Multi-material simulation of laser-produced plasmas by Smoothed Particle Hydrodynamics

A. Sunahara

MultiMAT2011@Arcachon, France2011 9/5-11.

Institute for Laser Technology, JapanInstitute of Laser Engineering, Osaka Univ.

Co-workers

• S. Misaki

• K. Kageyama

• Dr. K. Tanaka• Dr. T. Johzaki

Introduction and Motivations

Simulation for Laser produced plasmas

Droplet

Long scale expansion

Connection to DSMC* simulations

Simulation for inertial confinement fusion

Smoothed Particle Hydrodynamics (SPH) may be suitable for the above calculations.

(multi-materials)

(large deformation)

(large dynamic range in space)

(particle to particle)*Direct Simulation Monte-Carlo

ICF examples

CH

DT

CH

AuMulti-materials are usedfor the ICF target.

0.3 mm

0.3 mm

optical back light image

EUVimage

Tin droplet

Diameter

0.036 mm

(36microns)

1.06 micron

wavelength

Laser

Tin droplet is irradiated by the laser for EUV emission, where large deformation occurs.

Simulation of droplet

YAG Laser(Wavelength:355 nm,Pulse:6 ns,Frequency;10 Hz)

Plumes intersect each other in 90.

The point of intersection oftwo ablation plumes

Tungsten target

Tungsten plumes Carbon plumes

Carbon target

Laboratory Experiments on Aerosol Formation by Colliding Ablation Plumes, LEAF-CAP has been proposed for reactor wall study.

5cm

1.5cm0.5cm

YAG Laser(line focused)

Solid target (Carbon, Tungsten etc)

Target Close-up View

0

In order to model intersecting laser-produced plumes, we have conducted two types of simulations.

• Radiation hydrodynamic simulation for generation of the plume and its dynamics

• Direct simulation Monte Carlo (DSMC) for simulating the intersecting two plumes

Outline

• Introduction and motivations

• Smoothed Particle Hydrodynamics

• Laser ray-trace

• Direct Simulation Monte Carlo

• Summary and conclusions

• Future prospectives

SPH was developed by Lucy 1977, Gingold and Monagahan 1977 for astrophysics problems.

Smoothed Particle Hydrodynamics (SPH)

SPH is based on the δ-function theory.

W is the finite size smoothing kernel with radius h.

Hydro equation can be written by summation of each contribution.

SPH is fully Lagrangian particle method,which has advantage for the problem having a large dynamic range in space.

2h

Radius of influence

W(r-r’,h)

r

h

area = 1

r

r’

x=

r

hx=

Kernel function is differentiable, non-negative and symmetric. Integration over x=r/h is 1.

approximation

Governing equation

Continuity equation

Velocity equation

Internal energy equation

Change of the position

EOS

Kernel

Artificial viscosity

Smoothing length

piecewise quintic

Laser rayElectron density

Velocity equation of the laser ray

Change of the position

Electron density gradient

: critical density

Deposition of laser power

dr

t1t2t3

Laser ray

smoothing radius of the ray hray

P(x=r)

Smoothing length

hray = factor * wavelength of the laser = constant with time

estimation of ,

rrayn+1 = rray

n + vray * Δt

vrayn+1 = vray

n + aray * Δt Δt=Δr/c

4th order Runge-Kutta

Procedures

estimation of

for each ray, each position

factor is set to be 5

X4

2D Plane

foil (ideal gas γ=1.67)ρ=1000kg/m3=1g/cm3

100μm X10μmt

1.06μm wavelength laserIL = 1012 W/cm2

Flat top

50μm

100μm

Laser

Δt=10-12sec

2D PlaneDensity(kg/m3)

(m)

(m)

2D axis-symmetry

axis symmetry

mirror particlescopy ~ 2 max(hi)

V// mirror = V// i

V mirror = -V i

X// mirror = X// i

X mirror = -X i

ρ mirror = ρ i

m mirror = m i

h mirror = h i

e mirror = e i

mirror particles summation of deposited energyPdep = Pdep + Pmirror dep

original particles

axis symmetryLaser

1

2

return

foil (ideal gas γ=1.67)ρ=1000kg/m3=1g/cm3

100μm X10μmt

1.06μm wavelength laserIL = 1012 W/cm2

Flat top

50μm

100μm

Laser

Δt=10-12sec

2D axis-symmetry

Half (upper) sideis only calculated.

2D axis-symmetryDensity(kg/m3)

(m)

(m)

2D Plane

2D axis-symmetry

0

-0.0002

-0.0004

0.0005(m)

(m)

(m)

(m)axis symmetry

2D axis-symmetry (cylinder)

foil (ideal gas γ=1.67)ρ=1000kg/m3=1g/cm3

60μmΦ droplet

1.06μm wavelength laserIL = 1012 W/cm2

Flat top

60μmΦ

Δt=10-12sec

2D axis-symmetry (cylinder)Density(kg/m3)

(m)

(m)

DSMC

Direct Simulation Monte-Carlo was developed by Bird.

ν = n • σ • v

neutral-neutral collision

Coulomb collision (ion-ion)

ν = v3

4 π n ((Ze)2/m)2 lnΛ

if they collide

Cell

(*) G. A. Bird, “Molecular gas dynamics and the direct simulation of gas flows”, Clarendon Press, (1994)

*

(**) T. Takizuka and H. Abe, Journal of Computational Phys. 25, 205-219(1977)

**

Group1

Group2

drift velocity : 106cm/s

X

Y

0.75cm

0.39cm

v

Z

X

3D image

particle : Carbon, Tungsten (neutral, cluster, ion(+1,+3))density : 1013/cm3, 1015/cm3

initial temperature : 1eVdrift velocity : 106cm/snumber of particle : 35×104

calculating area : 3cm,3cm,3cmcell : 106

Simulation condition of direct simulation monte-carlo (DSMC)

estimated from experimental observations

炭素の中性粒子

Carbon neutral-neutral interaction n=1013cm-3

neutral-neutral

(m)

Collisionless

(m)

*)

一価の炭素イオン 三価の炭素イオン

Carbon ion-ion interaction n=1013cm-3

ion(+1)-ion(+1)

Collisional

ion(+3)-ion(+3)

Collisional

(m)

(m) (m)

(m)

Tungsten neutral-neutral interaction n=1013cm-3

炭素の中性粒子neutral-neutral

Collisionless

(m)

Tungsten ion-ion interaction n=1013cm-3

一価の炭素イオン 三価の炭素イオンion(+1)-ion(+1)

Collisionless

ion(+3)-ion(+3)

Collisionless

(m)

(m) (m)

(m)

1013cm-3 1015cm-3

neutral X

ion(+1) X X

ion(+3) X

Tungsten

1013cm-3 1015cm-3

neutral X

ion(+1)

ion(+3)

Carbon

Summary of simulations collisional

X collisionless

Simulated results successfully reproduced the experiments.

Summary and conclusions

We have developed the simulation codes for the laser ablated plasma by SPH and DSMC.We tested laser energy deposition with ray-tracing.

We demonstrated simulation for CH plate and droplet.

We showed DSMC simulation for C and W.

Future prospectives

Detailed comparison with other scheme, and solution.

Installation of Electron conduction and radiative transferCombination of SPH and DSMC.