ignition of fusion pellets with hydrodynamic shocks · single shaped pulse alternative schemes...

IGNITION OF FUSION PELLETS IGNITION OF FUSION PELLETS WITH HYDRODYNAMIC SHOCKSWITH HYDRODYNAMIC SHOCKS

M. Lafon, X. Ribeyre, G. Schurtz, S. Weber, V. T. TikhonchukCentre Lasers Intenses et Applications

Université Bordeaux 1, France

O. Klimo, J. LimpouchCzech Technical University in Prague, Prague, Czech Republic

International Workshop on High Energy Density Physics Beijing, May 20 - 21, 2010

Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 2

OutlineOutline

Basic ideas of the shock ignition scheme

Optimization of the shock ignition conditions, gain and robustness

Shock pressure amplification

Laser-plasma interaction physics: laser energy absorption and energy transport


LaserLaser--driven inertial fusiondriven inertial fusion

Laser-driven inertial fusion consists of four main stages• quasi-isentropic shell compression • adiabatic heating of a small portion of fuel• fuel ignition at the moment of stagnation• combustion of the cold fuel in the shell

Conventional schemessingle shaped pulse

Alternative schemesseparate ignition pulse

Indirect drive

Direct drive

Fast ignitionhole boring

Fast ignitioncone

Shock ignition

…

Separation of two steps allows to reduce the compression energy at least by a factor of 2 → higher gain is possibleHeating requires a higher power → more complicated laser technology


Shock ignition Shock ignition –– nonnon--isobaric isobaric schemescheme

Main advantages: • relatively low laser

power • relatively simple

hydrodynamics• conventional laser

technology

Lower compression velocity -> more stable compressionAdditional entropy is brought in with a shock

Betti et al Phys. Rev. Lett. 2007Ribeyre et al. Plas.Phys. Contr.Fus. 2009

Spike - converging shock : Ignition of central hot spot

Divergent return shock duringthe shell stagnation phase

Hotspot

Fuel

Laser

Typical laser pulse


10−2

10−1

100

101

10210

−1

100

101

102

103

EL (MJ)

G

ε = 1 ε = 1.25 ε = 2 ε = 3.5 ε = 5

0.01 mg

0.1 mg

0.5 mg

1 mg

5 mg

Rosen and Lindl UCRL-50021-83, 1984 α – adiabat at stagnation

EL – laser energy

NonNon--isobaric fuel assembly: higher gain isobaric fuel assembly: higher gain

0.270.17

L0.9L

cstG E 1E

fDT

L

MQE

⎛ ⎞ε= Φ ∝ −⎜ ⎟α ⎝ ⎠

non-isobaric parameter

A lower threshold and a higher gain for a non-isobaric configuration

Psh = 200 Gbar α =2

Pressure and density at the moment of ignition

ρsh

Phs

rhs rsh

Psh

ρhs

hs

sh

PP

ε =


Shock ignition of the baseline Shock ignition of the baseline HiPERHiPER targettarget

3ρ = 0.25 g/cm211 µm

833 µm

DT ice

DTgas

3ρ = 0.1 mg/cm

40 60 80 100 120 140 160

9.9

10

10.1

10.2

10.3

10.4

10.5

10.6

19

151917

10

1

18

23

21

16

1

21

1822

20

12

5

17

16

12

22

20

15

510

Absorbed spike power (TW)

1519

19

17

10

21

1

18

16

1

1812

20

16

5

17

12

5

15

10

1

Laun

chin

g tim

e (n

s)

Launching window

250 ps confidence interval at 80 TW absorbed power and 20 MJ yield

Compression (3ω) 180 kJ, 10 ns, 50 TWIgniton (3ω) 100 kJ, 500 ps, 200 TW

Thermonuclear energy yield

Spikepower

Shock launching

time

Pabs


Fusion yield dependence on the spike parametersFusion yield dependence on the spike parameters

Δt

tR tR

Spike power shape

t

Ps

Rise timetR = 200 ps

16171819

50100200300

250300400500

20243240

Spike absorbed energy and power Es, PsNuclear energy yield ETN

FWHM(ps)

Δt(ps)

ETN(MJ)

Es(kJ)

Standard

Ps/2

Spike duration: FWHM = 2 RT + ΔtSimulations with Δt = 50 – 300 ps

Target nuclear energy yield varies about 15 % and spike energy – about 50 %

The ignition mainly depends on the spike power and not on the spike energy

Lower shell implosion velocity requires higher intensity spike

ts


w/out ignition shock

ignition

Shell evolution under the shock pressureShell evolution under the shock pressure

with ignition shock

Three effects define the pressure enhancement:

Shock convergence

Shock collision

Shock collapse


Pressure amplification in a convergent shockPressure amplification in a convergent shock

Self-similar solution for the convergent shock: Guderley 1942 (for ρ = const)

For d = 3 and ɣ = 5/3 n = 0.688

Rankine-Hugoniot relation at the shock front

0( ) 1n

sf

tr t rt

⎛ ⎞= −⎜ ⎟

⎝ ⎠1/

01 / 1( )

n

nsf

nrdru tdt t r −= = −

2 /2 0.910

0 0 2 2 / 2

2( ) 0.351

n

nsf

rP t u rt r

−−= ρ = ρ ∝

γ +

agrees well with the simulation results


Pressure amplification in a shock collisionPressure amplification in a shock collisionDensity and pressure profiles before after shock collisions

Pressure enhancement after two shock collisions follows from the Rankine-Hugoniotconditions

ΔP1 = 1.5 Gbar

ΔP2 = 12 Gbar


Pressure amplification in the hot spotPressure amplification in the hot spot

Transmitted shock compresses the central hot spot like a piston

Pressure et the stagnation depends on the piston velocity

Model Mach scaling Model adiabatic compression

Assuming that the Mach number remains constant

Assuming the energy conservation

30

03

3.6hs

hs p

P MP

P V

=

∝

5

0

0

5

hs

hs

hs p

P rP r

P V

⎛ ⎞= ⎜ ⎟⎝ ⎠

∝


Effect of the implosion velocity on the HS pressureEffect of the implosion velocity on the HS pressure

The stagnation pressure for ignition depends only weakly on the implosion velocity

• Vimp < 250 km/s :

• Vimp > 250 km/s :

5

3

∝

∝hs p

hs p

P V

P V

The piston and shell implosion velocities are almost equal

Stagnation pressure for three runs with and w/out the shock

3∝hs pP V

5∝hs pP V

Vimp = 200 km/s

Vimp = 320 km/s

Vimp = 280 km/s w/out shock


Homothetic targetsHomothetic targets

The HiPER target can be rescaled to the reactor size

ε = 1 conventional implosionε = 5 implosion + shock ignition

Mf = 0.3 mgρR = 1.34 g/cm2Vimp = 285 km/s

EL = 0.25 MJG = 90

EL = 1.2 MJG = 17

Mf = 3.0 mgρR = 2.12 g/cm2Vimp = 265 km/s

EL = 1.5 MJG = 170

EL = 5.0 MJG = 50


PowerPower--energy diagram and limiting effectsenergy diagram and limiting effects

150 200 250 300 350 400 450Implosion velocity (km/s)

0

100

200

300

400

Abs

orbe

dla

ser p

ower

(TW

)

Laser energy(kJ)

Selfignition

Efficient ignition

Inefficient ignition

A compromise between the required energy and power is in the range of implosion velocities from 250-350 km/s

200 250 300 350 400 450Implosion velocity (km/s)

1

10

100

Inte

nsity

(10^

15 W

/cm

²)In

tens

ity(1

015W

/cm

²)

Parametric instabilities

Hydrodynam

ic instabilities

PL=110TW

PL=340TW

PL=130TW

h = 0.5h = 1.0h = 2.0

Shock ignition reduces the risk of hydrodynamic instabilities but the parametric instabilities present a serious danger

h = 2

h = 1


0 100 200 300 400 500Laser power (TW)

0

500

1000

1500

2000

Las

er E

nerg

y (k

J)

h = 0.5h = 1h = 1.5h = 2NIF

HiPER

For targets of a larger size the implosion velocities needed for the shock ignition can be accessed in a larger domain of energy and power

EnergyEnergy--power scalingpower scaling


TwoTwo--dimensional effects: electron thermal smoothingdimensional effects: electron thermal smoothing

symmetriccompression

bi-polar spike

Pressure evolution at stagnation

Laser spike need not to be strongly symmetric – fast electron transport in corona enables thermal smoothing of the pressure at the ablation surface

Target can be ignited event with bi-polar spike


Stabilization of low mode shell perturbationsStabilization of low mode shell perturbations

without shock with shock

100

µm

The compression beam is modulated with the mode l = 12: w/out shock the shell is destroyed at stagnationreturn shock mitigates the growth of low mode Rayleigh-Taylor perturbations


Parametric instabilities in the corona: SBS and SRSParametric instabilities in the corona: SBS and SRS

Hydro simulations define the density and temperature profiles at the spike launch time

PIC simulations of the spike absorption in the corona: Ilas = 1016 W/cm2: 1D×3V

laser

L = 3000 laser wavelengthsTe = 5 keV

ts +0.2 ns

temperature

density


Parametric instabilities in the corona: SBS and SRSParametric instabilities in the corona: SBS and SRS

Two series of PIC simulations with a short and long profile

laser

short profile: SBS dominated long profile: SRS dominated → better absorption

Time integrated spectrum for the short and longdensity profiles

Time-resolved spectrum of reflected light – long profile²

L = 3000 laser wavelengthsTe = 5 keV

short profile

long profile


Laser energy absorption in density cavitiesLaser energy absorption in density cavities

Backscattered electromagnetic wave produces secondary absolute SRS in the 1/16 of the critical density where multiple cavities are produced Major absorption takes place between 1/4 and 1/16 of nc

Energy absorption starts in the quarter critical density where SRS develops as an absolute parametric instability. Nonlinear saturation is accompanied by cavity development

SRS

2 2 /SRS e osc n SRSG k v L k


SBS: laser energy absorption in density cavitiesSBS: laser energy absorption in density cavities

Energy absorption starts in the cavities has been already observed in the case of SBS for higher laser intensities Iλ2 = 1016 W/cm2 and confirmed in 2D simulations

density

reflectivity

laserspectrum of reflected wave

laser

ion density

electron density

1D×3V simulation: cavity assisted laser absorption2D×3V simulation: intermittent cavities


Fast electron generation in coronaFast electron generation in corona

Tc = 6 kev

TH = 29 kev

The absorbed energy is transported by hot electrons into the dense plasma

Hot electron temperature qualitatively agrees with the Beg’s law ( )1/32

18250 keVh µmT I λ

Hot electron energy flux is reflected from the low density edge of plasma and is injected into the overdense plasma


Energy flux transported by fast electronsEnergy flux transported by fast electrons

Energy balance between the forward and backward fluxes agrees with the absorbed energy: nhot ≈ 0.022 nc

Kinetic simulations demonstrate feasibility of the shock ignition scenarioNonlinear effects dominate the absorption and the hot electrons are supposed to transport energy to the ablation zone


Kinetic simulations of the electron energy transportKinetic simulations of the electron energy transport

Low intensity: 1.5×1015 cos2θ W/cm2

Th = 3 keV Strong anisotropy

80 Mbar 400 Mbar

High intensity: 8×1015 cos2θ W/cm2

Th = 10 keV Weak anisotropy

Transport of the energy to the ablation zone by fast electrons enables the pressure homogenization Kinetic simulations of the electron energy transport A.Bell, 2009


USA: demonstration of the ignition and Q= 10 yield on NIF with X-ray drive;demonstration of the fuel assembly and ignition with the polar direct driveLIFE project – indirect drive compression for the repetitive combustion of a sequence of targetsLLE – PDD shock & fast ignition demonstration

Europe: HiPER project – demonstration of the repetitive combustion of a sequence of ~ 100 targets for the IFE demo reactorfast electron and shock ignition options, performance tests down selection of the target design in next 5 yearstarget fabrication technology, in-flight tracking and pointing of targetshigh rep rate laser technology

Japan: FIREX-I project: fast electron ignition – demonstration of the beam target coupling with the compressed fuelFIREX-II: high rep rate demo facility

Joint actions: open call for the joint NIF experiments in 2012-13 and on LMJ after 2016, collaboration with the MFE community for the reactor materials

Plans for the shock & fast ignition studies Plans for the shock & fast ignition studies

ignition of fusion pellets with hydrodynamic shocks · single shaped pulse alternative schemes...

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