S.Yu.Gus’kov. LPI RAS

S.Yu.Gus’kov. LPI RAS

Fast Ignition by Detonating Hydrodynamic Flow

S.Yu. Gus’kov*, M. Murakami**

*P.N. Lebedev Physical Institute of Russian Academy of Sciences, Moscow, Russia

**Institute of Laser Engineering. Osaka University. Japan

7-th Direct Drive and Fast Ignition Workshop. May 3-6, 2009. Prague

Contents:

1. Fast ignition by hydrodynamic flow

2. Fast ignition by detonating hydrodynamic flow - “target from target” ignition

3. Conclusion: Practicability of fast ignition at the impactor velocity of 300-500 km/s


Fast ignition by hydrodynamic flow

Fast Ignition Drivers

Igniting Drivers:

Fast particles from laser-produced plasma

• electrons (Ee ~ 0.5-1.5 MeV)

• light ions (Ei ~ 10 -100 MeV/nuclon)

Laser : IL > 1019 W/cm2, L< 10-20 ps.

Experiments: CD-target + cone

RAL (UK), ILE (Japan)

Neutron yield: 105 106

Hydrodynamic pulse

I u3 , u ~ 1000 km/s

Laser: IL 1015 W/cm2, L 1 ns

Experiments: CD-target + cone

ILE (Japan)

Neutron yield: 105 106


Compression =(300 - 500) g/cm3

R = (3 - 4) g/cm2

Ignition T=10 keV

Rign = 0. 4 g/cm2

Igniting Driver

Energy: Eign = (10-15)/1002 kJ Eign = (10-30) kJ

Beam radius: Rign= Rign / Rign 10-30m

Pulse duration: ign = Rign/108 ign 10 ps

Intensity: Iign (1018 - 1019) W/cm2


t=300-500 g/cm3 ! Tign=10keV. I imu3

General Requirements for Impact Ignition

Iign t (CDTTign)3/2, ign 0.5(im /t)1/2

=300-500 g/cm3

R=3-4 g/cm2

u 1.5(t /im)1/2 (CDTTign)1/2

t = im u = 1500 km/s,

t = 10im u > 4000 km/s,

Ignition of the Target

R=3-4 g/cm2

=300-500 g/cm3

I im (CDTTign)3/2

u (CDTTign)1/2

u ~1000 km/s

Ignition of the Impactor

Theoretical limit of low-entropy laser-driven acceleration of a foil: 1700 km/s

S.Yu.Gus’kov. LPI RASHydrodynamic fast ignition

Compression in a conical target. Detonating flow.

~ (100-200) g/cm3 V ~ (500 - 300) km/s, S. Gus’kov, M.Murakami XXX ECLIM, 2008

Impact along a cone ~ 1 g/cm3 V ~ 1000 km/s,

M.Murakami, H. NagatomoNucl. Inst. & Meth. Phys. Res. A544, 67, 2005

Profiling laser pulse

Simple laser pulse

ILE (Osaka University, Japan) experiments on impact ignition, EL~ (1-3) kJ, 3:

• Acceleration of the foil up to record velocity: 600–700 km/s.

• Impact neutron generation: (1 -2) 106 DD-neutrons/shot.

1000 km/s 300 km/

S.Yu.Gus’kov. LPI RASILE planar impact ignition experiments

impactorMain fuel

laser

600 m

Be plane(weight) Be frame

CD foils 20 mt

Laser energy :1.9 kJSpot size : 300 m

laser

Be frameCD foil 20 mt


laser

600 m

CH plane300 mt

Be frame

CD foils 20 mt


1. CD-foil - CD-target impact

2. CD-foil - CD-target impact

3. CD-foil - CH-target impact

Watari T, Sakaiya T, Azachi H et al Neutron generation from impact fast ignition Proc. 5-th IFSA conference (Kobe, Japan, September 2007)

N: 106 N: 1.3105N: 8.3105

1) impact nature of neutron generation and2) neutron generation in impact-produced plasma of impactor

>>

S.Yu.Gus’kov. LPI RASILE spherical impact ignition experiments

50m

275mAucone:90degree

CD shell7mt

500m

500m

CD shell 10mt

Impactor

Main

P M T

Plastic scintillator18 cm × 2.5 cm

47 cm 311 cm

190 cm178 cm

Pb 10 cm

25°

80°

52°

168°

Plastic scintillator10 cm × 5 cm

target

421 detectors

MANDALA

1344 cm

Target chamber

Watari T, Sakaiya T, Azachi H et al. Neutron generation from impact fast ignition. Proc. 5-th IFSA conference (Kobe, Japan, September 2007

1. Nmax= 2106

2. Ti=1.59 keV

3. Nmax corresponds to coincidence of the moments

of maximal compression and impact

S.Yu.Gus’kov. LPI RASImpactor’s state before collision.

Impactor’s density and velocity distributions along the central axis.

L = 600 m, t = 1.8 ns L = 1000 m, t = 2 ns

u u

u 600 km/s u 800 km/s

0.2 g / cc 0.08 g /cc

<>

S.Yu.Gus’kov. LPI RASImpact-produced plasma of impactor and target

Density, ion and electron temperature distributions along the central axis

L = 600 m, t = 1.8 ns L = 1000 m, t = 2 ns

Target Impactor ImpactorTarget

Ti Te

Ti Te

Ti=Te Ti=Te

Target Ti 80 eV, 3.8

g/cc

Impactor Ti 2.2 keV, Te 1.2 keV

0.18 g/ccTarget

Ti 60 eV, 3.8 g/cc

Impactor Ti 6.2 keV, Te 1.8 keV

0.12 g/cc

N 106 N 6.3106<<

>>


Gekko/HIPER

1. Impactor’s density significantly less than target’s density:

imp 0.6 g/cm3 << t 4 g/cm3

1. Predominant heating of impactor’s ions,Ti>>Te . Equilibrium target’s plasma Ti=Te .

Impactor’s temperature significantly larger than target’s temperature:

Timp (1.5 -3) keV >> Tt (0.1 -0.2) keV

1. Neutron yield from impactor significantly larger than neutron yield from the target:

Nm 107 >> Nm 106

Confirmation of the approach:

initial ignition of impactor and subsequent propagation of detonation wave

from impactor to compressed thermonuclear fuel of ICF-target


Fast ignition by detonating hydrodynamic flow

Detonating impactorS.Yu.Gus’kov.

LPI RAS

ICF-target

PusherAblator

Igniter

Development of “Cone-Guided Impactor” to “Target inside Target”

Ignition by Detonating Impactor - “Target From Target” Ignition

Conetarget

1. Cone target withhomogeneous DT-fuel

and profiled laser pulse

2. Cone target with spatial distributed

density

Multi-layer cone target

Conetarget

Conetarget

ICF-target ICF-target

Two well-known ICF-methods:1. Profiled Laser Pulse and 2. Initial Density Distribution

General requirement for ignition by detonating DT-impactor

(R )t ~ 3 -4 g /cm 2

t ~ 100-200 g /cm 3

tw = 4tDT-fuel

ShockedDT-fuel

Impactor

Cone

Ignition

1. Ignition of the impactor:

2. Detonation wave to DT-fuel:

ign2T = 10 keV, ρ Δ 0.4g/cmm m

1/ 220.15 /t g cmm m m

United requirement :


1/ 220.15 / if 0.14

20.4 / if 0.14

t mg cmm mm t

mg cmm mt

Minimal ignition energy, m= t :15 ,23/100 /

E kJg cmt

Factor of exceeding:

7 / 20.053 if 0.14min

2 if 0.14min

mtE Em t

mtE Em t

m t

1/ 23 ,( )

mP D C T Dm th DT t ig tht


“Target from Target” Ignition by Three-Layer Cone Target

3. DT-ice Igniter.

• Function: Self-burning and ignition of ICF-target DT fuel by the detonation wave

Three-layer cone target

M m

M p>>M m

m

p> >m

AblatorDT-ice Pusher

M a~M p

M p

p a

a< <p

M a

2. Pusher. • Heavy-element material: Cu, Pb, Au and others.

• Function: Impact-driven adiabatic compression of the igniter.

1. Ablator. • Light-element material: (CH)n-plastics, Be, Al and others.

•Function: Acceleration of impactor laser light absorption, ablation pressure creation.• Totally evaporated at the acceleration stage.


Statement of the Problem. Planar Approximation.

Initial pressure of DT-fuel5 / 33 32.17 ( / ) , ; 100 300 / (5 30)P g cm Mbar g cm Gbartt

Pressure in the igniter at a decelleration stage:2 3, 0.25 / , 1000 / 30 0 0 0P u g cm u km s P Gbarb m m m m b

1. Deceleration of the igniter by first shock wave, Pb0 << Pt

2. Deceleration of the pusher and adiabatic compression of the ignitor, Pb>>Pb0

3. Shock wave in ICF-Target DT-fuel; Effect of DT-fuel compressibility, Pb>Pt

(R )t ~ 3 -4 g /cm 2

t ~ 100-200 g /cm 3

tw = 4tDT-fuel

ShockedDT-fuel

Ignition

Cone

Cone

Igniter

Pusher

Impactor = Igniter+P usher

P s0=0Pm

U 0m

s0Tm2Ts0=0

DT-fuel DT-ign.

D sPs

s

Ts

P t>>Pm

t

Ablator


Pressure in the igniter at a burning stage: R=0.4 г/см2, T=10 keV, =100 г/см2 P~100-200 Gbar

S.Yu.Gus’kov. LPI RASCompression and heating of the igniter

P t0 PP P

D t

Uw1 U U

t twm s

T tw Tm Ts

DT-fuel DT-igniter Pusher

1 221 1

M Mm sP M M u E Em sb m w bm m s s

The moment of maximal compression: deceleration of the impactor down to the velocity of shock wave in ICF-target DT-fuel

Energy of shock wave in ICF-target DT-fuel

Residual kinetic energy of the impactor

1. Residual kinetic energy of the impactor: 1/ 2

1 22 ,2 1 0

PtE M M u um pb w w t t

2. Energy of shock wave in ICF-target DT-fuel: 1/ 22 1, ,

( 1) 2 20

M M uP P m s mt t tE D t D tw t b t b Pt b

Adiabatic compression at the initial entropy from first shock wave: 11/ 1/ 2/ , / , 02

mm sP P P ub m b sm s w m m

1/ 23. = 200 g/cm : E ~0.12 E , E ~ 0.03 E 0 t0 w 0 b 00

EbE E E Ew w bE

Final state of the igniter

P t0 PP P

D t

Uw1 U U

t twm s

T tw Tm Ts

DT-fuel DT-igniter Pusher

2 /( 1)1/ 21 1 01 1/ 2 1 /2 1 00 0

mP Pbc btm s

Au-pusher, Ms/Mm=20

Compressible ICF-target fuel:Pb/Pw 700; m 52 g/cm3; T=10 keV, at um 410 km/s; energy factor, 0.18


Exact solution for m= s= t= :

/( 1)11 2 ,021 /0 0

Mm sP P where P ub w w m m Mmm s

Compressibility factor“Uncompressible” solution

Uncompressible ICF-target fuel: Pb/Pw 1100,m 75 g/cm3; T=10 keV, at um 365 km/s; energy factor,

0.25

101

0 0

E Mm s mE Mm sb

Internal energy of igniter


t=200g/cc

t=500g/cc

t=300g/cc

- - - - uncompressible ICF-target fuel

Pusher and igniter mass ratio vsfinal igniter density

1, 2, 3, 4 - energy factor, Em / E0 = 0.35, 6, 7, 8 - energy factor, Em / E0 = 0.5

Tig=10 keV:initial impactor velocity vs final igniter density

( 1) / 21 0(100 / ) 1.521

mu km sm

Final igniter density and velocity of ignition

u 330 km/sAu-pusher: Mpusher/Migniter 38DT-igniter, ()ig=0.4 g/cm2:

ig 40 m Migniter 4 10-5 gMpusher 1.5 10-4 g

t=300 g/cm3

Eigniter/Eimpactor = 0,56

ig=100 g/cm3

Initial: Eimpactor 70 kJ

Final: Eigniter 40 kJ

Conical three - layer igniting target design


2

R ig ttgR igt


Ignition of the igniter: (R)ig=0.4 g/cm2 High gain of ICF-target (R)t=3-4 g/cm2

Cone opening angle

0.5 0.2ig

t

400-600

Igniting target. Requirements to the design

1/ 32 08,3 lnM

u IM f

Evaporation - 50%, M0 / Mf = 2 Mass of ablator = a half of total mass,

0.3, u 0.57(I2)1/3

Shell velocity:

2R0

L(R)ig , ig

(R)t , t

1/ 31/ 3 2 / 33.1 ,0 1/ 3 2 / 3

E tgimpactR cmu

Eimp=70 kJ, u = 3.3 107 cm/s, =0.3, =50o, = 0.35 m R0 0.153 cm, L0. 32 cm, 19.5ns

Igniting conical target designS.Yu.Gus’kov.

LPI RAS

igniter 21,3 m

pusher 10.7 m

ablator 115.6 m

R0 0.153 cm

DT-igniter: Migniter 4 10-5 g

Au-pusher: Mpusher 1.5 10-4 g

Be-ablator: Mablator=Mpusher

115.6 m

21,3 m

10.7 m

L 0. 32 cm

2R0 0.3 cm

=50o

Elaser= Eimpactor / Kabs

Eimpactor 70 kJ

= 0.3, Kabs= 0.7

Elaser 320 kJ

Conclusion:

Practicability of hydrodynamic ignition at the velocity of 300-500 km/s 1. Fast Ignition by Detonating Hydrodynamical Flow• Approach of “Target from Target” ignition• Conical three-layer igniting target:

Ignition at the initial velocity of hydrodynamical flow 330 km/s

and final density of detonating flow 100 g/cm3

Laser parameters: EL= 320 kJ, L= 19.5 ns

2. Key points: • Hydrodynamic instability• Impactor’s state before impact • EOS of heavy pusher

3. Experiments: collision of multi-layer impactor accelerated along conical or cyllindrical channels with a massive plane target.

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S.Yu.Gus’kov. LPI RAS