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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 3
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 of laser fusion pargets, Beijing, May 20 - 21, 2010 4
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 5
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 laser fusion pargets, Beijing, May 20 - 21, 2010 6
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 7
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 8
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 9
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 10
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 11
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
⎛ ⎞= ⎜ ⎟⎝ ⎠
∝
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 12
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 13
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 14
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 15
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 16
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 17
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 18
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 19
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 20
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 21
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 22
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 23
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 24
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
Shock Ignition of laser fusion pargets, Beijing, May 20 - 21, 2010 25
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