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

1. 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.

2. Co-workers • S. Misaki • K. Kageyama • Dr. T. Johzaki • Dr. K. Tanaka

3. Simulation for inertial confinement fusion Introduction and Motivations (multi-materials) (large deformation) Droplet Long scale expansion • Simulation for Laser produced plasmas (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.

4. ICF examples Multi-materials are used for the ICF target. Au CH CH DT

5. 0.3 mm 0.3 mm optical back light image EUVimage Tin droplet Diameter 0.036 mm (36microns) Simulation of droplet Tin droplet is irradiated by the laser for EUV emission, where large deformation occurs. 1.06 micron wavelength Laser

6. Plumes intersect each other in 90. 0.5cm The point of intersection of two ablation plumes Target Close-up View 1.5cm YAG Laser (line focused) Tungsten plumes Carbon plumes 5cm Solid target (Carbon, Tungsten etc) Carbon target Tungsten target Laboratory Experiments on Aerosol Formation by Colliding Ablation Plumes, LEAF-CAP has been proposed for reactor wall study. 0 YAG Laser (Wavelength:355 nm,Pulse:6 ns, Frequency;10 Hz)

7. 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

8. Outline • Smoothed Particle Hydrodynamics • Introduction and motivations • Laser ray-trace • Direct Simulation Monte Carlo • Summary and conclusions • Future prospectives

9. 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.

10. r h Radius of influence r x= h r’ 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=

11. Governing equation Continuity equation Velocity equation Change of the position Internal energy equation EOS

12. Kernel piecewise quintic Smoothing length Artificial viscosity

13. Laser ray Electron density Electron density gradient Velocity equation of the laser ray : critical density Change of the position Deposition of laser power

14. vrayn+1 = vrayn + aray * Δt rrayn+1 = rrayn + vray * Δt t2 t1 t3 Laser ray dr smoothing radius of the ray hray P(x=r) Smoothing length factor is set to be 5 hray = factor * wavelength of the laser = constant with time Procedures for each ray, each position estimation of , 4th order Runge-Kutta Δt=Δr/c X4 estimation of

15. 2D Plane foil (ideal gas γ=1.67) ρ=1000kg/m3=1g/cm3 100μm X10μmt 100μm 50μm Laser 1.06μm wavelength laser IL = 1012 W/cm2 Flat top Δt=10-12sec

16. 2D Plane Density (kg/m3) (m) (m)

17. 2D axis-symmetry 1 V// mirror = V// i ρ mirror = ρ i V mirror = -V i m mirror = m i e mirror = e i X// mirror = X// i X mirror = -X i h mirror = h i axis symmetry mirror particles copy ~ 2 max(hi) 2 original particles Laser axis symmetry return summation of deposited energy Pdep = Pdep + Pmirrordep mirror particles

18. 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

19. 2D axis-symmetry Density (kg/m3) (m) (m)

20. 2D Plane (m) (m) 2D axis-symmetry (m) axis symmetry 0 (m) -0.0002 0.0005 -0.0004

21. 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

22. 2D axis-symmetry (cylinder) Density (kg/m3) (m) (m)

23. 4 π n ((Ze)2/m)2 lnΛ ν = v3 * DSMC Direct Simulation Monte-Carlo was developed by Bird. if they collide neutral-neutral collision ν = n • σ • v Coulomb collision (ion-ion) ** 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)

25. v Simulation condition of direct simulation monte-carlo (DSMC) Group2 3D image Z Y Group1 X 0.39cm drift velocity : 106cm/s 0.75cm X particle : Carbon, Tungsten (neutral, cluster, ion(+1,+3)) density : 1013/cm3, 1015/cm3 initial temperature : 1eV drift velocity : 106cm/s number of particle : 35×104 calculating area : 3cm,3cm,3cm cell : 106 estimated from experimental observations

26. *) neutral-neutral interaction Carbon n=1013cm-3 (m) (m) 炭素の中性粒子 neutral-neutral Collisionless

27. ion-ion interaction Carbon n=1013cm-3 (m) (m) (m) (m) ion(+1)-ion(+1) ion(+3)-ion(+3) 一価の炭素イオン 三価の炭素イオン Collisional Collisional

28. neutral-neutral interaction Tungsten n=1013cm-3 (m) 炭素の中性粒子 neutral-neutral Collisionless

29. ion-ion interaction Tungsten n=1013cm-3 (m) (m) (m) (m) ion(+1)-ion(+1) ion(+3)-ion(+3) 一価の炭素イオン 三価の炭素イオン Collisionless Collisionless

30. Tungsten Carbon Summary of simulations collisional X collisionless Simulated results successfully reproduced the experiments.

31. 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.