Shock ignition modeling

Ribeyre X., Schurtz G., Lafon M., Weber S., Olazabal-Loumé M., Breil J. and Galera S.

CELIA

Collaborator Canaud B.

CEA/DIF/DPTA

7th Direct Drive and Fast Ignition Workshop

Shock ignition principle: How it works ?

Spike :Converging shock :

Ignition of the hot central region

Divergent return shock duringthe shell stagnation phase

Hotspot

Fuel

Typical laser pulse

Mesh

Laser

Shock ignition : Stagnation conditionsTwo steps process

With convergent shock

Shell stagnation

Standard quasi-isobaric configuration - Low implosion velocity: Vimp < 300 km/s

- Hot spot ignition failsIdentical to fast ignition compression

Non-isobaric configuration (1) Increased central pressure and temperature

ignites a central hot-spot

(1) Betti el al : PRL 98 (2007)

1

2

Compression phase

Ignition phase

ρsh

Phs

rhs rsh

(1) M.D.Rosen and J.D.Lindl (1984) UCRL-50021-83

α adiabat at stagnation

EL laser energy

Non-isobaric fuel assembly and Rosen Model (1)

Psh

ρhs

L

0.17L9.0

27.0

E

cst1EG

Non-isobaric parameter

Rosen model shows the low threshold and high gain possibility of a non-isobaric configuration

G

EL (MJ)

Without SpikeQuasi-isobaric Configuration

With SpikeNo FusionNon-isobaric Configuration

With Spikeand Fusion

Ignition and burn

CHIC 1D SIMULATIONS

Temperature

Temperature

Temperature

Density

Density

Density

Pressure

Pressure

Pressure

Grad P

Grad P

Grad P

Shock convergence model : Spherical NOH problem (1)

Shock Spike

V

Converging shock collision in spherical geometry

Pressure evolution

Radius (normalized)

Accreting shock:Divergent return shock

Pre

ssu

re

t =0 t > 0

Model : Spherical NOH problem (2)

Shock amplification during convergence and collision

Shock amplification during convergence and collision

Shock ignition pressure evolution:

spherical effect • Shock wave pressure amplification during convergence

0.9sP (r) r

CHIC shock pressure

Guderley solution

(1) Guderley 1942, Aleksandrova et al. 2003

Amplification after collision between shock spike and return shock

If pressure balance = X 6

Shock spike convergence

The shock pressure follows approximatively the Guderley solution

Guderley (1) self-similar spherical solution:

Return shock0.69

s 0r =ξ (t -t) 0.9sP (r) r (γ 5 / 3)

300 Gbar

700 Mbar

Shock collision

All DT target performances

3ρ = 0.25 g/cm211 µm

833 µm

DT ice

DTgas

3ρ = 0.1 mg/cm

One sector simulation

• Ray tracing with focal spot shape

nc

• One ray absorbed totally at critical density

• Same performances

Adiabat (α) ≈ 1.0

IFAR 0.75 Ri ≈ 30

Imploded mass Mimp (mg) ≈ 0.27

Implosion velocity :Vimp (km/s) ≈ 290

Peak density ρpeak (g/cm3) ≈ 650

Peak areal density ρRpeak (g/cm2) ≈ 1.4

• Total absorption design is

independant of the ablator composition and simpliflies the

analysis.

* Ref : Atzeni et al. POP (2007, 2008)

HiPER target *

Fusion + rad

EL=180 kJAbs = 70 %

EL=105 kJAbs = 100 %

Shock igniting of HiPER target

Iso-energy

Robustness study

Spikepower

250 ps confidence interval at 80 TW

Launching window

180 kJ, 10 ns - 50 TW for compression (3)

+70-100 kJ, ≈ 500 ps – 150-200 TW for

ignitor (3) 20 MJ (TN) : Gain ~ 80(1) Ribeyre et al. : PPCF (2009)

Pabs

tShock launching time

Spike duration effect on target thermonuclear energy

T

RT RT

Spike power time shape

t

Ps

Rise timeRT = 200 ps

500 300 19 40

400 200 18 32

300 100 17 24

250 50 16 20

Spike absorbed energy and powerEs, Ps

Thermonuclear energy ETN

FWHM(ps)

T(ps)

ETN

(MJ)Es

(kJ)

Standard

Target thermonuclear energy vary about 15 % and spike energy about 50 %

Ps/2

Spike duration: FWHM = 2 RT + TSimulation with

T between 50-300 ps with same rise time (RT)

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

ts

Implosion velocity and spike power requirement

Laser absorbed power for compression

Eabs= 105 kJ; Pmax= 26 TW Vimp=290 km/s

Eabs= 80 kJ; Pmax= 15 TW Vimp=225 km/s

Spike threshold: 60 TW

Spike absorbed power required for ignition: Ps

500 ps FWHM

Ps

t

500 ps FWHM

PsSpike threshold:140 TW

Ps ≈ 80 TW : 250 ps

Ps ≈ 200 TW : 200 ps

Low shell implosion velocity requires high power ignition spike, i.e., High intensity spike

tVimp= 290 km/s : Psabs= 80 TW : Plaser = 160 TW (Hyp: 50 % absorption)

Vimp= 225 km/s : Psabs= 200 TW : Plaser = 400 TW (Hyp: 50 % absorption)

Ignition Window

Homothetic targets study

cible

réf

rh=

r2

L LréfcibleP h P

3L LréfcibleE h E3

cible réfM h Mcible reft h t

cible réfρR h ρR

cible refG h G

Compression Energy (kJ) 25 85 180 312 600

h 0.5 0.8 1 1,2 1.5

Target mass (mg) 0.07 0.28 0,59 1,0 2.0

Threshold absorbed Spike power (TW)

60 60 60 60 60

R (g/cm2) 0.79 1.18 1.34 1.60 1.86

Thermonuclear energy (MJ) 1 8 17 38 80

IV = 290 km/s

= 3.5x1014 W/cm²LI

max = 650 g/cc

if =1.2

522 µm

814 µm1044 µm

1250 µm

1570 µmFor all targets

Spike power required for ignition is the same for all targets

Reference

h scaling factor

shh TR h

aahh RPRP 2/3

La IP

ref0.25

spike WhW

Ignition condition

Guderley model

Ablation pressure

Spike scaling have low

h dependence

Conclusions

• Shock convergence amplification follows approximatively the Guderley solution

• Rosen model is well adapted to give the gain for shock ignition configuration

• Shocks driven by 150 TW (3) peak power ignite HiPER target proposed by S. Atzeni et al., with target gains up to 80. In agreement with Rochester work (Betti et al).

• Shock timing robustness : 250 ps ignition window.

• Ignition: low dependence to spike duration or spike energy

• Low target implosion velocity requires high spike intensity

• Homothetic targets shows that shock ignition power is constant