Multi-material simulation of laser-produced
plasmas by Smoothed Particle Hydrodynamics
A. Sunahara
Institute for Laser Technology, Japan
Institute of Laser Engineering, Osaka Univ.
MultiMAT2011@Arcachon, France
2011 9/5-11.
Co-workers
• S. Misaki
• K. Kageyama
• Dr. T. Johzaki
• Dr. K. Tanaka
Introduction and Motivations
Simulation for inertial confinement fusion
(multi-materials)
Simulation for Laser produced plasmas
Droplet
(large deformation)
Long scale expansion
(large dynamic range in space)
Connection to DSMC* simulations
(particle to particle)
*Direct Simulation Monte-Carlo
Smoothed Particle Hydrodynamics (SPH)
may be suitable for the above calculations.
ICF examples
Multi-materials are used
for the ICF target.
Au
CH
CH
DT
0.3 mm
Tin droplet
Diameter
0.036 mm
(36microns)
1.06 micron
wavelength
optical back light
image
EUVimage
0.3 mm
Laser
Simulation of droplet
Tin droplet is irradiated by
the laser for EUV emission,
where large deformation
occurs.
Laboratory Experiments on Aerosol Formation by Colliding Ablation Plumes,
LEAF-CAP has been proposed for reactor wall study.
0
Plumes intersect each other in 90.
YAG Laser
(Wavelength:355 nm,Pulse:6 ns,
Frequency;10 Hz)
The point of intersection of
two ablation plumes
Tungsten plumes
Carbon plumes
Target Close-up View
0.5cm
1.5cm
YAG Laser
(line focused)
5cm
Tungsten target
Solid target (Carbon, Tungsten etc)
Carbon target
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
Smoothed Particle Hydrodynamics (SPH)
SPH was developed by Lucy 1977, Gingold and
Monagahan 1977 for astrophysics problems.
SPH is fully Lagrangian particle method,
which has advantage for the problem having a
large dynamic range in space.
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.
Radius of influence
x=
r’
r
h
2h
r
Kernel function is differentiable,
non-negative and symmetric.
Integration over x=r/h is 1.
W(r-r’,h)
area = 1
approximation
x=
r
h
Governing equation
Continuity equation
Velocity equation
Change of the position
Internal energy equation
EOS
Kernel
piecewise quintic
Smoothing length
Artificial viscosity
Laser ray
Electron density
Electron density gradient
Velocity equation of the laser ray
: critical density
Change of the position
Deposition of laser power
t2
t3
t1
Laser ray
dr
smoothing radius of the ray hray
P(x=r)
Smoothing length
hray = factor * wavelength of the laser
= constant with time
Procedures
factor is set to be 5
for each ray, each position
estimation of
,
rrayn+1 = rrayn + vray * Δt
vrayn+1 = vrayn + aray * Δt
estimation of
4th order Runge-Kutta
X4
Δt=Δr/c
2D Plane
100μm
foil (ideal gas γ=1.67)
ρ=1000kg/m3=1g/cm3
100μm X10μmt
50μm
Laser
1.06μm wavelength laser
IL = 1012 W/cm2
Flat top
Δt=10-12sec
2D Plane
Density
(kg/m3)
2D axis-symmetry
1
V// mirror = V// i
V
mirror
= -V
i
ρ mirror = ρ i
m mirror = m i
X// mirror = X// i
e mirror = e i
X
h mirror = h i
mirror
= -X
i
axis symmetry
copy
2
mirror particles
~ 2 max(hi)
original particles
Laser
axis symmetry
return
mirror particles
summation of deposited energy
Pdep = Pdep + Pmirror dep
2D axis-symmetry
1.06μm wavelength laser
IL = 1012 W/cm2
Flat top
100μm
50μm
Laser
Half (upper) side
is only calculated.
foil (ideal gas γ=1.67)
ρ=1000kg/m3=1g/cm3
100μm X10μmt
Δt=10-12sec
2D axis-symmetry
Density
(kg/m3)
2D Plane
2D axis-symmetry
axis symmetry
0
-0.0002
-0.0004
0.0005
2D axis-symmetry (cylinder)
1.06μm wavelength laser
IL = 1012 W/cm2
Flat top
60μmΦ
foil (ideal gas γ=1.67)
ρ=1000kg/m3=1g/cm3
60μmΦ droplet
Δt=10-12sec
2D axis-symmetry (cylinder)
Density
(kg/m3)
DSMC
*
Direct Simulation Monte-Carlo was developed by Bird.
if
they collide
neutral-neutral collision
ν=n•σ•v
Coulomb collision (ion-ion)
ν=
Cell
4π n
2
2
((Ze) /m)
lnΛ
v3
(*) 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)
**
Simulation condition of direct simulation monte-carlo (DSMC)
Y
Group2
3D image
Z
Group1
0.39cm
X
0.75cm
drift velocity : 106cm/s
X
particle : Carbon, Tungsten (neutral, cluster, ion(+1,+3))
density : 1013/cm3, 1015/cm3
estimated from experimental observations
initial temperature : 1eV
drift velocity : 106cm/s
number of particle : 35×104
calculating area : 3cm,3cm,3cm
cell : 106
Carbon
neutral-neutral interaction
(m)
炭素の中性粒子
neutral-neutral
Collisionless
(m)
*)
n=1013cm-3
Carbon
ion-ion interaction
(m)
n=1013cm-3
(m)
ion(+1)-ion(+1)
一価の炭素イオン
Collisional
(m)
ion(+3)-ion(+3)
三価の炭素イオン
Collisional
(m)
Tungsten
neutral-neutral interaction
(m)
炭素の中性粒子
neutral-neutral
Collisionless
n=1013cm-3
Tungsten
ion-ion interaction
(m)
n=1013cm-3
(m)
ion(+1)-ion(+1)
一価の炭素イオン
Collisionless
(m)
ion(+3)-ion(+3)
三価の炭素イオン
Collisionless
(m)
Summary of simulations
collisional
X collisionless
Carbon
Tungsten
1013cm-3 1015cm-3
neutral
X
ion(+1)
ion(+1)
X
ion(+3)
ion(+3)
X
neutral
X
1013cm-3 1015cm-3
X
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
transfer
Combination of SPH and DSMC.