Inertial Confinement Fusion:

Basic scaling of an ICF targetand

Numerical experiments

Catherine CHERFILS-CLEROUIN, CEA DAM DIF

NMCF, Porquerolles, April 2009

Outline

• Background

• Basic scaling laws for ICF (target and machine)

• Physical models/Numerical simulations/Experiments:• Numerical tools• Example of dedicated laser experiments• Ongoing developments

« Numerical experiment » (ICF integrated simulation)

Bibliography• Physics of shock waves and high-temperature hydrodynamic

phenomena, Y.B. Zeldovich and Y.P. Razier, Dover, NY (2002).

• La fusion thermonucléaire inertielle par laser,Collectif CEA ed. R. Dautray et J.P. Watteau, Eyrolles (1993)

• Inertial Confinement Fusion, J. Lindl, Springer (1998)(from Phys. Plasmas 1995)

• The physics of Inertial Fusion, S. Atzeni and J. Meyer-ter-Vehn,Oxford University Press (2004)

• High-Energy-Density Physics, R.P. Drake, Springer (2006)

Review of studies for thermonuclear ignition with LMJ• Note CEA-R-6182, P.A. Holstein et al. (2008)

Publications

The story began about 50 years ago

• Late 1950s-1960s: invention and development of lasertechnology intense pulsed lasers

• Publication of the first american gain curves as fonction of fuelcompression (Nuckolls et al., Nature, 1972) predicted

- Break even (Target gain 1 (G=Eth/Elaser)) with a laser energyof 1kJ- High gain (around 100) with a laser of about 1MJ

• First direct drive experiments were deceptive. Key issues:- I ~ 10 17 W/cm2 too large (Laser Plasma Instabilities)- deviations from an uniform spherical (1D) implosion

(Hydrodynamic Instabilities)

• Recommandations to control LPI primilarily based onexperiments, leading to I ~ 10 14 - 10 15 W/cm2

• Recommandations to control HDI essentially based onnumerical simulations, favorable to indirect drive scenario andleading to capsule surface finish specifications.

Nominal designs of NIF and LMJ targets requires about 1MJ to get a yield around 10.

Staying far from the threshold to be less sensitive to modeling assumptions

0D models leading to the main specifications of the machine and the ICF targets arecoming from scaling laws whose coefficients and exponents are fitted on completesimulations and experimental results.

KEY NOTIONS and PARAMETERS

First lesson

Laser Laser driven driven implosionsimplosions

Irradiation uniformityHydrodynamic stability

Hohlraum coupling efficiency

++-

-

Direct drive Indirect drive

LMJ and NIF nominal scenario

Plasma Plasma created created by laserby laser

Phenomenology of laser-matter interaction: energy recovered under different forms :

- hydrodynamic expansion of the plasma- X rays emission- shock penetrating into the medium

The relative importance of these different components is depending on theirradiation conditions and on the material of the target .

Radiation Radiation hydrodynamicshydrodynamics

Z

hydro

X

Low Z material : more energy converted into kinetic energyHigh Z material: more energy converted into radiative energy

Holhraums are made of high Z material, typically gold.

Hohlraum rely on Marshak waves• Marshak waves: the penetration of radiation from a constant

temperature boundary into an optically thick medium (manyradiation-mean-free-paths thick ).

• Features for simple cases– Depth

– Shape constant in time

(“self-similar” structure)

• These features remain approx. true in more complex cases

!

depth" time

One gets high temperatures because the Marshak wave moves slowly, penetrating few microns.

Holhraum Holhraum radiative radiative temperaturetemperature

Gekko XII

Phébus

Nova

Good agreement between modeling, experiments and simulations

100

200

300

400

500

10 13 10 14 10 15

Rad

iativ

e te

mpe

ratu

re (

eV)

P laser . Δt1/2

Scavité W.ns1/2

cm2

Why a cylindrical hohlraum??

1. Easier to make2. Easier to simulate with 2D codes (axi-symmetric geometry)

Spherical hohlraums should lead to:- Good spherical implosion- Better energetic efficiency (smaller heated volume/irradiated surface)BUT

Laser Entrance Holes (where?, how many? Energy loss ≈ 15% byLEH )Beams crossing

Ongoing improvements:- towards a « rugby shaped » hohlraum

(LMJ design)- Work on the holhraum mediumin order to optimize the coupling efficiencyof the walls (cocktail material)

Going back to capsule design

Coupling efficiency of a gold cylindrical hohlraum is around 10%(including a security margin for the energy lost by laserretrodiffusion)

Laser 1MJ 100kJ absorbed by the capsule

LPI experiments have led to a maximal hohlraum radiativetemperature of 300eV (1eV=1.16 104 K), which gives an ablationpressure around 100Mbars

Pa = 100Mbars

DTGDTG

DTSDTS

plasticplastic

The limited energy delivered by a laser requires :

- a quasi-isentropic compression to achieve a high compression of the fuel- « hot spot » ignition

AblatorPlastique dopéRext = 1.2mm

FuelDT cryogéniquem = 219 µgρ = 0,25 ; e = 120µm

Residual gasDT gazeuxm = 1 µgρ = qques 10-4 Rext = 0,9 mm

Hot and less dense DT (approx. 20µg) reaches the combustion conditions, it heats the denseand cold DT (approx 200 µg) which burns and delivers the fusion energy

Ti(MK) radius

time

DT gaz

Limite point chaud

DT cryogénique

Ablateur

Regimes of Plasma physics

Accessible by high-energyLasersOmega

LMJ

ICF target is devoted to High Energy Density Physics

• Dense plasmas regime

Key notions:Coupled Plasmas: dominated by potential energy

Degenerated Plasmas: electrons are « cold »i.e. , Temperature below Fermi temperature

A classical plasma is a not coupled, not degenerated plasma.

!

TF " 7.9eVne

1023cm

#3

$

% &

'

( ) 2 3

Electrons are hot in a diluted plasma at 100eVBut they are degenarated till 100eV in a 100 rho_0 plasma

ICF Plasma description

• Plasma = charged particles, so in principle electric andmagnetic fluids

• ICF Plasmas are modeled as gas, with some plasmaspecificities ( for example transport coefficients)

• General description: fluid, with corrections coming from thekinetic level

• 1D design studies of ICF capsules aim to optimize the transferof energy to the core of the capsule and to lead to ignition.

Main physical mecanisms:- energy transfer: radiative hydrodynamics- atomic physics and EOS of dense plasmas- combustion

1- Find a way to ignite the fuel

Basic scaling laws: crude 0D models

10-20

10-19

10-18

10-17

10-16

10-15

1 10 100

< σv > (cm3/s)

Ti (KeV)

D-T

D-H e3

D-D

D + T ——> He4 + n

3,6 MeV 14 MeV

Reaction equation:

Conditions of volume combustion of a DT sphere

!

dn

dt= N

DNT"v

n reaction products

!

ND

= NT

= 0.5N0" n

Unknown: burn fraction

!

" =2n

N0

!

"vDT

# CsteHyp:

!

"

1#"=N0$

2%v

DT

Estimation of the combustion time τ

Limited by deconfinement of the capsule(rarefaction wave)

!

" #r

cs

$ " =r

3cs

and cs estimated for T=30keV

!

"vDT

!

N0 = 6.02 1023 Z

A";Z

A=1

2.5

Burn fraction:

!

" =#r

#r +6g/cm2

Areal density ρr is the key parameter of combustion in ICF

!

" = 33%# $r = 3g/cm2

!

" = 50%# $r = 6g/cm2

Goal is 33% combustion

•What is the energy gain??Gain comes from the neutrons, because α particles can heat the fuel butcan’t escape from the capsule.

!

Y = "m f

Amp

#14.1MeV $180mDT (mg)MJ

Specific gain is 1.8 1011 J/g.

ICF « Lawson criteria »

2- Getting

!

"r = 3g /cm2 ??

Starting with solid (cryogenic) DT

!

" = 0.25g /cc

Using this density, the DT mass required to get is

!

4"

3

#r( )3

#2= 2.5kgDT

High compression required compression of 1000 corresponds to a few mg of DT.

!

M = 3mg" =190g /cc

r =150µm

#

$ %

& %

Key points to optimize compression:

• Using a DT shell rather than a sphere helps getting high compression.• Keeping DT under Fermi degenerescence state during compression.

!

"r = 3g/cm2

A little help for the physicists

Modelling EOS of dense plasmas

Perfect gas Degenerated Plasma (T<TF)

!

p = 9.9"

A Z

#

$ %

&

' (

53

Mbars

!

p =" 1+ Z( )kBT

Amp

= nekBT

BUT a degenerated plasma can still be considered as a polytropic gas withγ=5/3:

!

p =2

5ne"F

!

p =2

3"#

Consequence for ignition:

Energy required to compress DT 1000 times from initial solid density 0.25g/cc:

Hyp DT stays Fermi degenerated: 107J/gHyp DT perfect gas reaching 5keV: 6.4 108J/g

DT EOS is a key parameter of the capsule design

Compressing cold DT requires a lot less energy thanheating it to a temperature close to ignition temperature

(table EOS SESAME LANL)

Credit Lindl

With a energy coupling efficiency of 10%, required laser energy for 3mgis then

6.4 108 * 3 10-3 * 10 = 20MJ.

volume combustion hot spot combustionmatch + propagation of a combustion waveLike a forest fire.

α particles are tracked till and T=10keV.

!

"r = 0.3g/cm2

Heat only a few % of the volume compression energy + heating energy is about 107 J/gRequired laser energy goes down to 1MJfactor >1000 with expected specific gain (1.8 1011 J/g) (in 000D crude model….).

Is it worth doing it??

3- Achieving a highly compressed state

The shell compressibility is determined by its entropy:

T

Qs

!=!

Figure tracée àpartir des EOSSESAME(LANL)(Crédit NIF)

Heat sources: shocks, radiative preheating, suprathermal electrons (LPI)….

Convention:s = 0 for T=11,6K, ρ = 0,25g/cc

The goal is to keep Δs < 4 108 J/g/keV in order tominimize the energy to invest.

The shock Hugoniotrepresents the set ofpossible final statesreached in a singleshock from the initialstate.

Shaping of the pressure law

In practice, a series of 3 to 5 shocks whose pressure ratio and timing are adjustedIs easier to achieve experimentally than a continuous isentropic pressure law ( final steep part leading to earlier shocks coalescence)

!

p2

p1="2 # +1( )$ "1 # $1( )"1 # +1( )$ "2 # $1( )

or"2"1

=p2 # +1( ) + p1 # $1( )p1 # +1( ) + p2 # $1( )

Maximum compression ratio:

Hugoniot relationships

For a strong shock :

!

p1

<< p2"Max

#2

#1

$

% &

'

( ) =

* +1

* +1

For γ=5/3, maximum compression ratio is 4

Motor of implosion is ablation of a low Z materialsurrounding the DT shell

The rocket modelThe rocket model reproduces correctlythe acceleration phase.

Vimplo= Vejection Log(M[DT+ablator] / Mleft)

Incident flux

pressure

P ablation

density

The goal is to accelerate the shell till a high enough velocity, and then to delecerateit, in order to convert its kinetic energy into potential energy.For 3mg of DT, the required compression energy is 30kJ.Implosion velocity has then to be greater than 1.41 e7 cm/s( 141 km/s).

1D realistic modeling gives an implosion velocity around 350 - 400km/s.(To compare to 100kJ absorbed by the capsule with good ablation efficiency)

Implosion velocity is limited by the control of hydrodynamic instabilities(see Bruno Despres’s talk).

Dépot d'é

nerg

ie

chaleur Choc

ablateur

déflagrationradiative

The ablation front is RT unstable during the acceleration stage

Hydrodynamic separation

Dépot d'é

nerg

ie

chaleur

ablateur

Formation of the thermal front

ChocChoctransmis

DT solideablateur

Interface

déflagrationradiative

détente réfléchie

Interaction shock interface ablator/DT

ChocChoctransmis

DT solideablateur

déflagrationradiative

détente réfléchie

quasiisotherme

quasiisobare

region comprimée

Formation of the ablation zone

The ablation zoneis quasi isobaric

T ρ

One motivation of HDI models is to give an idea of dominant modes and of stabilized modes in order to predict the minimal mesh discretization necessary to catch the physics.

Hot spot

Density map near ignition time

IHD Simulations help specify the roughness requirements

The main numerical tool for target design is the 2D code FCI2, allowingintegrated simulations in a « standard » way, and numerical experiments.

FCI2 code

Base : radiative hydrodynamics, 3D ray-tracing, combustion diagnostics post-processor

The fluid approach works quite well but not always…

Corrections can be brought by kinetic simulations when the macroscopic approach seems doubtful:Exemple: study of hot spot ignition with a FP code ( O. Larroche, code FPION)

For capsules, a fluid description seems « reasonnable »

Hyp Hydrodynamics equation closed by EOS and transport coefficients

Mean free path lTime between collisions t << Plasma dimensions

implosion and combustion time

T ni(cm-3) l t Hot spot 10keV 1025 1µm 1psCold fuel 1keV 1026 10−3 µm 10-2ps

?? 10-100µm1-10ns , 10-100ps

Dense regions: OKUnderdense regions (ablated plasma, hot spot): evaluation of kinetic effects.

2 temperature-model (Ti,Te)Coupling to radiative tranfer equationLagrangian formalism, ALE

Interaction laser-matièreConversion X

Transfert radiatif

Physique cavité loi de Température

radiative

Interaction : Instabilités de plasma

traversée fenêtre et plasma cavité

Physique cavitéSymétrie de l’éclairement

Phys. microballonInstabilités Hydro

Phys. microballonAblateur-couplage

chronométrie des chocs

Phys. implosionvitesse d ’implosionconditions finales

11 22

33445566

77

Integrated Integrated simulation of an simulation of an indirectly driven targetindirectly driven target

1 2

Methodology of hohlraum design

Typical computational time :1 week on Tera.

ablateur

Bulleexterne Bords

trou

HHe

Cône interne Cône externe

The goal is to determine, simultaneously :

The shape of the laser pulse driving the implosion of the capsule(shocks, entropy control, implosion velocity) to get ignition,

LEH length, and beams focusing

Hohlraum shape, density of the filling gas, and 2 cônes power balancein order to get a symmetric implosion,

The size of the focal spots and the composition of the filling gas in orderto limit LPI (evaluated by the post-processor code PIRANAH).

A 3D code (TROLL) is developed, already used for capsule simulations

A crucial point: physical constants

EOS, opacities, ionization, nuclear reaction cross sectionsare tabulated.

• EOSIterative methods used to solve hydro-rad system require theknowledge of the derivatives of the thermodynamic variables.

• Opacities are tabulated for Local Thermodynamic Equilibriumconditions. Coupling to an atomic physics code is mandatory to dealwith non LTE plasma.

• Sensivity studies are done to evaluate the impact of misknowingof these constants on the target design, in order to take securitymargins, and if possible, to define dedicated laser experiments for thecritical points.

Dedicated laser experiments are mandatory to validate numerical designs

DT Ablateur

-

Rayon (cm)

Den

sité

(g/

cm3 )

DT Ablateur

Den

sité

(g/

cm

Graded doped plastic CH+0.40%Ge

-

DT gaz

DT cryo

CH

CH+0.75%Ge

controlling interface DT/ablator

Rayon (cm)

Goal: define a discriminantDedicated laser experiment(sensibility to plastic EOS)

A. Casner et al., APS 2008

Time (ns)

Opt

ical

dep

the

EOS Sésame 7590EOS Sésame 7592

avec MTF

Perturbation initialeλ = 35 µm et a0 = 1 µm

Temps (ns)

Fondamental

Harmonique

OpacitéCC213Opacitémélange

Sésame7590

CHOGe20%

CHOGe0.75%

6 ns

Sésame7592

Rayonnement XCHOGe20% at.

CH CHOGe0.75 % at.

0

0,05

0,1

0,15

0,2

0 2 4 6 8 10

aniso_50_01

data iso_50_02

data aniso_50_03

data aniso_50_01

iso_50_02

aniso_50_03

contraste de profondeur optique

temps ns

Optimization by theoretical modeling of the ablator structure to limitthe growth of ablative RTI (Laurent Masse, PRL 2007).Validated experimentally on the Omega laser (LLE) in July 2008.

Opt

ical

dep

th

Dedicated laser experiments help checking new theoretical concepts

Standard ablator

Layered ablator

How are these experiments representative of the LMJconditions?

Indirect drive Today’s experiments LMJ

Drive temperature 160-180 eV 275-300 eVDuration acceleration phase 3  ns 8 nsAccélération (ablation front) 5 1015 cm/s2 1.2 1016 cm/s2

Convergence (ablation front) 2-4 8-10Modes l 10-32 1-100

• OK for hohlraum physics on the Omega laser

• The LIL prototype is a good tool for ILP experimentsand pulse shaping studies • IHD experiments

• First shots on NIF are a major milestone

• For the time being, numerical experiments

Thanks for your attention