conductionlossesarerecycledbymassablation into the hot spot and do not change the hot-spot pressure

Ti(1le)

Ti(4le)

t

R (nm) R (nm)

t(g

/cc)

T i(k

eV)

Pre

ssu

re (

Gb

ar)

0

200

0

400

600

800

1000

1200

10 20 30 40 50 100 20 30 40 500

2

4

6

8

10

12700

600500400300200100

0

Ti(0.25le)

T

t

P

FSC

The hot-spot ignition condition is given by the balance ofalphaheatingwiththeexpansionlosses

TC7595a

FSC

P = Phs = Ps

r

Rhs

Rs

tsshell

ths

Hot spot

Isobaric fuelassembly

0>EE 1 1

exphs

hs -x x=a

o

~ vn P1 2hs hsfx va a Alpha heating

(fa = 3.5 MeV)

~ R R1 exp hs hsx p Expansion

M R P R4s2

hs hs hsr=p shell Newton’s law

vT24P exp

2

hs x f v=

a

Lawson criterion

Theexpansionlossesrepresenttheinternalenergylostby the hot spot and transferred to the surrounding dense shell as kinetic energy

TC7914

~ R R1 exp hs hsx p Expansion

M R P R4s2

hs hs hsr=p Shell Newton’s law

FSC

RhsPhs

Hot spot

Shell

Dsts

~M Rs s s s2t D

Shell arealdensity

Ds = shell thickness

~P R1

exp s

hs hsx M

Shell mass

The ignition condition depends on shell areal density, implosion velocity, and hot-spot ion temperature

TC7916a

FSC

vRP

MT

const>si2hs

hs v

Hot-spot pressure and temperature

Hot-spot radius Shell mass

v C T

T keV8for 4 < <i

3+v a

• ~ ~P P R R M V Rs s s s3 3 2 3

hs hs` `j j

• ~M Rs s s s2t D

• Rs ~ Rhs

VT constC

>s s it Da

_ i

Shell areal density Implosion velocity

Eliminating the velocity and energy leads to an ignition condition depending on the shell areal density and hot-spot ion temperature

TC7918a

FSC

T const C. 0.83i2 1 .0 03

2atD aif^ h: D

Hydro-variablesscaling from Ref. 1

~V T E. .ifi L

0 8 0 15a .0 056-

~E VifL s s3 0.18.1 75t aD

-_ i

1C. Zhou and R. Betti, Phys. Plasmas 14, 072703 (2007).

Verify that the theory is right. Simulate many marginally igniting targets and plot the total areal density versus the ion temperature

TC8234a

FSC

1-D simulations show that all marginally ignited targets lie on a single curve in the ,R Ti

no not a a- - plane.

• Simulationdatabase– marginal ignited targets

(Gain = 1)– laser energy

35 kJ to 10 MJ– implosion velocity

170 to 530 km/s

R nn

ot a- = neutron-averaged total areal density

Tino

n

a- = neutron-averaged

ion temperature2

0

1

2

3

4

5

6

3 4 65

Ignition1-D simulations

Fit of simulations

GtR

H n

(g

/cm

2 )n

o-a

GTHno-a (keV)n

C. D. Zhou and R. Betti, Phys. Plasmas 15, 102707 (2008).

The analytic model agrees reasonably well with the simulations;thelattercanbeaccuratelyfitbyasimplepower law tR × T2 > 20 for 3.5 < T < 7 keV

TC8634a

FSC

D-.

7.RT

T4

1 3 57

> < <1

2

g cmno

n

keVno

n keVno

2/| t aa

a--

-f p1-D ignitionparameter

Ignition condition

4

Best fit for3.5 < T < 7 keVtR = 20/T2

0.5

0.0

1.0

1.5

2.0

5 6 7

IgnitionGt

R Hn

o-a

(g/c

m2 )

n

GTHno-a (keV)n

When can Tno-a, tRno-a be measured and the Lawson criterion be assessed?

TC8550b

• SurrogateD2 implosions

• SurrogateTHDimplosions

• DTimplosionsonOMEGA

• DTimplosionsontheNIFwithGain< 0.1

• DTimplosionsontheNIFwith0.1< Gain < 1.0: T > Tno-a

• DTimplosionsontheNIFwithGain> 1:T > Tno-a and tR < tRno-a

For those, no need for a Lawson criterion.Just look at the neutron detector.

FSC

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

Outline

TC8633b





FSC

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

TC8635

• Inhydro-equivalenttargets,massandsizedependonlaserenergy

Mass ~ EL Radius = ~R EL1 3 Thickness = ~ EL

1 3D

IPV V350

300780

300Gbar

km sg cc

km s.

.maxi i0 9

2

150 13

stst . .a

t a] ^ ^ ^g h h h= =G G

FSC

shellPPadiabat measure the entropyF&/a =

Vi

a

Vi

a

Hydro-equivalent implosions have similar Rayleigh–Taylor growth factors and nonlinear bubble-front penetration

TC8636

• Hydro-equivalentimplosionshavethe same in-flight aspect ratio (IFAR)*

IR V40

300IFARkm s

.i0

0 6

2

151 4

if./

aD

-^ h= G

• Hydro-equivalentimplosionshaveasimilarlineargrowthfactor

~ ~ ~ ~e t k R Rk gt IFARifif if

t0

2h h c DD D

= c

• Hydro-equivalentimplosionshaveasimilarnonlineargrowth

~ ~ ~h Rgt

IFARif if if

2bubble

:b b

bD D D

0.05

~R ~1

FSC

R0

Dif

1

tp

I15

t

*J.D.Lindl,“InertialConfinementFusion:TheQuestforIgnitionandEnergyGain 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

TC8637

FSC

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

~RV

EiL1 3

totta .0 6

.0 06

~V

ET ..

iLi0 07

15

1 25

a .0

C. D. Zhou and R. Betti, Phys. Plasmas 14, 072703 (2007).

Ti

tR

tot

Marginalignition

Hydro-equivalentcurveVi = constanta = constantEL varies

EL

Ignition

NIF

OMEGA

Progress in ICF can be assessed on the tR, Ti plane through hydro-equivalent curves

TC8638b

This diagram measures progress in 1-D compression; it does not include a good measure of implosion uniformity.

FSC

* T. C. Sangster et al., Phys. Rev. Lett. 100, 185006 (2008).

10

0.1

0.2

0.5

1.0

2.0 1.5 MJ

Marginal ignition

2

Tota

l Gt

RH n

(g/c

m2 )

3 4 5 6 7 8

Ignition

1.5 MJ

23 kJOMEGA Goal

0.5 MJ

OMEGA23 kJ2009OMEGA

17 kJ2007*

V = 2.2 × 107

a = 2.5CH ablator

V = 3.5 × 107

a = 2.0CH ablator

GTiHn (keV)no-a

no

-a

Outline

TC8633c





FSC

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

TC8551

• Theyield-over-cleanYOC= 3-D fusion yield;1-Dyieldisapproximatelyequal to the ratio clean volume/1-D volume

FSC

~ ~V R V R<3 Dclean

clean3

1D 1D3

- - -

YOCN

NV

V

neutron1Dneutron3 D

1D

3 Dclean

/ .-

-

-

-

Rclean

Hot spotCold

Shell

R1-DGvvH ≈ 0

Can be measured

~ ~N n v NV

VVneutron

3 D3 D neutron

D

1D

3 Dclean

cleanburni

2 1v x--

-

-

-

YOC withouta-depositionYOCno–a

TheYOCisusedtoextendthemeasurableLawsoncriterion to three dimensions

TC8552b

Back to the 1-D Lawson criterion (simple analytic model)

3-D measurable Lawson criterion

FSC

R T YOC const>2.1 1.2

stno

stno not a a a- - -^ a _h k i

~C v dVv va #

~C v dV CV

VC YOCV

3 D 1D

1D

3 D 1D no3 D

:. .va a aa- -

-

- - --

#

R T Cconst>. .2 1 1 2

stno

stnot a a

a- -^ ah k

clean

The clean volume analysis is validated by comparing 2-D simulations with inner-surface roughness and 1-D simulations having reduced GvvH→GvvHV3-D / V1-D ≈ GvvHYOCno-a

TC8553

• Inthe1-Dsimulations,GvvH is reduced by the YOC (or clean volume fraction) until the hot-spot temperature reaches 10 keV.

FSC

YOCno-a (%) YOCno-a (%)

Gai

n

Gai

n

Direct-drive 1.5-MJ all-DT target design

Direct-drive surrogate of NIF 1.0-MJ indirect drive

0 604020020

25

454035302520151050

20

15

10

5

06040 8080 100 100

1-D code2-D code

1-D code2-D code

clean

Results from a 2-D + pseudo 2-D simulation database are in reasonable agreement with the ignition model

TC8640

FSC

• 3-DmeasurableLawsoncriterion(fitfromsimulations)

.

RT4 7 YOC 1>

.3 Dfit

20 7

stno st

nono| t= a

aa

--

--^ f `h p j

0.00.0

0.2

0.4

0.6

0.8N

orm

aliz

ed g

ain

G/G

1-D

Minimizedspread

1.0

0.5 1.0 1.5 2.0

.YOCR

T4 7st

no stno

no2

0.7| t= -a

aa-

-

^ e ^h o h

• WheredoesOMEGAcurrentlystand?

/0.2 g cmRn

2.t 2.1 keVTni . YOC á 10%

Igniton parameter | = 0.0083

• Ascale1:60(25 kJ:1.5 MJ) hydro-equivalent demonstration of ignition on OMEGA requires

/0.3 g cmRn

2.t 3. keVT 4ni . YOC á 15%

Ignition parameter | = 0.045

• Anearlyscale1:1demonstrationofignitionontheNIF-THD*requires

/1.8 g cmRn

2.t 4.8 keVTni . YOC á 37%

Ignition parameter | = 1

OMEGA (DT) and NIF (THD) campaigns aim toachieve an early hydro-equivalent demonstrationof ignition (on different scales)

TC8662b

FSC

*THD = Tritium–Hydrogen–Deuterium targets

.YOCR T

4 7.2 0 7/| t b l

Measurable ITF

The measurable Lawson criterion leads to the ignition threshold factor (ITF) and the energy margin (M)FSC

TC8728

~ , ~

1

R E T E

E

E R T

22

Use scalings:

3 D D

.

.. .

min

i

i

1 3 0 07

2 2 161 5 1 5

n kin n kin

ignkin n

t

t- -ITF YOC ITF YOC. .= ^ f ^h p h

ITF (3-D) . ITF (1-D) × YOC1.5

MYOCNIF pt. design = 5.3–0.66 . 33% . 37% in 2-D simulations

Margin = ITF - 1

st = stagnationkeVR T YOC 22gcm>

.no no no2 0 7 2st st

2t -a a a- - -^ _ ^h i h

Outline

TC8633d





FSC

A3-DconfinementtimeforICFcanbederived from the ignition condition (simple model)

TC8729

• StartfromtheLawsoncriterionandthemeasurablecondition

• Rewritethe1-Dconfinementtimeusingtheimplosionvelocity

• Extractthe3-Dconfinementtime.The1-Dconfinementtime is reduced by the Rayleigh–Taylor instability

YOC:D1-Ex=D3- .

E0 6x

/ =1 D-4 P R

MV

RE

ist st

sh stxr R2 Pst

3str=2

21 M Vish

Energy conservation

stst .

vT

P R T4 724

YOC. ..

D2 30 83 2 0 7

0 83.

f vx | t=a

- ^ bh l= G 3-D effects

FSC

SimulationsshowaconfinementtimeforOMEGA of about 17 ps and a pressure of about 70 Gbar, leading to PxE ~ 1 atm × s

TC8722a

• OMEGAcryogenicDTimplosions:simulation/experimentalresults

R V22 m 3 10 cm s YOC 0.1i7

stsim sim exp#. . .n

VR

7YOC 1 ps.E

i

0 6st./x

Pst . 70 Gbar

Pst xE . 1.2 atm × s

FSC

0 302010 40

Den

sity

(g

/cm

3 )

Radius (nm)

40

0

160

120

80

Pre

ssu

re (

Gb

ar)

20

0

100

60

80

40

Simulation of shot 52729

Hot spot

P

t

Sh

ell

Simulations show that NIF (THD) needs to achievea Lawson parameter PxE ~ 20 atm × s for an hydro-equivalent demonstration of ignition

TC8730

800700600500

400300200100 200

400

600

800

1000

1200

1400

0 10 20 30 40 50

Stagnation densityand pressure

P (

Gb

ar)

Den

sity

(g

/cc)

R (nm)

P t

Hot spot

Denseshell

650V

R

P

37YOC ps

Gbar

.E

i

0 6st

st

/

.

.x

P 21atm sEst .x -

• NIFsurrogateimplosion:simulationresults

.85 37R V2 m 3 10 cm s YOC 0.mini7

stsim sim sim#. . .n

A measurable PxE for ICF can be constructed using the ignition model and compared with PxE in MCF

TC8663b *“ReviewofBurningPlasmaPhysics,”FESACReportDOE/SC-0041(September 2001).

FSC

• DefineaxE from the ignition model

Pstag T24E

2.x f voa

|0.83

• UseGvvH ~ CaT3 consistent with the analytic model

• OMEGA: 8.3 10 , 2 keV 1 atmT P sE3

&# #. . .| x-

• NIF(THD): , 4.8 keVT P1 21E&. . .| x atm s#

keVatmP

Ts100

ICFEn

#.x| .0 83

^ ^h h

The Lawson plots show the current performanceand the future directions for OMEGA

TC8678b

FSC

* Figure courtesy of J. P. Freidberg (MIT) ** Assuming the YOC prediction is correct

OMEGA hydro-equivalent ignition:** | á 0.045, GTH á 3.4 keV, pxE á 2.5 atm × s

How to resolve the discrepancywith the thermonuclear Q = Pfus/Pinput?

*Deuterium–Tritium Plasmas

Central ion temperature (keV)

W =energy

0.00010.1 1 10 100

0.001

0.01

0.1

1

10

100

Law

son

fu

sio

n p

aram

eter

, niT

ixE

(102

0 m

–3 k

ev s

)

Ignition

Q ~ 1

Q ~ 0.1

Q ~ 0.01

Q ~ 0.001

Q ~ 0.0001

Q ~ 0.00001

Q ~ 10

Q = WFusion/WInput

OMEGA (2009)OMEGA H. E. I.

Tokamaks

*

GTH (keV)

GPHx

E (

atm

× s

)

10–1

10–4

10–3

10–2

10–1

100

101

102

103

100 10–1 102

Jet

ITER

TFTRDIIID

C-mod

LHD

NSTX

LSX

MST

SSPX

OMEGA (2009)Q = 2

IgnitionCTFFRCSpheromakRFPSTStellaratorTokamakTokamakTokamakTokamakITER

NIF (THD)OMEGAhydro-equivalent

ignition

The discrepancy on Qisresolvedbydefininga physics-based thermonuclear Q

TC8679

FSC

• “Conventional”hot-spotenergybalance

• FindPxE from the energy balance

• DefineaphysicalthermonuclearQ for ICF Measured neutron yield: 6 × 1012 For a measured T = 2 keV,

the previous result is recovered

For NIF:

1 atmTQ

Q sP 245E

2#.x f vo

=+a

TQ

QP 245E

2x f vo

=+a

QWW

ICFphysics

hot spot

fusion=QWW

ICFhysics

laser

fusionp!

24 kJWlaserOMEGA =

440 JWhot spotOMEGA .

From 1-Dsimulations

. %Q 3 8physicsOMEGA .

W W W P23

in losses Ex+ = =a

5 5WWW

WQ

P1 123

fus

inEx

+ = + =a af cp m

,.T Q P T244 8keV E

2"3. .x f vo

=a

22 atm s#

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)

TC8563b

FSC

Summary/Conclusions

* 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.

• CryogenicimplosionsonOMEGAhaveachievedaLawsonparameter PxE á 1 atm-s comparable to large tokamaks

• Performancerequirementsforhydroequivalentignition on OMEGA and NIF (THD)*

Hydro-equivalent ignitionGtRHng/cm2

GTiHnkeV

YOC PxE(atm s)

OMEGA (25 kJ)1:60 ~0.30 ~3.4

15%(~3 × 1013 neutrons)

2.5

NIF (THD) (1 MJ) 1:1 ~1.8 ~4.8 ~37% 21

Documents

Ignition, the Lawson Criterion, and Perfomance … the Lawson Criterion, and Perfomance Assessment for ICF implosions FSC Review of the National Ignition Campaign Livermore, CA 9–11